def save_simulation():
    class ForceInfo:
        def __init__(self, startFrame, duration, force):
            self.startFrame = startFrame    # frame
            self.duration = duration        # sec
            self.force = force              # Newton
            self.targetBody = None

    #===============================================================================
    # load motion
    #===============================================================================
    MULTI_VIEWER = True
    CAMERA_TRACKING = True
    TORQUE_PLOT = False
    NO_FOOT_SLIDING = True
    
    SAVE_SIMULATION = True
    SAVE_DIR = './saved_simulation/'
    
    # global parameters
    Kt = 20.;       Dt = 2*(Kt**.5)
    Ks = 2000.;    Ds = 2*(Ks**.5)
    K_stb_vel = .1
    mu = 1.
    
    # constaants
    c_min_contact_vel = 100.
#    c_min_contact_vel = 2.
    c_min_contact_time = .7
    c_landing_duration = .2
    c_taking_duration = .3
    c_swf_mid_offset = .0
    c_swf_stability = .5
    c_locking_vel = .05
    
    dir = './ppmotion/'
    
    K_swp_vel_sag = .1; K_swp_vel_cor = .4; K_swp_pos_sag = .3; K_swp_pos_cor = 0.
#    K_stp_pos = 0.
#    K_stb_vel = .2
    K_stp_pos = 1.
    filename = 'wd2_WalkSameSame01.bvh'
#    filename = 'wd2_WalkSameSame01_REPEATED.bvh'

#    K_swp_vel_sag = .1; K_swp_vel_cor = .4; K_swp_pos_sag = .3; K_swp_pos_cor = 0.
#    K_stp_pos = 1.
#    filename = 'wd2_WalkForwardSlow01.bvh'
##    filename = 'wd2_WalkForwardSlow01_REPEATED.bvh' # 3 frame diff

##    mu = 12.

#    K_swp_vel_sag = .1; K_swp_vel_cor = .4; K_swp_pos_sag = 1.; K_swp_pos_cor = 0.
#    K_stp_pos = .6
#    filename = 'wd2_WalkForwardNormal00.bvh'
##    filename = 'wd2_WalkForwardNormal00_REPEATED.bvh'

#    K_swp_vel_sag = .1; K_swp_vel_cor = .4; K_swp_pos_sag = .3; K_swp_pos_cor = 0.
#    K_stp_pos = 0.
#    filename = 'wd2_WalkHandWav00.bvh'
##    filename = 'wd2_WalkHandWav00_REPEATED.bvh'

#    mu = 2.
#    K_swp_vel_sag = .1; K_swp_vel_cor = .4; K_swp_pos_sag = .3; K_swp_pos_cor = 0.
#    K_stp_pos = 0.
##    filename = 'wd2_WalkForwardFast00.bvh'
###    filename = 'wd2_WalkForwardFast00_REPEATED.bvh'

#    mu = 2.
#    K_swp_vel_sag = .1; K_swp_vel_cor = .4; K_swp_pos_sag = .3; K_swp_pos_cor = 0.
#    K_stp_pos = 0.
#    filename = 'wd2_WalkAzuma01.bvh'
##    filename = 'wd2_WalkAzuma01_REPEATED.bvh'   # 2 frame diff

#    K_swp_vel_sag = .1; K_swp_vel_cor = .4; K_swp_pos_sag = 1.; K_swp_pos_cor = 0.
#    K_stp_pos = 0.
#    filename = 'wd2_WalkSoldier00.bvh'    # K_swp_pos_sag = .0
##    filename = 'wd2_WalkSoldier00_REPEATED.bvh'

#    mu = 2.
#    K_swp_vel_sag = .2; K_swp_vel_cor = .4; K_swp_pos_sag = .5;K_swp_pos_cor = 0.
#    K_stp_pos = 0.
#    filename = 'wd2_WalkForwardVFast00.bvh'
##    filename = 'wd2_WalkForwardVFast00_REPEATED.bvh'

#    K_swp_vel_sag = .1; K_swp_vel_cor = .4; K_swp_pos_sag = 1.; K_swp_pos_cor = 0.
#    K_stp_pos = 0.
#    K_stb_vel = .2
#    filename = 'wd2_WalkBackward00.bvh'
###    filename = 'wd2_WalkBackward00_REPEATED.bvh'

##    K_swp_vel_sag = .15; K_swp_vel_cor = .35; K_swp_pos_sag = 1.; K_swp_pos_cor = 0.
##    K_stp_pos = 0.
###    filename = 'wd2_WalkLean00.bvh'
##    filename = 'wd2_WalkLean00_REPEATED.bvh'


    motion_ori = yf.readBvhFile(dir+filename)
    frameTime = 1/motion_ori.fps
    
    if 'REPEATED' in filename:
        REPEATED = True
        CAMERA_TRACKING = True
    else:
        REPEATED = False

    #===============================================================================
    # options
    #===============================================================================
    SEGMENT_EDITING =           True
    STANCE_FOOT_STABILIZE =     True
    MATCH_STANCE_LEG =          True
    SWING_FOOT_PLACEMENT =      True
    SWING_FOOT_HEIGHT =         True
    
    SWING_FOOT_ORIENTATION =    False
    
    STANCE_FOOT_PUSH =          True
    STANCE_FOOT_BALANCING =     True
    
    stitch_func = lambda x : 1. - yfg.hermite2nd(x)
    stf_stabilize_func = yfg.concatenate([yfg.hermite2nd, yfg.one], [c_landing_duration])
    match_stl_func = yfg.hermite2nd
#    match_stl_func_y = yfg.hermite2nd
    swf_placement_func = yfg.hermite2nd
    swf_height_func = yfg.hermite2nd
    swf_height_sine_func = yfg.sine
    stf_balancing_func = yfg.concatenate([yfg.hermite2nd, yfg.one], [c_landing_duration])
    
#    forceInfos = [ForceInfo(70, .4, (100,0,0))]
    forceInfos = []

    #===============================================================================
    # initialize character
    #===============================================================================
    mcfgfile = open(dir + 'mcfg', 'r')
    mcfg = cPickle.load(mcfgfile)
    mcfgfile.close()
    
    wcfg = ypc.WorldConfig()
    wcfg.planeHeight = 0.
    wcfg.useDefaultContactModel = False
    wcfg.lockingVel = c_locking_vel
    stepsPerFrame = 30
    wcfg.timeStep = (frameTime)/stepsPerFrame
    
    vpWorld = cvw.VpWorld(wcfg)
    motionModel = cvm.VpMotionModel(vpWorld, motion_ori[0], mcfg)
    controlModel = cvm.VpControlModel(vpWorld, motion_ori[0], mcfg)
    vpWorld.initialize()
    print controlModel
    
    motionModel.recordVelByFiniteDiff()
    controlModel.initializeHybridDynamics()
    
    #===============================================================================
    # load segment info
    #===============================================================================
    skeleton = motion_ori[0].skeleton
    
    segname = os.path.splitext(filename)[0]+'.seg'
    segfile = open(dir+segname, 'r')
    seginfo = cPickle.load(segfile)
    segfile.close()
    
    intervals = [info['interval'] for info in seginfo]
    states = [info['state'] for info in seginfo]
    temp_motion = copy.deepcopy(motion_ori)
    segments = yma.splitMotionIntoSegments(temp_motion, intervals)    
    print len(intervals), 'segments'
    for i in range(len(intervals)):
        print '%dth'%i, yba.GaitState.text[states[i]], intervals[i], ',', 
    print

    motion_seg_orig = ym.JointMotion()
    motion_seg_orig += segments[0]
    motion_seg = ym.JointMotion()
    motion_seg += segments[0]
    motion_stitch = ym.JointMotion()
    motion_stitch += segments[0]

    motion_stf_stabilize = ym.JointMotion()
    motion_match_stl = ym.JointMotion()
    motion_swf_placement = ym.JointMotion()
    motion_swf_height = ym.JointMotion()
    motion_swf_orientation = ym.JointMotion()
    motion_stf_balancing = ym.JointMotion()
    motion_stf_push = ym.JointMotion()
    motion_control = ym.JointMotion()

    motion_debug1 = ym.JointMotion()
    motion_debug2 = ym.JointMotion()
    motion_debug3 = ym.JointMotion()
    
    P = ym.JointMotion()
    P_hat = ym.JointMotion()
    M_tc = ym.JointMotion()
    M_hat_tc_1 = ym.JointMotion()

    if SAVE_SIMULATION:
        motion_simulation = ym.JointMotion()
    
    #===============================================================================
    # loop variable
    #===============================================================================
    seg_index = [0]
    acc_offset = [0]
    extended = [False]
    prev_R_swp = [None]
    stl_y_limit_num = [0]
    stl_xz_limit_num = [0]
    avg_dCM = [mm.O_Vec3()]
#    avg_stf_v = [mm.O_Vec3()]
#    avg_stf_av = [mm.O_Vec3()]
    
#    stf_push_func = [yfg.zero]
    step_length_cur = [0.]

    step_length_tar = [0.]
    step_axis = [mm.O_Vec3()]
            
    #===============================================================================
    # information
    #===============================================================================
    bodyIDsToCheck = range(vpWorld.getBodyNum())
    mus = [mu]*len(bodyIDsToCheck)
    
    bodyMasses = controlModel.getBodyMasses()
    totalMass = controlModel.getTotalMass()

    lID = controlModel.name2id('LeftFoot');      rID = controlModel.name2id('RightFoot')
    lUpLeg = skeleton.getJointIndex('LeftUpLeg');rUpLeg = skeleton.getJointIndex('RightUpLeg')
    lKnee = skeleton.getJointIndex('LeftLeg');   rKnee = skeleton.getJointIndex('RightLeg')
    lFoot = skeleton.getJointIndex('LeftFoot');  rFoot = skeleton.getJointIndex('RightFoot')
    spine = skeleton.getJointIndex('Spine')
    
    uppers = [skeleton.getJointIndex(name) for name in ['Hips', 'Spine', 'Spine1', 'LeftArm', 'LeftForeArm', 'RightArm', 'RightForeArm']]
    upperMass = sum([bodyMasses[i] for i in uppers])
    lLegs = [skeleton.getJointIndex(name) for name in ['LeftUpLeg', 'LeftLeg', 'LeftFoot']]
    rLegs = [skeleton.getJointIndex(name) for name in ['RightUpLeg', 'RightLeg', 'RightFoot']]
    allJoints = set(range(skeleton.getJointNum()))
    
    halfFootHeight = controlModel.getBodyShape(lFoot)[1] / 2.
    
    for fi in forceInfos:
        fi.targetBody = spine
        
    #===========================================================================
    # data collection
    #===========================================================================
    rhip_torques = []
    rknee_torques = []
    rankle_torques = []

    #===============================================================================
    # rendering
    #===============================================================================
    rd_CM = [None]; rd_CP = [None]; rd_CMP = [None]
    rd_forces = [None]; rd_force_points = [None]
    rd_torques = []; rd_joint_positions = []
    
    rd_point1 = [None]
    rd_point2 = [None]
    rd_vec1 = [None];   rd_vecori1 = [None] 
    rd_vec2 = [None];   rd_vecori2 = [None]
    rd_frame1 = [None]
    rd_frame2 = [None]
    
    if MULTI_VIEWER:
        viewer = ymv.MultiViewer(800, 655)
#        viewer = ymv.MultiViewer(1600, 1255)
        viewer.setRenderers1([cvr.VpModelRenderer(motionModel, MOTION_COLOR, yr.POLYGON_FILL)])
        viewer.setRenderers2([cvr.VpModelRenderer(controlModel, CHARACTER_COLOR, yr.POLYGON_FILL)])
    else:
        viewer = ysv.SimpleViewer()
    #    viewer.record(False)
    
        viewer.doc.addRenderer('motionModel', cvr.VpModelRenderer(motionModel, (0,150,255), yr.POLYGON_LINE))
        viewer.doc.addRenderer('controlModel', cvr.VpModelRenderer(controlModel, (200,200,200), yr.POLYGON_LINE))
        
    #    viewer.doc.addObject('motion_ori', motion_ori)
    #    viewer.doc.addRenderer('motion_ori', yr.JointMotionRenderer(motion_ori, (0,100,255), yr.LINK_BONE))
#        viewer.doc.addRenderer('motion_seg_orig', yr.JointMotionRenderer(motion_seg_orig, (0,100,255), yr.LINK_BONE))
#        viewer.doc.addRenderer('motion_seg', yr.JointMotionRenderer(motion_seg, (0,150,255), yr.LINK_BONE))
#        viewer.doc.addRenderer('motion_stitch', yr.JointMotionRenderer(motion_stitch, (0,255,200), yr.LINK_BONE))
#        viewer.doc.addRenderer('motion_stf_stabilize', yr.JointMotionRenderer(motion_stf_stabilize, (255,0,0), yr.LINK_BONE))
#        viewer.doc.addRenderer('motion_match_stl', yr.JointMotionRenderer(motion_match_stl, (255,200,0), yr.LINK_BONE))
#        viewer.doc.addRenderer('motion_swf_placement', yr.JointMotionRenderer(motion_swf_placement, (255,100,255), yr.LINK_BONE))
#        viewer.doc.addRenderer('motion_swf_height', yr.JointMotionRenderer(motion_swf_height, (50,255,255), yr.LINK_BONE))
        viewer.doc.addRenderer('motion_swf_orientation', yr.JointMotionRenderer(motion_swf_orientation, (255,100,0), yr.LINK_BONE))
        viewer.doc.addRenderer('motion_stf_push', yr.JointMotionRenderer(motion_stf_push, (50,255,200), yr.LINK_BONE))
    #    viewer.doc.addRenderer('motion_stf_balancing', yr.JointMotionRenderer(motion_stf_balancing, (255,100,255), yr.LINK_BONE))
#        viewer.doc.addRenderer('motion_control', yr.JointMotionRenderer(motion_control, (255,0,0), yr.LINK_BONE))
    
#        viewer.doc.addRenderer('motion_debug1', yr.JointMotionRenderer(motion_debug1, (0,255,0), yr.LINK_BONE))
#        viewer.doc.addRenderer('motion_debug2', yr.JointMotionRenderer(motion_debug2, (255,0,255), yr.LINK_BONE))
#        viewer.doc.addRenderer('motion_debug3', yr.JointMotionRenderer(motion_debug3, (255,255,0), yr.LINK_BONE))

#        viewer.doc.addRenderer('M_tc', yr.JointMotionRenderer(M_tc, (255,255,0), yr.LINK_BONE))
#        viewer.doc.addRenderer('P_hat', yr.JointMotionRenderer(P_hat, (255,255,0), yr.LINK_BONE))
#        viewer.doc.addRenderer('P', yr.JointMotionRenderer(P, (255,255,0), yr.LINK_BONE))
#        viewer.doc.addRenderer('M_hat_tc_1', yr.JointMotionRenderer(M_hat_tc_1, (255,255,0), yr.LINK_BONE))
    
    #    viewer.doc.addRenderer('rd_CM', yr.PointsRenderer(rd_CM, (255,255,0)))
    #    viewer.doc.addRenderer('rd_CP', yr.PointsRenderer(rd_CP, (255,0,0)))
    #    viewer.doc.addRenderer('rd_CMP', yr.PointsRenderer(rd_CMP, (0,255,0)))
    #    viewer.doc.addRenderer('forces', yr.ForcesRenderer(rd_forces, rd_force_points, (255,0,0), ratio=.01, fromPoint=False))
#        viewer.doc.addRenderer('torques', yr.VectorsRenderer(rd_torques, rd_joint_positions, (255,0,0)))
    
    #    viewer.doc.addRenderer('rd_point1', yr.PointsRenderer(rd_point1, (0,255,0)))
    #    viewer.doc.addRenderer('rd_point2', yr.PointsRenderer(rd_point2, (255,0,0)))
#        viewer.doc.addRenderer('rd_vec1', yr.VectorsRenderer(rd_vec1, rd_vecori1, (255,0,0)))
    #    viewer.doc.addRenderer('rd_vec2', yr.VectorsRenderer(rd_vec2, rd_vecori2, (0,255,0)))
    #    viewer.doc.addRenderer('rd_frame1', yr.FramesRenderer(rd_frame1, (0,200,200)))
    #    viewer.doc.addRenderer('rd_frame2', yr.FramesRenderer(rd_frame2, (200,200,0)))
    #    viewer.setMaxFrame(len(motion_ori)-1)

    if not REPEATED:
        viewer.setMaxFrame(len(motion_ori)-1)
    else:
        viewer.setMaxFrame(1000)
        
    if CAMERA_TRACKING:
        if MULTI_VIEWER:
            cameraTargets1 = [None] * (viewer.getMaxFrame()+1)
            cameraTargets2 = [None] * (viewer.getMaxFrame()+1)
        else:
            cameraTargets = [None] * (viewer.getMaxFrame()+1)
            
    if TORQUE_PLOT:
        rhip_torques = [0.]*viewer.getMaxFrame()
        rknee_torques = [0.]*viewer.getMaxFrame()
        rankle_torques = [0.]*viewer.getMaxFrame()
        
#    pt = [0.]
    def postFrameCallback_Always(frame):
#        if frame==1: pt[0] = time.time()
#        if frame==31: print 'elapsed time for 30 frames:', time.time()-pt[0]
        if CAMERA_TRACKING:
            if MULTI_VIEWER:
                if cameraTargets1[frame]==None:
                    cameraTargets1[frame] = motionModel.getBodyPositionGlobal(0)
#                    cameraTargets1[frame] = motion_ori[frame].getJointPositionGlobal(0)
                viewer.setCameraTarget1(cameraTargets1[frame])
                
                if cameraTargets2[frame]==None:
                    cameraTargets2[frame] = controlModel.getJointPositionGlobal(0)
                viewer.setCameraTarget2(cameraTargets2[frame])
                
            else:
                if cameraTargets[frame]==None:
                    cameraTargets[frame] = controlModel.getJointPositionGlobal(0)
                viewer.setCameraTarget(cameraTargets[frame])
        if plot!=None:
            plot.updateVline(frame)
    viewer.setPostFrameCallback_Always(postFrameCallback_Always)

    plot = None
#    plot = ymp.InteractivePlot()
    if plot!=None:
        plot.setXlimit(0, len(motion_ori))
        plot.setYlimit(0., 1.)
        plot.addDataSet('zero')
        plot.addDataSet('diff')
        plot.addDataSet('debug1')
        plot.addDataSet('debug2')

    def viewer_onClose(data):
        if plot!=None:
            plot.close()
        viewer.onClose(data)
    viewer.callback(viewer_onClose)
         
    def simulateCallback(frame):
        # seginfo
        segIndex = seg_index[0]
        curState = seginfo[segIndex]['state']
        curInterval = yma.offsetInterval(acc_offset[0], seginfo[segIndex]['interval'])
        stanceLegs = seginfo[segIndex]['stanceHips']
        swingLegs = seginfo[segIndex]['swingHips']
        stanceFoots = seginfo[segIndex]['stanceFoots']
        swingFoots = seginfo[segIndex]['swingFoots']
        swingKnees = seginfo[segIndex]['swingKnees']
        groundHeight = seginfo[segIndex]['ground_height']
        maxStfPushFrame = seginfo[segIndex]['max_stf_push_frame']
        
        prev_frame = frame-1 if frame>0 else 0
#        prev_frame = frame
        
        # information
#        dCM_tar = yrp.getCM(motion_seg.getJointVelocitiesGlobal(frame), bodyMasses, upperMass, uppers)
#        CM_tar = yrp.getCM(motion_seg.getJointPositionsGlobal(frame), bodyMasses, upperMass, uppers)
##        dCM_tar = yrp.getCM(motion_seg.getJointVelocitiesGlobal(frame), bodyMasses, totalMass)
##        CM_tar = yrp.getCM(motion_seg.getJointPositionsGlobal(frame), bodyMasses, totalMass)
#        stf_tar = motion_seg.getJointPositionGlobal(stanceFoots[0], frame)
#        CMr_tar = CM_tar - stf_tar

        dCM_tar = motion_seg.getJointVelocityGlobal(0, prev_frame)
        CM_tar = motion_seg.getJointPositionGlobal(0, prev_frame)
#        dCM_tar = yrp.getCM(motion_seg.getJointVelocitiesGlobal(prev_frame), bodyMasses, upperMass, uppers)
#        CM_tar = yrp.getCM(motion_seg.getJointPositionsGlobal(prev_frame), bodyMasses, upperMass, uppers)
#        dCM_tar = yrp.getCM(motion_seg.getJointVelocitiesGlobal(prev_frame), bodyMasses, totalMass)
#        CM_tar = yrp.getCM(motion_seg.getJointPositionsGlobal(prev_frame), bodyMasses, totalMass)
        stf_tar = motion_seg.getJointPositionGlobal(stanceFoots[0], prev_frame)
        CMr_tar = CM_tar - stf_tar
            
        dCM = avg_dCM[0]
        CM = controlModel.getJointPositionGlobal(0)
#        CM = yrp.getCM(controlModel.getJointPositionsGlobal(), bodyMasses, upperMass, uppers)
#        CM = yrp.getCM(controlModel.getJointPositionsGlobal(), bodyMasses, totalMass)
        CMreal = yrp.getCM(controlModel.getJointPositionsGlobal(), bodyMasses, totalMass)
        stf = controlModel.getJointPositionGlobal(stanceFoots[0])
        CMr = CM - stf
        
        diff_dCM = mm.projectionOnPlane(dCM-dCM_tar, (1,0,0), (0,0,1))
        diff_dCM_axis = np.cross((0,1,0), diff_dCM)
        rd_vec1[0] = diff_dCM; rd_vecori1[0] = CM_tar
        
        diff_CMr = mm.projectionOnPlane(CMr-CMr_tar, (1,0,0), (0,0,1))
#        rd_vec1[0] = diff_CMr; rd_vecori1[0] = stf_tar
        diff_CMr_axis = np.cross((0,1,0), diff_CMr)
        
        direction = mm.normalize2(mm.projectionOnPlane(dCM_tar, (1,0,0), (0,0,1)))
#        direction = mm.normalize2(mm.projectionOnPlane(dCM, (1,0,0), (0,0,1)))
        directionAxis = np.cross((0,1,0), direction)
        
        diff_dCM_sag, diff_dCM_cor = mm.projectionOnVector2(diff_dCM, direction)
#        rd_vec1[0] = diff_dCM_sag; rd_vecori1[0] = CM_tar
        diff_dCM_sag_axis = np.cross((0,1,0), diff_dCM_sag)
        diff_dCM_cor_axis = np.cross((0,1,0), diff_dCM_cor)
            
        diff_CMr_sag, diff_CMr_cor = mm.projectionOnVector2(diff_CMr, direction)
        diff_CMr_sag_axis = np.cross((0,1,0), diff_CMr_sag)
        diff_CMr_cor_axis = np.cross((0,1,0), diff_CMr_cor)
            
        t = (frame-curInterval[0])/float(curInterval[1]-curInterval[0])
        t_raw = t
        if t>1.: t=1.
        
        
        p_root = motion_stitch[frame].getJointPositionGlobal(0)
        R_root = motion_stitch[frame].getJointOrientationGlobal(0)

        motion_seg_orig.goToFrame(frame)
        motion_seg.goToFrame(frame)
        motion_stitch.goToFrame(frame)
        
        motion_debug1.append(motion_stitch[frame].copy())
        motion_debug1.goToFrame(frame)
        motion_debug2.append(motion_stitch[frame].copy())
        motion_debug2.goToFrame(frame)
        motion_debug3.append(motion_stitch[frame].copy())
        motion_debug3.goToFrame(frame)
        
        # paper implementation
        M_tc.append(motion_stitch[prev_frame])
        M_tc.goToFrame(frame)
        P_hat.append(M_tc[frame].copy())
        P_hat.goToFrame(frame)
        
        p_temp = ym.JointPosture(skeleton)
        p_temp.rootPos = controlModel.getJointPositionGlobal(0)
        p_temp.setJointOrientationsLocal(controlModel.getJointOrientationsLocal())
        P.append(p_temp)
        P.goToFrame(frame)
        
        # stance foot stabilize
        motion_stf_stabilize.append(motion_stitch[frame].copy())
        motion_stf_stabilize.goToFrame(frame)
        if STANCE_FOOT_STABILIZE:
            for stanceFoot in stanceFoots:
                R_target_foot = motion_seg[frame].getJointOrientationGlobal(stanceFoot)
                R_current_foot = motion_stf_stabilize[frame].getJointOrientationGlobal(stanceFoot)
                motion_stf_stabilize[frame].setJointOrientationGlobal(stanceFoot, cm.slerp(R_current_foot, R_target_foot , stf_stabilize_func(t)))
#                R_target_foot = motion_seg[frame].getJointOrientationLocal(stanceFoot)
#                R_current_foot = motion_stf_stabilize[frame].getJointOrientationLocal(stanceFoot)
#                motion_stf_stabilize[frame].setJointOrientationLocal(stanceFoot, cm.slerp(R_current_foot, R_target_foot , stf_stabilize_func(t)))

        # match stance leg 
        motion_match_stl.append(motion_stf_stabilize[frame].copy())
        motion_match_stl.goToFrame(frame)
        if MATCH_STANCE_LEG:
            if curState!=yba.GaitState.STOP:
                for i in range(len(stanceLegs)):
                    stanceLeg = stanceLegs[i]
                    stanceFoot = stanceFoots[i]
                    
#                    # motion stance leg -> character stance leg as time goes
                    R_motion = motion_match_stl[frame].getJointOrientationGlobal(stanceLeg)
                    R_character = controlModel.getJointOrientationGlobal(stanceLeg)
                    motion_match_stl[frame].setJointOrientationGlobal(stanceLeg, cm.slerp(R_motion, R_character, match_stl_func(t)))

#                    t_y = match_stl_func_y(t)
#                    t_xz = match_stl_func(t)
#                    
#                    R_motion = motion_match_stl[frame].getJointOrientationGlobal(stanceLeg)
#                    R_character = controlModel.getJointOrientationGlobal(stanceLeg)
#                    R = np.dot(R_character, R_motion.T)
#                    R_y, R_xz = mm.projectRotation((0,1,0), R)
#                    motion_match_stl[frame].mulJointOrientationGlobal(stanceLeg, mm.scaleSO3(R_xz, t_xz))
#                    motion_match_stl[frame].mulJointOrientationGlobal(stanceLeg, mm.scaleSO3(R_y, t_y))

        # swing foot placement
        motion_swf_placement.append(motion_match_stl[frame].copy())
        motion_swf_placement.goToFrame(frame)
        if SWING_FOOT_PLACEMENT:
            t_swing_foot_placement = swf_placement_func(t);
            
            if extended[0]:
                R_swp_sag = prev_R_swp[0][0]
                R_swp_cor = prev_R_swp[0][1]
            else:
                R_swp_sag = mm.I_SO3(); R_swp_cor = mm.I_SO3()
                R_swp_sag = np.dot(R_swp_sag, mm.exp(diff_dCM_sag_axis * K_swp_vel_sag * -t_swing_foot_placement))
                R_swp_cor = np.dot(R_swp_cor, mm.exp(diff_dCM_cor_axis * K_swp_vel_cor * -t_swing_foot_placement))
                if np.dot(direction, diff_CMr_sag) < 0:
                    R_swp_sag = np.dot(R_swp_sag, mm.exp(diff_CMr_sag_axis * K_swp_pos_sag * -t_swing_foot_placement))
                R_swp_cor = np.dot(R_swp_cor, mm.exp(diff_CMr_cor_axis * K_swp_pos_cor * -t_swing_foot_placement))

            for i in range(len(swingLegs)):
                swingLeg = swingLegs[i]
                swingFoot = swingFoots[i] 
                
                # save swing foot global orientation
#                R_swf = motion_swf_placement[frame].getJointOrientationGlobal(swingFoot)
                
                # rotate swing leg
                motion_swf_placement[frame].mulJointOrientationGlobal(swingLeg, R_swp_sag)
                motion_swf_placement[frame].mulJointOrientationGlobal(swingLeg, R_swp_cor)
                
                # restore swing foot global orientation
#                motion_swf_placement[frame].setJointOrientationGlobal(swingFoot, R_swf)
                
                prev_R_swp[0] = (R_swp_sag, R_swp_cor)

        # swing foot height
        motion_swf_height.append(motion_swf_placement[frame].copy())
        motion_swf_height.goToFrame(frame)
        if SWING_FOOT_HEIGHT:
            for swingFoot in swingFoots:
                stanceFoot = stanceFoots[0]

                # save foot global orientation
                R_foot = motion_swf_height[frame].getJointOrientationGlobal(swingFoot)
                R_stance_foot = motion_swf_height[frame].getJointOrientationGlobal(stanceFoot)

                height_tar = motion_swf_height[frame].getJointPositionGlobal(swingFoot)[1] - motion_swf_height[frame].getJointPositionGlobal(stanceFoot)[1]
#                motion_debug1[frame] = motion_swf_height[frame].copy()

                # rotate
                motion_swf_height[frame].rotateByTarget(controlModel.getJointOrientationGlobal(0))
#                motion_debug2[frame] = motion_swf_height[frame].copy()
#                motion_debug2[frame].translateByTarget(controlModel.getJointPositionGlobal(0))

                height_cur = motion_swf_height[frame].getJointPositionGlobal(swingFoot)[1] - motion_swf_height[frame].getJointPositionGlobal(stanceFoot)[1]

                offset_height = (height_tar - height_cur) * swf_height_func(t) * c_swf_stability
                offset_sine = c_swf_mid_offset * swf_height_sine_func(t)
                
                offset = 0.
                offset += offset_height
                offset += offset_sine

                if offset > 0.:
                    newPosition =  motion_swf_height[frame].getJointPositionGlobal(swingFoot)
                    newPosition[1] += offset
                    aik.ik_analytic(motion_swf_height[frame], swingFoot, newPosition)
                else:
                    newPosition =  motion_swf_height[frame].getJointPositionGlobal(stanceFoot)
                    newPosition[1] -= offset
                    aik.ik_analytic(motion_swf_height[frame], stanceFoot, newPosition)

                # return
#                motion_debug3[frame] = motion_swf_height[frame].copy()
#                motion_debug3[frame].translateByTarget(controlModel.getJointPositionGlobal(0))
                motion_swf_height[frame].rotateByTarget(R_root)
                
                # restore foot global orientation
                motion_swf_height[frame].setJointOrientationGlobal(swingFoot, R_foot)
                motion_swf_height[frame].setJointOrientationGlobal(stanceFoot, R_stance_foot)

                if plot!=None:
                    plot.addDataPoint('debug1', frame, height_tar)
                    plot.addDataPoint('debug2', frame, height_cur)
#                    plot.addDataPoint('diff', frame, diff)

        # swing foot orientation
        motion_swf_orientation.append(motion_swf_height[frame].copy())
        motion_swf_orientation.goToFrame(frame)
        if SWING_FOOT_ORIENTATION:
#    swf_orientation_func = yfg.concatenate([yfg.zero, yfg.hermite2nd, yfg.one], [.25, .75])
            for swingFoot in swingFoots:
                R_target_foot = motion_seg[curInterval[1]].getJointOrientationGlobal(swingFoot)
                R_current_foot = motion_swf_orientation[frame].getJointOrientationGlobal(swingFoot)
                motion_swf_orientation[frame].setJointOrientationGlobal(swingFoot, cm.slerp(R_current_foot, R_target_foot, swf_orientation_func(t)))
#    swf_stabilize_func = yfg.concatenate([yfg.hermite2nd, yfg.one], [c_taking_duration])
            # push orientation
#            for swingFoot in swingFoots:
#                R_target_foot = motion_seg[frame].getJointOrientationGlobal(swingFoot)
#                R_current_foot = motion_swf_orientation[frame].getJointOrientationGlobal(swingFoot)
#                motion_swf_orientation[frame].setJointOrientationGlobal(swingFoot, cm.slerp(R_current_foot, R_target_foot , swf_stabilize_func(t)))
            
        # stance foot push                
        motion_stf_push.append(motion_swf_orientation[frame].copy())
        motion_stf_push.goToFrame(frame)
        if STANCE_FOOT_PUSH:
            for swingFoot in swingFoots:
#                max_t = (maxStfPushFrame)/float(curInterval[1]-curInterval[0])
#                stf_push_func = yfg.concatenate([yfg.sine, yfg.zero], [max_t*2])
                stf_push_func = yfg.concatenate([yfg.sine, yfg.zero], [c_taking_duration*2])
                
                R_swp_sag = mm.I_SO3()
#                R_swp_sag = np.dot(R_swp_sag, mm.exp(diff_dCM_sag_axis * K_stp_vel * -stf_push_func(t)))
                
#                if step_length_cur[0] < step_length_tar[0]:
#                    ratio = step_length_cur[0] / step_length_tar[0]
#                    R_max = maxmaxStfPushFrame
#                    R_zero = 
                R_swp_sag = np.dot(R_swp_sag, mm.exp((step_length_tar[0] - step_length_cur[0])*step_axis[0] * K_stp_pos * -stf_push_func(t)))
                    
                motion_stf_push[frame].mulJointOrientationGlobal(swingFoot, R_swp_sag)
                
        # stance foot balancing 
        motion_stf_balancing.append(motion_stf_push[frame].copy())
        motion_stf_balancing.goToFrame(frame)
        if STANCE_FOOT_BALANCING:
            R_stb = mm.exp(diff_dCM_axis * K_stb_vel * stf_balancing_func(t))
            for stanceFoot in stanceFoots:
                if frame < 5: continue
                motion_stf_balancing[frame].mulJointOrientationGlobal(stanceFoot, R_stb)
                    
        # control trajectory
        motion_control.append(motion_stf_balancing[frame].copy())
        motion_control.goToFrame(frame)
        
        #=======================================================================
        # tracking with inverse dynamics
        #=======================================================================
        th_r = motion_control.getDOFPositions(frame)
        th = controlModel.getDOFPositions()
        dth_r = motion_control.getDOFVelocities(frame)
        dth = controlModel.getDOFVelocities()
        ddth_r = motion_control.getDOFAccelerations(frame)
        ddth_des = yct.getDesiredDOFAccelerations(th_r, th, dth_r, dth, ddth_r, Kt, Dt)

        #=======================================================================
        # simulation
        #=======================================================================
        CP = mm.v3(0.,0.,0.)
        F = mm.v3(0.,0.,0.)
        avg_dCM[0] = mm.v3(0.,0.,0.)
        
        # external force rendering info
        del rd_forces[:]; del rd_force_points[:]
        for fi in forceInfos:
            if fi.startFrame <= frame and frame < fi.startFrame + fi.duration*(1/frameTime):
                rd_forces.append(fi.force)
                rd_force_points.append(controlModel.getBodyPositionGlobal(fi.targetBody))
                    
        for i in range(stepsPerFrame):
            
            bodyIDs, contactPositions, contactPositionLocals, contactForces = vpWorld.calcPenaltyForce(bodyIDsToCheck, mus, Ks, Ds)
            vpWorld.applyPenaltyForce(bodyIDs, contactPositionLocals, contactForces)
            
            # apply external force
            for fi in forceInfos:
                if fi.startFrame <= frame and frame < fi.startFrame + fi.duration*(1/frameTime):
                    controlModel.applyBodyForceGlobal(fi.targetBody, fi.force)
            
            controlModel.setDOFAccelerations(ddth_des)
            controlModel.solveHybridDynamics()
            
            if TORQUE_PLOT:
                rhip_torques[frame] += mm.length(controlModel.getJointTorqueLocal(rUpLeg))
                rknee_torques[frame] += mm.length(controlModel.getJointTorqueLocal(rKnee))
                rankle_torques[frame] += mm.length(controlModel.getJointTorqueLocal(rFoot))
            
            rd_torques[:] = [controlModel.getJointTorqueLocal(i)/100. for i in range(skeleton.getJointNum())]
            rd_joint_positions[:] = controlModel.getJointPositionsGlobal()
        
            vpWorld.step()
#            yvu.align2D(controlModel)

            if len(contactForces) > 0:
                CP += yrp.getCP(contactPositions, contactForces)
                F += sum(contactForces)
            avg_dCM[0] += controlModel.getJointVelocityGlobal(0)
#            avg_dCM[0] += yrp.getCM(controlModel.getJointVelocitiesGlobal(), bodyMasses, upperMass, uppers)
#            avg_dCM[0] += yrp.getCM(controlModel.getJointVelocitiesGlobal(), bodyMasses, totalMass)

#            if len(stanceFoots)>0:
#                avg_stf_v[0] += controlModel.getJointVelocityGlobal(stanceFoots[0])
#                avg_stf_av[0] += controlModel.getJointAngVelocityGlobal(stanceFoots[0])
        
        CP /= stepsPerFrame
        F /= stepsPerFrame
        avg_dCM[0] /= stepsPerFrame
        
#        if len(stanceFoots)>0:
#            avg_stf_v[0] /= stepsPerFrame
#            avg_stf_av[0] /= stepsPerFrame
#            rd_vec1[0] = avg_stf_av[0]; rd_vec1[0][0] = 0.; rd_vec1[0][2] = 0.
#            rd_vecori1[0]= controlModel.getJointPositionGlobal(stanceFoots[0])

        #=======================================================================
        # segment editing
        #=======================================================================
        lastFrame = False
        
        if SEGMENT_EDITING:
            if curState==yba.GaitState.STOP:
                if frame == len(motion_seg)-1:
                    lastFrame = True
                    
            elif (curState==yba.GaitState.LSWING or curState==yba.GaitState.RSWING) and t>c_min_contact_time:
                swingID = lID if curState==yba.GaitState.LSWING else rID

                contact = False
                if swingID in bodyIDs:
                    minContactVel = 1000.
                    for i in range(len(bodyIDs)):
                        if bodyIDs[i]==swingID:
                            vel = controlModel.getBodyVelocityGlobal(swingID, contactPositionLocals[i])
                            vel[1] = 0
                            contactVel = mm.length(vel)
                            if contactVel < minContactVel: minContactVel = contactVel 
                    if minContactVel < c_min_contact_vel: contact = True
                
                extended[0] = False
                
                if contact:
#                    print frame, 'foot touch'
                    lastFrame = True
                    acc_offset[0] += frame - curInterval[1]
                    
                elif frame == len(motion_seg)-1:
                    print frame, 'extend frame', frame+1
                    
                    preserveJoints = []
#                    preserveJoints = [lFoot, rFoot]
#                    preserveJoints = [lFoot, rFoot, lKnee, rKnee]
#                    preserveJoints = [lFoot, rFoot, lKnee, rKnee, lUpLeg, rUpLeg]
                    stanceKnees = [rKnee] if curState==yba.GaitState.LSWING else [lKnee]   
                    preserveJoints = [stanceFoots[0], stanceKnees[0], stanceLegs[0]]
   
                    diff = 3
                    motion_seg_orig.extend([motion_seg_orig[-1]])
                    motion_seg.extend(ymt.extendByIntegration_root(motion_seg, 1, diff))
                    
                    motion_stitch.extend(ymt.extendByIntegration_constant(motion_stitch, 1, preserveJoints, diff))

#                    # extend for swing foot ground speed matching & swing foot height lower
##                    extendedPostures = ymt.extendByIntegration(motion_stitch, 1, preserveJoints, diff)
##                    extendedPostures = [motion_stitch[-1]] 
##
#                    extendFrameNum = frame - curInterval[1] + 1
#                    k = 1.-extendFrameNum/5.
#                    if k<0.: k=0.
#                    extendedPostures = ymt.extendByIntegrationAttenuation(motion_stitch, 1, preserveJoints, diff, k)
#
##                    if len(swingFoots)>0 and np.inner(dCM_tar, dCM)>0.:
##                        print frame, 'speed matching'
##                        R_swf = motion_stitch[-1].getJointOrientationGlobal(swingFoots[0])
##                        
##                        p_swf = motion_stitch[-1].getJointPositionGlobal(swingFoots[0])
##                        v_swf = motion_stitch.getJointVelocityGlobal(swingFoots[0], frame-diff, frame)
##                        a_swf = motion_stitch.getJointAccelerationGlobal(swingFoots[0], frame-diff, frame)
##                        p_swf += v_swf * (frameTime) + a_swf * (frameTime)*(frameTime)
##                        aik.ik_analytic(extendedPostures[0], swingFoots[0], p_swf)
##                        
##                        extendedPostures[0].setJointOrientationGlobal(swingFoots[0], R_swf)
#
#                    motion_stitch.extend(extendedPostures)
                    
                    extended[0] = True
        else:
            if frame == len(motion_seg)-1: lastFrame = True
                    
        if lastFrame:
            if segIndex < len(segments)-1:
                print '%d (%d): end of %dth seg (%s, %s)'%(frame, frame-curInterval[1],segIndex, yba.GaitState.text[curState], curInterval)
                if plot!=None: plot.addDataPoint('diff', frame, (frame-curInterval[1])*.01)
                
                if len(stanceFoots)>0 and len(swingFoots)>0:
#                    step_cur = controlModel.getJointPositionGlobal(swingFoots[0]) - controlModel.getJointPositionGlobal(stanceFoots[0])
#                    step_tar = motion_seg[curInterval[1]].getJointPositionGlobal(swingFoots[0]) - motion_seg[curInterval[1]].getJointPositionGlobal(stanceFoots[0])
                    step_cur = controlModel.getJointPositionGlobal(0) - controlModel.getJointPositionGlobal(stanceFoots[0])
                    step_tar = motion_seg[curInterval[1]].getJointPositionGlobal(0) - motion_seg[curInterval[1]].getJointPositionGlobal(stanceFoots[0])
                    
                    step_cur = mm.projectionOnPlane(step_cur, (1,0,0), (0,0,1))
                    step_tar = mm.projectionOnPlane(step_tar, (1,0,0), (0,0,1))
                    
                    step_cur_sag, step_cur_cor = mm.projectionOnVector2(step_cur, direction)
                    step_tar_sag, step_tar_cor = mm.projectionOnVector2(step_tar, direction)
                    
                    step_length_tar[0] = mm.length(step_tar_sag)
                    if np.inner(step_tar_sag, step_cur_sag) > 0:
                        step_length_cur[0] = mm.length(step_cur_sag)
                    else:
                        step_length_cur[0] = -mm.length(step_cur_sag)
                    
                    step_axis[0] = directionAxis
                    
#                    rd_vec1[0] = step_tar_sag
#                    rd_vecori1[0] = motion_seg[curInterval[1]].getJointPositionGlobal(stanceFoots[0])
#                    rd_vec2[0] = step_cur_sag
#                    rd_vecori2[0] = controlModel.getJointPositionGlobal(stanceFoots[0])

                seg_index[0] += 1
                curSeg = segments[seg_index[0]]
                stl_y_limit_num[0] = 0
                stl_xz_limit_num[0] = 0
                
                del motion_seg_orig[frame+1:]
                motion_seg_orig.extend(ymb.getAttachedNextMotion(curSeg, motion_seg_orig[-1], False, False))
                
                del motion_seg[frame+1:]
                del motion_stitch[frame+1:]
                transitionLength = len(curSeg)-1

#                motion_seg.extend(ymb.getAttachedNextMotion(curSeg, motion_seg[-1], False, False))
#                motion_stitch.extend(ymb.getStitchedNextMotion(curSeg, motion_control[-1], transitionLength, stitch_func, True, False))

                d = motion_seg[-1] - curSeg[0]
                d.rootPos[1] = 0.
                motion_seg.extend(ymb.getAttachedNextMotion(curSeg, d, True, False))
                
                if NO_FOOT_SLIDING:
                    if segIndex == len(segments)-2:
                        Rl = motion_control[-1].getJointOrientationLocal(lUpLeg)
                        Rr = motion_control[-1].getJointOrientationLocal(rUpLeg)
                        Rlk = motion_control[-1].getJointOrientationLocal(lKnee)
                        Rrk = motion_control[-1].getJointOrientationLocal(rKnee)
                        Rlf = motion_control[-1].getJointOrientationLocal(lFoot)
                        Rrf = motion_control[-1].getJointOrientationLocal(rFoot)
                        for p in curSeg:
                            p.setJointOrientationLocal(lUpLeg, Rl, False)
                            p.setJointOrientationLocal(rUpLeg, Rr, False)
                            p.setJointOrientationLocal(lKnee, Rlk, False)
                            p.setJointOrientationLocal(rKnee, Rrk, False)
                            p.setJointOrientationLocal(lFoot, Rlf, False)
                            p.setJointOrientationLocal(rFoot, Rrf, False)
                            p.updateGlobalT()                
                d = motion_control[-1] - curSeg[0]
                d.rootPos[1] = 0.
                motion_stitch.extend(ymb.getStitchedNextMotion(curSeg, d, transitionLength, stitch_func, True, False))
                
#                motion_seg.extend(ymb.getAttachedNextMotion(curSeg, motion_seg[-1], False, True))
#                motion_stitch.extend(ymb.getStitchedNextMotion(curSeg, motion_control[-1], transitionLength, stitch_func, True, True))
            else:
                motion_seg_orig.append(motion_seg_orig[-1])
                motion_seg.append(motion_seg[-1])
                motion_stitch.append(motion_control[-1])
                
                
        # rendering
        motionModel.update(motion_ori[frame])
#        motionModel.update(motion_seg[frame])
        
        if SAVE_SIMULATION:
            p_temp = ym.JointPosture(skeleton)
            p_temp.initLocalRs()
            p_temp.rootPos = controlModel.getJointPositionGlobal(0)
            p_temp.setJointOrientationsLocal(controlModel.getJointOrientationsLocal())
            motion_simulation.append(p_temp)
            
            if frame == viewer.getMaxFrame():
                saveFilePath = SAVE_DIR+'simulated_'+filename
                yf.writeBvhFile(saveFilePath, motion_simulation)
                print saveFilePath, 'saved'
        
    viewer.setSimulateCallback(simulateCallback)
    
    viewer.startTimer(frameTime / 1.4)
#    viewer.startTimer(frameTime * .4)
    viewer.show()
    
    Fl.run()
Пример #2
0
    def simulateCallback(frame):
        # seginfo
        segIndex = seg_index[0]
        curState = seginfo[segIndex]['state']
        curInterval = yma.offsetInterval(acc_offset[0], seginfo[segIndex]['interval'])
        stanceLegs = seginfo[segIndex]['stanceHips']
        swingLegs = seginfo[segIndex]['swingHips']
        stanceFoots = seginfo[segIndex]['stanceFoots']
        swingFoots = seginfo[segIndex]['swingFoots']
        swingKnees = seginfo[segIndex]['swingKnees']
        groundHeight = seginfo[segIndex]['ground_height']
#        maxStfPushFrame = seginfo[segIndex]['max_stf_push_frame']
        
        prev_frame = frame-1 if frame>0 else 0
#        prev_frame = frame
        
        # information
#        dCM_tar = yrp.getCM(motion_seg.getJointVelocitiesGlobal(frame), bodyMasses, upperMass, uppers)
#        CM_tar = yrp.getCM(motion_seg.getJointPositionsGlobal(frame), bodyMasses, upperMass, uppers)
##        dCM_tar = yrp.getCM(motion_seg.getJointVelocitiesGlobal(frame), bodyMasses, totalMass)
##        CM_tar = yrp.getCM(motion_seg.getJointPositionsGlobal(frame), bodyMasses, totalMass)
#        stf_tar = motion_seg.getJointPositionGlobal(stanceFoots[0], frame)
#        CMr_tar = CM_tar - stf_tar

        dCM_tar = motion_seg.getJointVelocityGlobal(0, prev_frame)
        CM_tar = motion_seg.getJointPositionGlobal(0, prev_frame)
#        dCM_tar = yrp.getCM(motion_seg.getJointVelocitiesGlobal(prev_frame), bodyMasses, upperMass, uppers)
#        CM_tar = yrp.getCM(motion_seg.getJointPositionsGlobal(prev_frame), bodyMasses, upperMass, uppers)
#        dCM_tar = yrp.getCM(motion_seg.getJointVelocitiesGlobal(prev_frame), bodyMasses, totalMass)
#        CM_tar = yrp.getCM(motion_seg.getJointPositionsGlobal(prev_frame), bodyMasses, totalMass)
        stf_tar = motion_seg.getJointPositionGlobal(stanceFoots[0], prev_frame)
        CMr_tar = CM_tar - stf_tar
            
        dCM = avg_dCM[0]
        CM = controlModel.getJointPositionGlobal(0)
#        CM = yrp.getCM(controlModel.getJointPositionsGlobal(), bodyMasses, upperMass, uppers)
#        CM = yrp.getCM(controlModel.getJointPositionsGlobal(), bodyMasses, totalMass)
        CMreal = yrp.getCM(controlModel.getJointPositionsGlobal(), bodyMasses, totalMass)
        stf = controlModel.getJointPositionGlobal(stanceFoots[0])
        CMr = CM - stf
        
        diff_dCM = mm.projectionOnPlane(dCM-dCM_tar, (1,0,0), (0,0,1))
        diff_dCM_axis = np.cross((0,1,0), diff_dCM)
        rd_vec1[0] = diff_dCM; rd_vecori1[0] = CM_tar
        
        diff_CMr = mm.projectionOnPlane(CMr-CMr_tar, (1,0,0), (0,0,1))
#        rd_vec1[0] = diff_CMr; rd_vecori1[0] = stf_tar
        diff_CMr_axis = np.cross((0,1,0), diff_CMr)
        
        direction = mm.normalize2(mm.projectionOnPlane(dCM_tar, (1,0,0), (0,0,1)))
#        direction = mm.normalize2(mm.projectionOnPlane(dCM, (1,0,0), (0,0,1)))
        directionAxis = np.cross((0,1,0), direction)
        
        diff_dCM_sag, diff_dCM_cor = mm.projectionOnVector2(diff_dCM, direction)
#        rd_vec1[0] = diff_dCM_sag; rd_vecori1[0] = CM_tar
        diff_dCM_sag_axis = np.cross((0,1,0), diff_dCM_sag)
        diff_dCM_cor_axis = np.cross((0,1,0), diff_dCM_cor)
            
        diff_CMr_sag, diff_CMr_cor = mm.projectionOnVector2(diff_CMr, direction)
        diff_CMr_sag_axis = np.cross((0,1,0), diff_CMr_sag)
        diff_CMr_cor_axis = np.cross((0,1,0), diff_CMr_cor)
            
        t = (frame-curInterval[0])/float(curInterval[1]-curInterval[0])
        t_raw = t
        if t>1.: t=1.
        
        
        p_root = motion_stitch[frame].getJointPositionGlobal(0)
        R_root = motion_stitch[frame].getJointOrientationGlobal(0)

        motion_seg_orig.goToFrame(frame)
        motion_seg.goToFrame(frame)
        motion_stitch.goToFrame(frame)
        
        motion_debug1.append(motion_stitch[frame].copy())
        motion_debug1.goToFrame(frame)
        motion_debug2.append(motion_stitch[frame].copy())
        motion_debug2.goToFrame(frame)
        motion_debug3.append(motion_stitch[frame].copy())
        motion_debug3.goToFrame(frame)
        
        # paper implementation
        M_tc.append(motion_stitch[prev_frame])
        M_tc.goToFrame(frame)
        P_hat.append(M_tc[frame].copy())
        P_hat.goToFrame(frame)
        
        p_temp = ym.JointPosture(skeleton)
        p_temp.rootPos = controlModel.getJointPositionGlobal(0)
        p_temp.setJointOrientationsLocal(controlModel.getJointOrientationsLocal())
        P.append(p_temp)
        P.goToFrame(frame)
        
        # stance foot stabilize
        motion_stf_stabilize.append(motion_stitch[frame].copy())
        motion_stf_stabilize.goToFrame(frame)
        if STANCE_FOOT_STABILIZE:
            for stanceFoot in stanceFoots:
                R_target_foot = motion_seg[frame].getJointOrientationGlobal(stanceFoot)
                R_current_foot = motion_stf_stabilize[frame].getJointOrientationGlobal(stanceFoot)
                motion_stf_stabilize[frame].setJointOrientationGlobal(stanceFoot, cm.slerp(R_current_foot, R_target_foot , stf_stabilize_func(t)))
#                R_target_foot = motion_seg[frame].getJointOrientationLocal(stanceFoot)
#                R_current_foot = motion_stf_stabilize[frame].getJointOrientationLocal(stanceFoot)
#                motion_stf_stabilize[frame].setJointOrientationLocal(stanceFoot, cm.slerp(R_current_foot, R_target_foot , stf_stabilize_func(t)))

        # match stance leg 
        motion_match_stl.append(motion_stf_stabilize[frame].copy())
        motion_match_stl.goToFrame(frame)
        if MATCH_STANCE_LEG:
            if curState!=yba.GaitState.STOP:
                for i in range(len(stanceLegs)):
                    stanceLeg = stanceLegs[i]
                    stanceFoot = stanceFoots[i]
                    
#                    # motion stance leg -> character stance leg as time goes
                    R_motion = motion_match_stl[frame].getJointOrientationGlobal(stanceLeg)
                    R_character = controlModel.getJointOrientationGlobal(stanceLeg)
                    motion_match_stl[frame].setJointOrientationGlobal(stanceLeg, cm.slerp(R_motion, R_character, match_stl_func(t)))

#                    t_y = match_stl_func_y(t)
#                    t_xz = match_stl_func(t)
#                    
#                    R_motion = motion_match_stl[frame].getJointOrientationGlobal(stanceLeg)
#                    R_character = controlModel.getJointOrientationGlobal(stanceLeg)
#                    R = np.dot(R_character, R_motion.T)
#                    R_y, R_xz = mm.projectRotation((0,1,0), R)
#                    motion_match_stl[frame].mulJointOrientationGlobal(stanceLeg, mm.scaleSO3(R_xz, t_xz))
#                    motion_match_stl[frame].mulJointOrientationGlobal(stanceLeg, mm.scaleSO3(R_y, t_y))

        # swing foot placement
        motion_swf_placement.append(motion_match_stl[frame].copy())
        motion_swf_placement.goToFrame(frame)
        if SWING_FOOT_PLACEMENT:
            t_swing_foot_placement = swf_placement_func(t);
            
            if extended[0]:
                R_swp_sag = prev_R_swp[0][0]
                R_swp_cor = prev_R_swp[0][1]
            else:
                R_swp_sag = mm.I_SO3(); R_swp_cor = mm.I_SO3()
                R_swp_cor = np.dot(R_swp_cor, mm.exp(diff_dCM_cor_axis * K_swp_vel_cor * -t_swing_foot_placement))
                if np.dot(direction, diff_CMr_sag) < 0:
                    R_swp_sag = np.dot(R_swp_sag, mm.exp(diff_dCM_sag_axis * K_swp_vel_sag * -t_swing_foot_placement))
                    R_swp_sag = np.dot(R_swp_sag, mm.exp(diff_CMr_sag_axis * K_swp_pos_sag * -t_swing_foot_placement))
                else:
                    R_swp_sag = np.dot(R_swp_sag, mm.exp(diff_dCM_sag_axis * K_swp_vel_sag_faster * -t_swing_foot_placement))
                    R_swp_sag = np.dot(R_swp_sag, mm.exp(diff_CMr_sag_axis * K_swp_pos_sag_faster * -t_swing_foot_placement))
                R_swp_cor = np.dot(R_swp_cor, mm.exp(diff_CMr_cor_axis * K_swp_pos_cor * -t_swing_foot_placement))

            for i in range(len(swingLegs)):
                swingLeg = swingLegs[i]
                swingFoot = swingFoots[i] 
                
                # save swing foot global orientation
#                R_swf = motion_swf_placement[frame].getJointOrientationGlobal(swingFoot)
                
                # rotate swing leg
                motion_swf_placement[frame].mulJointOrientationGlobal(swingLeg, R_swp_sag)
                motion_swf_placement[frame].mulJointOrientationGlobal(swingLeg, R_swp_cor)
                
                # restore swing foot global orientation
#                motion_swf_placement[frame].setJointOrientationGlobal(swingFoot, R_swf)
                
                prev_R_swp[0] = (R_swp_sag, R_swp_cor)

        # swing foot height
        motion_swf_height.append(motion_swf_placement[frame].copy())
        motion_swf_height.goToFrame(frame)
        if SWING_FOOT_HEIGHT:
            for swingFoot in swingFoots:
                stanceFoot = stanceFoots[0]

                # save foot global orientation
                R_foot = motion_swf_height[frame].getJointOrientationGlobal(swingFoot)
                R_stance_foot = motion_swf_height[frame].getJointOrientationGlobal(stanceFoot)

                if OLD_SWING_HEIGHT:
                    height_tar = motion_swf_height[frame].getJointPositionGlobal(swingFoot)[1] - motion_swf_height[frame].getJointPositionGlobal(stanceFoot)[1]
                else:
                    height_tar = motion_swf_height[prev_frame].getJointPositionGlobal(swingFoot)[1] - groundHeight
                    d_height_tar = motion_swf_height.getJointVelocityGlobal(swingFoot, prev_frame)[1]
#                    height_tar += c_swf_mid_offset * swf_height_sine_func(t)
#                motion_debug1[frame] = motion_swf_height[frame].copy()

                # rotate
                motion_swf_height[frame].rotateByTarget(controlModel.getJointOrientationGlobal(0))
#                motion_debug2[frame] = motion_swf_height[frame].copy()
#                motion_debug2[frame].translateByTarget(controlModel.getJointPositionGlobal(0))

                if OLD_SWING_HEIGHT:
                    height_cur = motion_swf_height[frame].getJointPositionGlobal(swingFoot)[1] - motion_swf_height[frame].getJointPositionGlobal(stanceFoot)[1]
                else:
                    height_cur = controlModel.getJointPositionGlobal(swingFoot)[1] - halfFootHeight - c_swf_offset
                    d_height_cur = controlModel.getJointVelocityGlobal(swingFoot)[1]

                if OLD_SWING_HEIGHT:
                    offset_height = (height_tar - height_cur) * swf_height_func(t) * c5
                else:
                    offset_height = ((height_tar - height_cur) * c5
                                     + (d_height_tar - d_height_cur) * c6) * swf_height_func(t)

                offset_sine = c_swf_mid_offset * swf_height_sine_func(t)
#                offset_sine = 0.
                
                offset = 0.
                offset += offset_height
                offset += offset_sine

                if offset > 0.:
                    newPosition =  motion_swf_height[frame].getJointPositionGlobal(swingFoot)
                    newPosition[1] += offset
                    aik.ik_analytic(motion_swf_height[frame], swingFoot, newPosition)
                else:
                    if HIGHER_OFFSET:
                        newPosition =  motion_swf_height[frame].getJointPositionGlobal(stanceFoot)
                        newPosition[1] -= offset
                        aik.ik_analytic(motion_swf_height[frame], stanceFoot, newPosition)

                # return
#                motion_debug3[frame] = motion_swf_height[frame].copy()
#                motion_debug3[frame].translateByTarget(controlModel.getJointPositionGlobal(0))
                motion_swf_height[frame].rotateByTarget(R_root)
                
                # restore foot global orientation
                motion_swf_height[frame].setJointOrientationGlobal(swingFoot, R_foot)
                motion_swf_height[frame].setJointOrientationGlobal(stanceFoot, R_stance_foot)

                if plot!=None:
                    plot.addDataPoint('debug1', frame, offset_height)
                    plot.addDataPoint('debug2', frame, height_tar - height_cur)
#                    plot.addDataPoint('diff', frame, diff)


        # swing foot orientation
        motion_swf_orientation.append(motion_swf_height[frame].copy())
        motion_swf_orientation.goToFrame(frame)
        if SWING_FOOT_ORIENTATION:
            swf_orientation_func = yfg.concatenate([yfg.zero, yfg.hermite2nd, yfg.one], [.25, .75])
            for swingFoot in swingFoots:
                R_target_foot = motion_seg[curInterval[1]].getJointOrientationGlobal(swingFoot)
                R_current_foot = motion_swf_orientation[frame].getJointOrientationGlobal(swingFoot)
                motion_swf_orientation[frame].setJointOrientationGlobal(swingFoot, cm.slerp(R_current_foot, R_target_foot, swf_orientation_func(t)))
#    swf_stabilize_func = yfg.concatenate([yfg.hermite2nd, yfg.one], [c_taking_duration])
            # push orientation
#            for swingFoot in swingFoots:
#                R_target_foot = motion_seg[frame].getJointOrientationGlobal(swingFoot)
#                R_current_foot = motion_swf_orientation[frame].getJointOrientationGlobal(swingFoot)
#                motion_swf_orientation[frame].setJointOrientationGlobal(swingFoot, cm.slerp(R_current_foot, R_target_foot , swf_stabilize_func(t)))
            
        # stance foot push                
        motion_stf_push.append(motion_swf_orientation[frame].copy())
        motion_stf_push.goToFrame(frame)
        if STANCE_FOOT_PUSH:
            for swingFoot in swingFoots:
#                max_t = (maxStfPushFrame)/float(curInterval[1]-curInterval[0])
#                stf_push_func = yfg.concatenate([yfg.sine, yfg.zero], [max_t*2])
                stf_push_func = yfg.concatenate([yfg.sine, yfg.zero], [c_taking_duration*2])
                
                R_swp_sag = mm.I_SO3()
#                R_swp_sag = np.dot(R_swp_sag, mm.exp(diff_dCM_sag_axis * K_stp_vel * -stf_push_func(t)))
                
#                if step_length_cur[0] < step_length_tar[0]:
#                    ratio = step_length_cur[0] / step_length_tar[0]
#                    R_max = maxmaxStfPushFrame
#                    R_zero = 
                R_swp_sag = np.dot(R_swp_sag, mm.exp((step_length_tar[0] - step_length_cur[0])*step_axis[0] * K_stp_pos * -stf_push_func(t)))
                    
                motion_stf_push[frame].mulJointOrientationGlobal(swingFoot, R_swp_sag)
                
        # stance foot balancing 
        motion_stf_balancing.append(motion_stf_push[frame].copy())
        motion_stf_balancing.goToFrame(frame)
        if STANCE_FOOT_BALANCING:
            R_stb = mm.exp(diff_dCM_axis * K_stb_vel * stf_balancing_func(t))
            R_stb = np.dot(R_stb, mm.exp(diff_CMr_axis * K_stb_pos * stf_balancing_func(t)))
            for stanceFoot in stanceFoots:
                if frame < 5: continue
                motion_stf_balancing[frame].mulJointOrientationGlobal(stanceFoot, R_stb)
                    
        # control trajectory
        motion_control.append(motion_stf_balancing[frame].copy())
        motion_control.goToFrame(frame)
        
        #=======================================================================
        # tracking with inverse dynamics
        #=======================================================================
        th_r = motion_control.getDOFPositions(frame)
        th = controlModel.getDOFPositions()
        dth_r = motion_control.getDOFVelocities(frame)
        dth = controlModel.getDOFVelocities()
        ddth_r = motion_control.getDOFAccelerations(frame)
        ddth_des = yct.getDesiredDOFAccelerations(th_r, th, dth_r, dth, ddth_r, Kt, Dt)

        #=======================================================================
        # simulation
        #=======================================================================
        CP = mm.v3(0.,0.,0.)
        F = mm.v3(0.,0.,0.)
        avg_dCM[0] = mm.v3(0.,0.,0.)
        
        # external force rendering info
        del rd_forces[:]; del rd_force_points[:]
        for fi in forceInfos:
            if fi.startFrame <= frame and frame < fi.startFrame + fi.duration*(1/frameTime):
                rd_forces.append(fi.force)
                rd_force_points.append(controlModel.getBodyPositionGlobal(fi.targetBody)  + -mm.normalize2(fi.force)*.2)
                    
        for i in range(stepsPerFrame):
            
            bodyIDs, contactPositions, contactPositionLocals, contactForces = vpWorld.calcPenaltyForce(bodyIDsToCheck, mus, Ks, Ds)
            vpWorld.applyPenaltyForce(bodyIDs, contactPositionLocals, contactForces)
            
            # apply external force
            for fi in forceInfos:
                if fi.startFrame <= frame and frame < fi.startFrame + fi.duration*(1/frameTime):
                    controlModel.applyBodyForceGlobal(fi.targetBody, fi.force)
                                
            controlModel.setDOFAccelerations(ddth_des)
            controlModel.solveHybridDynamics()
            
#            # apply external force
#            for fi in forceInfos:
#                if fi.startFrame <= frame and frame < fi.startFrame + fi.duration*(1/frameTime):
#                    controlModel.applyBodyForceGlobal(fi.targetBody, fi.force)
            
            vpWorld.step()
#            yvu.align2D(controlModel)

            if len(contactForces) > 0:
                CP += yrp.getCP(contactPositions, contactForces)
                F += sum(contactForces)
            avg_dCM[0] += controlModel.getJointVelocityGlobal(0)
#            avg_dCM[0] += yrp.getCM(controlModel.getJointVelocitiesGlobal(), bodyMasses, upperMass, uppers)
#            avg_dCM[0] += yrp.getCM(controlModel.getJointVelocitiesGlobal(), bodyMasses, totalMass)

#            if len(stanceFoots)>0:
#                avg_stf_v[0] += controlModel.getJointVelocityGlobal(stanceFoots[0])
#                avg_stf_av[0] += controlModel.getJointAngVelocityGlobal(stanceFoots[0])
        
        CP /= stepsPerFrame
        F /= stepsPerFrame
        avg_dCM[0] /= stepsPerFrame
        
#        if len(stanceFoots)>0:
#            avg_stf_v[0] /= stepsPerFrame
#            avg_stf_av[0] /= stepsPerFrame
#            rd_vec1[0] = avg_stf_av[0]; rd_vec1[0][0] = 0.; rd_vec1[0][2] = 0.
#            rd_vecori1[0]= controlModel.getJointPositionGlobal(stanceFoots[0])

        #=======================================================================
        # segment editing
        #=======================================================================
        lastFrame = False
        
        if SEGMENT_EDITING:
            if curState==yba.GaitState.STOP:
                if frame == len(motion_seg)-1:
                    lastFrame = True
                    
            elif (curState==yba.GaitState.LSWING or curState==yba.GaitState.RSWING) and t>c_min_contact_time:
                swingID = lID if curState==yba.GaitState.LSWING else rID

                contact = False
                if swingID in bodyIDs:
                    minContactVel = 1000.
                    for i in range(len(bodyIDs)):
                        if bodyIDs[i]==swingID:
                            vel = controlModel.getBodyVelocityGlobal(swingID, contactPositionLocals[i])
                            vel[1] = 0
                            contactVel = mm.length(vel)
                            if contactVel < minContactVel: minContactVel = contactVel 
                    if minContactVel < c_min_contact_vel: contact = True
                
                extended[0] = False
                
                if contact:
#                    print frame, 'foot touch'
                    lastFrame = True
                    acc_offset[0] += frame - curInterval[1]
                    
                elif frame == len(motion_seg)-1:
                    print frame, 'extend frame', frame+1
                    
                    preserveJoints = []
#                    preserveJoints = [lFoot, rFoot]
#                    preserveJoints = [lFoot, rFoot, lKnee, rKnee]
#                    preserveJoints = [lFoot, rFoot, lKnee, rKnee, lUpLeg, rUpLeg]
                    stanceKnees = [rKnee] if curState==yba.GaitState.LSWING else [lKnee]   
                    preserveJoints = [stanceFoots[0], stanceKnees[0], stanceLegs[0]]
   
                    diff = 3
                    motion_seg_orig.extend([motion_seg_orig[-1]])
                    motion_seg.extend(ymt.extendByIntegration_root(motion_seg, 1, diff))
                    
                    motion_stitch.extend(ymt.extendByIntegration_constant(motion_stitch, 1, preserveJoints, diff))

#                    # extend for swing foot ground speed matching & swing foot height lower
##                    extendedPostures = ymt.extendByIntegration(motion_stitch, 1, preserveJoints, diff)
##                    extendedPostures = [motion_stitch[-1]] 
##
#                    extendFrameNum = frame - curInterval[1] + 1
#                    k = 1.-extendFrameNum/5.
#                    if k<0.: k=0.
#                    extendedPostures = ymt.extendByIntegrationAttenuation(motion_stitch, 1, preserveJoints, diff, k)
#
##                    if len(swingFoots)>0 and np.inner(dCM_tar, dCM)>0.:
##                        print frame, 'speed matching'
##                        R_swf = motion_stitch[-1].getJointOrientationGlobal(swingFoots[0])
##                        
##                        p_swf = motion_stitch[-1].getJointPositionGlobal(swingFoots[0])
##                        v_swf = motion_stitch.getJointVelocityGlobal(swingFoots[0], frame-diff, frame)
##                        a_swf = motion_stitch.getJointAccelerationGlobal(swingFoots[0], frame-diff, frame)
##                        p_swf += v_swf * (frameTime) + a_swf * (frameTime)*(frameTime)
##                        aik.ik_analytic(extendedPostures[0], swingFoots[0], p_swf)
##                        
##                        extendedPostures[0].setJointOrientationGlobal(swingFoots[0], R_swf)
#
#                    motion_stitch.extend(extendedPostures)
                    
                    extended[0] = True
        else:
            if frame == len(motion_seg)-1: lastFrame = True
                    
        if lastFrame:
            if segIndex < len(segments)-1:
                print '%d (%d): end of %dth seg (%s, %s)'%(frame, frame-curInterval[1],segIndex, yba.GaitState.text[curState], curInterval)
                if plot!=None: plot.addDataPoint('diff', frame, (frame-curInterval[1])*.01)
                
                if len(stanceFoots)>0 and len(swingFoots)>0:
#                    step_cur = controlModel.getJointPositionGlobal(swingFoots[0]) - controlModel.getJointPositionGlobal(stanceFoots[0])
#                    step_tar = motion_seg[curInterval[1]].getJointPositionGlobal(swingFoots[0]) - motion_seg[curInterval[1]].getJointPositionGlobal(stanceFoots[0])
                    step_cur = controlModel.getJointPositionGlobal(0) - controlModel.getJointPositionGlobal(stanceFoots[0])
                    step_tar = motion_seg[curInterval[1]].getJointPositionGlobal(0) - motion_seg[curInterval[1]].getJointPositionGlobal(stanceFoots[0])
                    
                    step_cur = mm.projectionOnPlane(step_cur, (1,0,0), (0,0,1))
                    step_tar = mm.projectionOnPlane(step_tar, (1,0,0), (0,0,1))
                    
                    step_cur_sag, step_cur_cor = mm.projectionOnVector2(step_cur, direction)
                    step_tar_sag, step_tar_cor = mm.projectionOnVector2(step_tar, direction)
                    
                    step_length_tar[0] = mm.length(step_tar_sag)
                    if np.inner(step_tar_sag, step_cur_sag) > 0:
                        step_length_cur[0] = mm.length(step_cur_sag)
                    else:
                        step_length_cur[0] = -mm.length(step_cur_sag)
                    
                    step_axis[0] = directionAxis
                    
#                    rd_vec1[0] = step_tar_sag
#                    rd_vecori1[0] = motion_seg[curInterval[1]].getJointPositionGlobal(stanceFoots[0])
#                    rd_vec2[0] = step_cur_sag
#                    rd_vecori2[0] = controlModel.getJointPositionGlobal(stanceFoots[0])

                seg_index[0] += 1
                curSeg = segments[seg_index[0]]
                stl_y_limit_num[0] = 0
                stl_xz_limit_num[0] = 0
                
                del motion_seg_orig[frame+1:]
                motion_seg_orig.extend(ymb.getAttachedNextMotion(curSeg, motion_seg_orig[-1], False, False))
                
                del motion_seg[frame+1:]
                del motion_stitch[frame+1:]
                transitionLength = len(curSeg)-1

#                motion_seg.extend(ymb.getAttachedNextMotion(curSeg, motion_seg[-1], False, False))
#                motion_stitch.extend(ymb.getStitchedNextMotion(curSeg, motion_control[-1], transitionLength, stitch_func, True, False))

                d = motion_seg[-1] - curSeg[0]
                d.rootPos[1] = 0.
                motion_seg.extend(ymb.getAttachedNextMotion(curSeg, d, True, False))
                d = motion_control[-1] - curSeg[0]
                d.rootPos[1] = 0.
                motion_stitch.extend(ymb.getStitchedNextMotion(curSeg, d, transitionLength, stitch_func, True, False))
                
#                motion_seg.extend(ymb.getAttachedNextMotion(curSeg, motion_seg[-1], False, True))
#                motion_stitch.extend(ymb.getStitchedNextMotion(curSeg, motion_control[-1], transitionLength, stitch_func, True, True))
            else:
                motion_seg_orig.append(motion_seg_orig[-1])
                motion_seg.append(motion_seg[-1])
                motion_stitch.append(motion_control[-1])
                
                
        # rendering
        motionModel.update(motion_ori[frame])
#        motionModel.update(motion_seg[frame])
        
        rd_CP[0] = CP
        rd_CMP[0] = (CMreal[0] - (F[0]/F[1])*CMreal[1], 0, CMreal[2] - (F[2]/F[1])*CMreal[1])
        
        if plot!=None:
            plot.addDataPoint('zero', frame, 0)
            plot.updatePoints()
    def simulateCallback(frame):
        # seginfo
        segIndex = seg_index[0]
        curState = seginfo[segIndex]['state']
        curInterval = yma.offsetInterval(acc_offset[0], seginfo[segIndex]['interval'])
        stanceLegs = seginfo[segIndex]['stanceHips']
        swingLegs = seginfo[segIndex]['swingHips']
        stanceFoots = seginfo[segIndex]['stanceFoots']
        swingFoots = seginfo[segIndex]['swingFoots']
        swingKnees = seginfo[segIndex]['swingKnees']
        groundHeight = seginfo[segIndex]['ground_height']
        maxStfPushFrame = seginfo[segIndex]['max_stf_push_frame']
        
        prev_frame = frame-1 if frame>0 else 0
#        prev_frame = frame
        
        # information
#        dCM_tar = yrp.getCM(motion_seg.getJointVelocitiesGlobal(frame), bodyMasses, upperMass, uppers)
#        CM_tar = yrp.getCM(motion_seg.getJointPositionsGlobal(frame), bodyMasses, upperMass, uppers)
##        dCM_tar = yrp.getCM(motion_seg.getJointVelocitiesGlobal(frame), bodyMasses, totalMass)
##        CM_tar = yrp.getCM(motion_seg.getJointPositionsGlobal(frame), bodyMasses, totalMass)
#        stf_tar = motion_seg.getJointPositionGlobal(stanceFoots[0], frame)
#        CMr_tar = CM_tar - stf_tar

        dCM_tar = motion_seg.getJointVelocityGlobal(0, prev_frame)
        CM_tar = motion_seg.getJointPositionGlobal(0, prev_frame)
#        dCM_tar = yrp.getCM(motion_seg.getJointVelocitiesGlobal(prev_frame), bodyMasses, upperMass, uppers)
#        CM_tar = yrp.getCM(motion_seg.getJointPositionsGlobal(prev_frame), bodyMasses, upperMass, uppers)
#        dCM_tar = yrp.getCM(motion_seg.getJointVelocitiesGlobal(prev_frame), bodyMasses, totalMass)
#        CM_tar = yrp.getCM(motion_seg.getJointPositionsGlobal(prev_frame), bodyMasses, totalMass)
        stf_tar = motion_seg.getJointPositionGlobal(stanceFoots[0], prev_frame)
        CMr_tar = CM_tar - stf_tar
            
        dCM = avg_dCM[0]
        CM = controlModel.getJointPositionGlobal(0)
#        CM = yrp.getCM(controlModel.getJointPositionsGlobal(), bodyMasses, upperMass, uppers)
#        CM = yrp.getCM(controlModel.getJointPositionsGlobal(), bodyMasses, totalMass)
        CMreal = yrp.getCM(controlModel.getJointPositionsGlobal(), bodyMasses, totalMass)
        stf = controlModel.getJointPositionGlobal(stanceFoots[0])
        CMr = CM - stf
        
        diff_dCM = mm.projectionOnPlane(dCM-dCM_tar, (1,0,0), (0,0,1))
        diff_dCM_axis = np.cross((0,1,0), diff_dCM)
        rd_vec1[0] = diff_dCM; rd_vecori1[0] = CM_tar
        
        diff_CMr = mm.projectionOnPlane(CMr-CMr_tar, (1,0,0), (0,0,1))
#        rd_vec1[0] = diff_CMr; rd_vecori1[0] = stf_tar
        diff_CMr_axis = np.cross((0,1,0), diff_CMr)
        
        direction = mm.normalize2(mm.projectionOnPlane(dCM_tar, (1,0,0), (0,0,1)))
#        direction = mm.normalize2(mm.projectionOnPlane(dCM, (1,0,0), (0,0,1)))
        directionAxis = np.cross((0,1,0), direction)
        
        diff_dCM_sag, diff_dCM_cor = mm.projectionOnVector2(diff_dCM, direction)
#        rd_vec1[0] = diff_dCM_sag; rd_vecori1[0] = CM_tar
        diff_dCM_sag_axis = np.cross((0,1,0), diff_dCM_sag)
        diff_dCM_cor_axis = np.cross((0,1,0), diff_dCM_cor)
            
        diff_CMr_sag, diff_CMr_cor = mm.projectionOnVector2(diff_CMr, direction)
        diff_CMr_sag_axis = np.cross((0,1,0), diff_CMr_sag)
        diff_CMr_cor_axis = np.cross((0,1,0), diff_CMr_cor)
            
        t = (frame-curInterval[0])/float(curInterval[1]-curInterval[0])
        t_raw = t
        if t>1.: t=1.
        
        
        p_root = motion_stitch[frame].getJointPositionGlobal(0)
        R_root = motion_stitch[frame].getJointOrientationGlobal(0)

        motion_seg_orig.goToFrame(frame)
        motion_seg.goToFrame(frame)
        motion_stitch.goToFrame(frame)
        
        motion_debug1.append(motion_stitch[frame].copy())
        motion_debug1.goToFrame(frame)
        motion_debug2.append(motion_stitch[frame].copy())
        motion_debug2.goToFrame(frame)
        motion_debug3.append(motion_stitch[frame].copy())
        motion_debug3.goToFrame(frame)
        
        # paper implementation
        M_tc.append(motion_stitch[prev_frame])
        M_tc.goToFrame(frame)
        P_hat.append(M_tc[frame].copy())
        P_hat.goToFrame(frame)
        
        p_temp = ym.JointPosture(skeleton)
        p_temp.rootPos = controlModel.getJointPositionGlobal(0)
        p_temp.setJointOrientationsLocal(controlModel.getJointOrientationsLocal())
        P.append(p_temp)
        P.goToFrame(frame)
        
        # stance foot stabilize
        motion_stf_stabilize.append(motion_stitch[frame].copy())
        motion_stf_stabilize.goToFrame(frame)
        if STANCE_FOOT_STABILIZE:
            for stanceFoot in stanceFoots:
                R_target_foot = motion_seg[frame].getJointOrientationGlobal(stanceFoot)
                R_current_foot = motion_stf_stabilize[frame].getJointOrientationGlobal(stanceFoot)
                motion_stf_stabilize[frame].setJointOrientationGlobal(stanceFoot, cm.slerp(R_current_foot, R_target_foot , stf_stabilize_func(t)))
#                R_target_foot = motion_seg[frame].getJointOrientationLocal(stanceFoot)
#                R_current_foot = motion_stf_stabilize[frame].getJointOrientationLocal(stanceFoot)
#                motion_stf_stabilize[frame].setJointOrientationLocal(stanceFoot, cm.slerp(R_current_foot, R_target_foot , stf_stabilize_func(t)))

        # match stance leg 
        motion_match_stl.append(motion_stf_stabilize[frame].copy())
        motion_match_stl.goToFrame(frame)
        if MATCH_STANCE_LEG:
            if curState!=yba.GaitState.STOP:
                for i in range(len(stanceLegs)):
                    stanceLeg = stanceLegs[i]
                    stanceFoot = stanceFoots[i]
                    
#                    # motion stance leg -> character stance leg as time goes
                    R_motion = motion_match_stl[frame].getJointOrientationGlobal(stanceLeg)
                    R_character = controlModel.getJointOrientationGlobal(stanceLeg)
                    motion_match_stl[frame].setJointOrientationGlobal(stanceLeg, cm.slerp(R_motion, R_character, match_stl_func(t)))

#                    t_y = match_stl_func_y(t)
#                    t_xz = match_stl_func(t)
#                    
#                    R_motion = motion_match_stl[frame].getJointOrientationGlobal(stanceLeg)
#                    R_character = controlModel.getJointOrientationGlobal(stanceLeg)
#                    R = np.dot(R_character, R_motion.T)
#                    R_y, R_xz = mm.projectRotation((0,1,0), R)
#                    motion_match_stl[frame].mulJointOrientationGlobal(stanceLeg, mm.scaleSO3(R_xz, t_xz))
#                    motion_match_stl[frame].mulJointOrientationGlobal(stanceLeg, mm.scaleSO3(R_y, t_y))

        # swing foot placement
        motion_swf_placement.append(motion_match_stl[frame].copy())
        motion_swf_placement.goToFrame(frame)
        if SWING_FOOT_PLACEMENT:
            t_swing_foot_placement = swf_placement_func(t);
            
            if extended[0]:
                R_swp_sag = prev_R_swp[0][0]
                R_swp_cor = prev_R_swp[0][1]
            else:
                R_swp_sag = mm.I_SO3(); R_swp_cor = mm.I_SO3()
                R_swp_sag = np.dot(R_swp_sag, mm.exp(diff_dCM_sag_axis * K_swp_vel_sag * -t_swing_foot_placement))
                R_swp_cor = np.dot(R_swp_cor, mm.exp(diff_dCM_cor_axis * K_swp_vel_cor * -t_swing_foot_placement))
                if np.dot(direction, diff_CMr_sag) < 0:
                    R_swp_sag = np.dot(R_swp_sag, mm.exp(diff_CMr_sag_axis * K_swp_pos_sag * -t_swing_foot_placement))
                R_swp_cor = np.dot(R_swp_cor, mm.exp(diff_CMr_cor_axis * K_swp_pos_cor * -t_swing_foot_placement))

            for i in range(len(swingLegs)):
                swingLeg = swingLegs[i]
                swingFoot = swingFoots[i] 
                
                # save swing foot global orientation
#                R_swf = motion_swf_placement[frame].getJointOrientationGlobal(swingFoot)
                
                # rotate swing leg
                motion_swf_placement[frame].mulJointOrientationGlobal(swingLeg, R_swp_sag)
                motion_swf_placement[frame].mulJointOrientationGlobal(swingLeg, R_swp_cor)
                
                # restore swing foot global orientation
#                motion_swf_placement[frame].setJointOrientationGlobal(swingFoot, R_swf)
                
                prev_R_swp[0] = (R_swp_sag, R_swp_cor)

        # swing foot height
        motion_swf_height.append(motion_swf_placement[frame].copy())
        motion_swf_height.goToFrame(frame)
        if SWING_FOOT_HEIGHT:
            for swingFoot in swingFoots:
                stanceFoot = stanceFoots[0]

                # save foot global orientation
                R_foot = motion_swf_height[frame].getJointOrientationGlobal(swingFoot)
                R_stance_foot = motion_swf_height[frame].getJointOrientationGlobal(stanceFoot)

                height_tar = motion_swf_height[frame].getJointPositionGlobal(swingFoot)[1] - motion_swf_height[frame].getJointPositionGlobal(stanceFoot)[1]
#                motion_debug1[frame] = motion_swf_height[frame].copy()

                # rotate
                motion_swf_height[frame].rotateByTarget(controlModel.getJointOrientationGlobal(0))
#                motion_debug2[frame] = motion_swf_height[frame].copy()
#                motion_debug2[frame].translateByTarget(controlModel.getJointPositionGlobal(0))

                height_cur = motion_swf_height[frame].getJointPositionGlobal(swingFoot)[1] - motion_swf_height[frame].getJointPositionGlobal(stanceFoot)[1]

                offset_height = (height_tar - height_cur) * swf_height_func(t) * c_swf_stability
                offset_sine = c_swf_mid_offset * swf_height_sine_func(t)
                
                offset = 0.
                offset += offset_height
                offset += offset_sine

                if offset > 0.:
                    newPosition =  motion_swf_height[frame].getJointPositionGlobal(swingFoot)
                    newPosition[1] += offset
                    aik.ik_analytic(motion_swf_height[frame], swingFoot, newPosition)
                else:
                    newPosition =  motion_swf_height[frame].getJointPositionGlobal(stanceFoot)
                    newPosition[1] -= offset
                    aik.ik_analytic(motion_swf_height[frame], stanceFoot, newPosition)

                # return
#                motion_debug3[frame] = motion_swf_height[frame].copy()
#                motion_debug3[frame].translateByTarget(controlModel.getJointPositionGlobal(0))
                motion_swf_height[frame].rotateByTarget(R_root)
                
                # restore foot global orientation
                motion_swf_height[frame].setJointOrientationGlobal(swingFoot, R_foot)
                motion_swf_height[frame].setJointOrientationGlobal(stanceFoot, R_stance_foot)

                if plot!=None:
                    plot.addDataPoint('debug1', frame, height_tar)
                    plot.addDataPoint('debug2', frame, height_cur)
#                    plot.addDataPoint('diff', frame, diff)

        # swing foot orientation
        motion_swf_orientation.append(motion_swf_height[frame].copy())
        motion_swf_orientation.goToFrame(frame)
        if SWING_FOOT_ORIENTATION:
#    swf_orientation_func = yfg.concatenate([yfg.zero, yfg.hermite2nd, yfg.one], [.25, .75])
            for swingFoot in swingFoots:
                R_target_foot = motion_seg[curInterval[1]].getJointOrientationGlobal(swingFoot)
                R_current_foot = motion_swf_orientation[frame].getJointOrientationGlobal(swingFoot)
                motion_swf_orientation[frame].setJointOrientationGlobal(swingFoot, cm.slerp(R_current_foot, R_target_foot, swf_orientation_func(t)))
#    swf_stabilize_func = yfg.concatenate([yfg.hermite2nd, yfg.one], [c_taking_duration])
            # push orientation
#            for swingFoot in swingFoots:
#                R_target_foot = motion_seg[frame].getJointOrientationGlobal(swingFoot)
#                R_current_foot = motion_swf_orientation[frame].getJointOrientationGlobal(swingFoot)
#                motion_swf_orientation[frame].setJointOrientationGlobal(swingFoot, cm.slerp(R_current_foot, R_target_foot , swf_stabilize_func(t)))
            
        # stance foot push                
        motion_stf_push.append(motion_swf_orientation[frame].copy())
        motion_stf_push.goToFrame(frame)
        if STANCE_FOOT_PUSH:
            for swingFoot in swingFoots:
#                max_t = (maxStfPushFrame)/float(curInterval[1]-curInterval[0])
#                stf_push_func = yfg.concatenate([yfg.sine, yfg.zero], [max_t*2])
                stf_push_func = yfg.concatenate([yfg.sine, yfg.zero], [c_taking_duration*2])
                
                R_swp_sag = mm.I_SO3()
#                R_swp_sag = np.dot(R_swp_sag, mm.exp(diff_dCM_sag_axis * K_stp_vel * -stf_push_func(t)))
                
#                if step_length_cur[0] < step_length_tar[0]:
#                    ratio = step_length_cur[0] / step_length_tar[0]
#                    R_max = maxmaxStfPushFrame
#                    R_zero = 
                R_swp_sag = np.dot(R_swp_sag, mm.exp((step_length_tar[0] - step_length_cur[0])*step_axis[0] * K_stp_pos * -stf_push_func(t)))
                    
                motion_stf_push[frame].mulJointOrientationGlobal(swingFoot, R_swp_sag)
                
        # stance foot balancing 
        motion_stf_balancing.append(motion_stf_push[frame].copy())
        motion_stf_balancing.goToFrame(frame)
        if STANCE_FOOT_BALANCING:
            R_stb = mm.exp(diff_dCM_axis * K_stb_vel * stf_balancing_func(t))
            for stanceFoot in stanceFoots:
                if frame < 5: continue
                motion_stf_balancing[frame].mulJointOrientationGlobal(stanceFoot, R_stb)
                    
        # control trajectory
        motion_control.append(motion_stf_balancing[frame].copy())
        motion_control.goToFrame(frame)
        
        #=======================================================================
        # tracking with inverse dynamics
        #=======================================================================
        th_r = motion_control.getDOFPositions(frame)
        th = controlModel.getDOFPositions()
        dth_r = motion_control.getDOFVelocities(frame)
        dth = controlModel.getDOFVelocities()
        ddth_r = motion_control.getDOFAccelerations(frame)
        ddth_des = yct.getDesiredDOFAccelerations(th_r, th, dth_r, dth, ddth_r, Kt, Dt)

        #=======================================================================
        # simulation
        #=======================================================================
        CP = mm.v3(0.,0.,0.)
        F = mm.v3(0.,0.,0.)
        avg_dCM[0] = mm.v3(0.,0.,0.)
        
        # external force rendering info
        del rd_forces[:]; del rd_force_points[:]
        for fi in forceInfos:
            if fi.startFrame <= frame and frame < fi.startFrame + fi.duration*(1/frameTime):
                rd_forces.append(fi.force)
                rd_force_points.append(controlModel.getBodyPositionGlobal(fi.targetBody))
                    
        for i in range(stepsPerFrame):
            
            bodyIDs, contactPositions, contactPositionLocals, contactForces = vpWorld.calcPenaltyForce(bodyIDsToCheck, mus, Ks, Ds)
            vpWorld.applyPenaltyForce(bodyIDs, contactPositionLocals, contactForces)
            
            # apply external force
            for fi in forceInfos:
                if fi.startFrame <= frame and frame < fi.startFrame + fi.duration*(1/frameTime):
                    controlModel.applyBodyForceGlobal(fi.targetBody, fi.force)
            
            controlModel.setDOFAccelerations(ddth_des)
            controlModel.solveHybridDynamics()
            
            if TORQUE_PLOT:
                rhip_torques[frame] += mm.length(controlModel.getJointTorqueLocal(rUpLeg))
                rknee_torques[frame] += mm.length(controlModel.getJointTorqueLocal(rKnee))
                rankle_torques[frame] += mm.length(controlModel.getJointTorqueLocal(rFoot))
            
            rd_torques[:] = [controlModel.getJointTorqueLocal(i)/100. for i in range(skeleton.getJointNum())]
            rd_joint_positions[:] = controlModel.getJointPositionsGlobal()
        
            vpWorld.step()
#            yvu.align2D(controlModel)

            if len(contactForces) > 0:
                CP += yrp.getCP(contactPositions, contactForces)
                F += sum(contactForces)
            avg_dCM[0] += controlModel.getJointVelocityGlobal(0)
#            avg_dCM[0] += yrp.getCM(controlModel.getJointVelocitiesGlobal(), bodyMasses, upperMass, uppers)
#            avg_dCM[0] += yrp.getCM(controlModel.getJointVelocitiesGlobal(), bodyMasses, totalMass)

#            if len(stanceFoots)>0:
#                avg_stf_v[0] += controlModel.getJointVelocityGlobal(stanceFoots[0])
#                avg_stf_av[0] += controlModel.getJointAngVelocityGlobal(stanceFoots[0])
        
        CP /= stepsPerFrame
        F /= stepsPerFrame
        avg_dCM[0] /= stepsPerFrame
        
#        if len(stanceFoots)>0:
#            avg_stf_v[0] /= stepsPerFrame
#            avg_stf_av[0] /= stepsPerFrame
#            rd_vec1[0] = avg_stf_av[0]; rd_vec1[0][0] = 0.; rd_vec1[0][2] = 0.
#            rd_vecori1[0]= controlModel.getJointPositionGlobal(stanceFoots[0])

        #=======================================================================
        # segment editing
        #=======================================================================
        lastFrame = False
        
        if SEGMENT_EDITING:
            if curState==yba.GaitState.STOP:
                if frame == len(motion_seg)-1:
                    lastFrame = True
                    
            elif (curState==yba.GaitState.LSWING or curState==yba.GaitState.RSWING) and t>c_min_contact_time:
                swingID = lID if curState==yba.GaitState.LSWING else rID

                contact = False
                if swingID in bodyIDs:
                    minContactVel = 1000.
                    for i in range(len(bodyIDs)):
                        if bodyIDs[i]==swingID:
                            vel = controlModel.getBodyVelocityGlobal(swingID, contactPositionLocals[i])
                            vel[1] = 0
                            contactVel = mm.length(vel)
                            if contactVel < minContactVel: minContactVel = contactVel 
                    if minContactVel < c_min_contact_vel: contact = True
                
                extended[0] = False
                
                if contact:
#                    print frame, 'foot touch'
                    lastFrame = True
                    acc_offset[0] += frame - curInterval[1]
                    
                elif frame == len(motion_seg)-1:
                    print frame, 'extend frame', frame+1
                    
                    preserveJoints = []
#                    preserveJoints = [lFoot, rFoot]
#                    preserveJoints = [lFoot, rFoot, lKnee, rKnee]
#                    preserveJoints = [lFoot, rFoot, lKnee, rKnee, lUpLeg, rUpLeg]
                    stanceKnees = [rKnee] if curState==yba.GaitState.LSWING else [lKnee]   
                    preserveJoints = [stanceFoots[0], stanceKnees[0], stanceLegs[0]]
   
                    diff = 3
                    motion_seg_orig.extend([motion_seg_orig[-1]])
                    motion_seg.extend(ymt.extendByIntegration_root(motion_seg, 1, diff))
                    
                    motion_stitch.extend(ymt.extendByIntegration_constant(motion_stitch, 1, preserveJoints, diff))

#                    # extend for swing foot ground speed matching & swing foot height lower
##                    extendedPostures = ymt.extendByIntegration(motion_stitch, 1, preserveJoints, diff)
##                    extendedPostures = [motion_stitch[-1]] 
##
#                    extendFrameNum = frame - curInterval[1] + 1
#                    k = 1.-extendFrameNum/5.
#                    if k<0.: k=0.
#                    extendedPostures = ymt.extendByIntegrationAttenuation(motion_stitch, 1, preserveJoints, diff, k)
#
##                    if len(swingFoots)>0 and np.inner(dCM_tar, dCM)>0.:
##                        print frame, 'speed matching'
##                        R_swf = motion_stitch[-1].getJointOrientationGlobal(swingFoots[0])
##                        
##                        p_swf = motion_stitch[-1].getJointPositionGlobal(swingFoots[0])
##                        v_swf = motion_stitch.getJointVelocityGlobal(swingFoots[0], frame-diff, frame)
##                        a_swf = motion_stitch.getJointAccelerationGlobal(swingFoots[0], frame-diff, frame)
##                        p_swf += v_swf * (frameTime) + a_swf * (frameTime)*(frameTime)
##                        aik.ik_analytic(extendedPostures[0], swingFoots[0], p_swf)
##                        
##                        extendedPostures[0].setJointOrientationGlobal(swingFoots[0], R_swf)
#
#                    motion_stitch.extend(extendedPostures)
                    
                    extended[0] = True
        else:
            if frame == len(motion_seg)-1: lastFrame = True
                    
        if lastFrame:
            if segIndex < len(segments)-1:
                print '%d (%d): end of %dth seg (%s, %s)'%(frame, frame-curInterval[1],segIndex, yba.GaitState.text[curState], curInterval)
                if plot!=None: plot.addDataPoint('diff', frame, (frame-curInterval[1])*.01)
                
                if len(stanceFoots)>0 and len(swingFoots)>0:
#                    step_cur = controlModel.getJointPositionGlobal(swingFoots[0]) - controlModel.getJointPositionGlobal(stanceFoots[0])
#                    step_tar = motion_seg[curInterval[1]].getJointPositionGlobal(swingFoots[0]) - motion_seg[curInterval[1]].getJointPositionGlobal(stanceFoots[0])
                    step_cur = controlModel.getJointPositionGlobal(0) - controlModel.getJointPositionGlobal(stanceFoots[0])
                    step_tar = motion_seg[curInterval[1]].getJointPositionGlobal(0) - motion_seg[curInterval[1]].getJointPositionGlobal(stanceFoots[0])
                    
                    step_cur = mm.projectionOnPlane(step_cur, (1,0,0), (0,0,1))
                    step_tar = mm.projectionOnPlane(step_tar, (1,0,0), (0,0,1))
                    
                    step_cur_sag, step_cur_cor = mm.projectionOnVector2(step_cur, direction)
                    step_tar_sag, step_tar_cor = mm.projectionOnVector2(step_tar, direction)
                    
                    step_length_tar[0] = mm.length(step_tar_sag)
                    if np.inner(step_tar_sag, step_cur_sag) > 0:
                        step_length_cur[0] = mm.length(step_cur_sag)
                    else:
                        step_length_cur[0] = -mm.length(step_cur_sag)
                    
                    step_axis[0] = directionAxis
                    
#                    rd_vec1[0] = step_tar_sag
#                    rd_vecori1[0] = motion_seg[curInterval[1]].getJointPositionGlobal(stanceFoots[0])
#                    rd_vec2[0] = step_cur_sag
#                    rd_vecori2[0] = controlModel.getJointPositionGlobal(stanceFoots[0])

                seg_index[0] += 1
                curSeg = segments[seg_index[0]]
                stl_y_limit_num[0] = 0
                stl_xz_limit_num[0] = 0
                
                del motion_seg_orig[frame+1:]
                motion_seg_orig.extend(ymb.getAttachedNextMotion(curSeg, motion_seg_orig[-1], False, False))
                
                del motion_seg[frame+1:]
                del motion_stitch[frame+1:]
                transitionLength = len(curSeg)-1

#                motion_seg.extend(ymb.getAttachedNextMotion(curSeg, motion_seg[-1], False, False))
#                motion_stitch.extend(ymb.getStitchedNextMotion(curSeg, motion_control[-1], transitionLength, stitch_func, True, False))

                d = motion_seg[-1] - curSeg[0]
                d.rootPos[1] = 0.
                motion_seg.extend(ymb.getAttachedNextMotion(curSeg, d, True, False))
                
                if NO_FOOT_SLIDING:
                    if segIndex == len(segments)-2:
                        Rl = motion_control[-1].getJointOrientationLocal(lUpLeg)
                        Rr = motion_control[-1].getJointOrientationLocal(rUpLeg)
                        Rlk = motion_control[-1].getJointOrientationLocal(lKnee)
                        Rrk = motion_control[-1].getJointOrientationLocal(rKnee)
                        Rlf = motion_control[-1].getJointOrientationLocal(lFoot)
                        Rrf = motion_control[-1].getJointOrientationLocal(rFoot)
                        for p in curSeg:
                            p.setJointOrientationLocal(lUpLeg, Rl, False)
                            p.setJointOrientationLocal(rUpLeg, Rr, False)
                            p.setJointOrientationLocal(lKnee, Rlk, False)
                            p.setJointOrientationLocal(rKnee, Rrk, False)
                            p.setJointOrientationLocal(lFoot, Rlf, False)
                            p.setJointOrientationLocal(rFoot, Rrf, False)
                            p.updateGlobalT()                
                d = motion_control[-1] - curSeg[0]
                d.rootPos[1] = 0.
                motion_stitch.extend(ymb.getStitchedNextMotion(curSeg, d, transitionLength, stitch_func, True, False))
                
#                motion_seg.extend(ymb.getAttachedNextMotion(curSeg, motion_seg[-1], False, True))
#                motion_stitch.extend(ymb.getStitchedNextMotion(curSeg, motion_control[-1], transitionLength, stitch_func, True, True))
            else:
                motion_seg_orig.append(motion_seg_orig[-1])
                motion_seg.append(motion_seg[-1])
                motion_stitch.append(motion_control[-1])
                
                
        # rendering
        motionModel.update(motion_ori[frame])
#        motionModel.update(motion_seg[frame])
        
        if SAVE_SIMULATION:
            p_temp = ym.JointPosture(skeleton)
            p_temp.initLocalRs()
            p_temp.rootPos = controlModel.getJointPositionGlobal(0)
            p_temp.setJointOrientationsLocal(controlModel.getJointOrientationsLocal())
            motion_simulation.append(p_temp)
            
            if frame == viewer.getMaxFrame():
                saveFilePath = SAVE_DIR+'simulated_'+filename
                yf.writeBvhFile(saveFilePath, motion_simulation)
                print saveFilePath, 'saved'
Пример #4
0
def push_simbicon_mass():
# Trunk   29.27
# Head    5.89
# Pelvis  16.61
# Thigh   8.35
# Shank   4.16
# Foot    1.34
# Arm     2.79
# Forearm 1.21
# Hand    0.55
    
    class ForceInfo:
        def __init__(self, startFrame, duration, force):
            self.startFrame = startFrame    # frame
            self.duration = duration        # sec
            self.force = force              # Newton
            self.targetBody = None

    #===============================================================================
    # load motion
    #===============================================================================
    MULTI_VIEWER = False
    CAMERA_TRACKING = True
    TORQUE_PLOT = False
    
    # global parameters
    Kt = 60.;       Dt = 2*(Kt**.5)
    Ks = 4000.;    Ds = 2*(Ks**.5)
    K_stb_vel = .1
    mu = 2.
    
    # constaants
    c_min_contact_vel = 100.
#    c_min_contact_vel = 2.
    c_min_contact_time = .7
    c_landing_duration = .2
    c_taking_duration = .3
#    c_swf_mid_offset = .0
    c_swf_mid_offset = .02
    c_swf_stability = .5
    c_locking_vel = .05
    

#    c_swf_offset = .0
    c_swf_offset = .01
#    c_swf_offset = .005
    K_stp_pos = 0.
    
#    c5 = .5;    c6 = .01
    c5 = .5;    c6 = .02
#    c5 = .5;    c6 = .05
#    c5 = 1.;    c6 = .05
#    c5 = .0;    c6 = .0
    
    K_stb_vel = .1
    K_stb_pos = .1
    
    OLD_SWING_HEIGHT = False
#    OLD_SWING_HEIGHT = True
    HIGHER_OFFSET = True
#    HIGHER_OFFSET = False

    
    dir = './ppmotion/'
    

    # max push
#    forceInfos = []

    # maximum
#    forceInfos = [ForceInfo(4*i*30, .4, (160,0,0)) for i in range(2,12)]
#    forceInfos = [ForceInfo(4*i*30, .4, (-130,0,0)) for i in range(2,12)]
#    forceInfos = [ForceInfo(4*i*30, .4, (0,0,80)) for i in range(2,12)]
    forceInfos = [ForceInfo(4*i*30+1, .4, (0,0,-105)) for i in range(2,12)]

#    # maximum with more checking
#    forceInfos = [ForceInfo(4*i*30, .4, (145,0,0)) for i in range(2,12)]
#    forceInfos = [ForceInfo(4*i*30+1, .4, (-120,0,0)) for i in range(2,12)]
#    forceInfos = [ForceInfo(4*i*30+1, .4, (0,0,80)) for i in range(2,12)]
#    forceInfos = [ForceInfo(4*i*30, .4, (0,0,-105)) for i in range(2,12)]

#    # for video
#    forceInfos = [ForceInfo(4*i*30+2, .4, (160,0,0)) for i in range(2,4)] \
#                + [ForceInfo(4*i*30+2, .4, (0,0,-105)) for i in range(4,6)] \
#                + [ForceInfo(4*i*30+2, .4, (-130,0,0)) for i in range(6,8)] \
#                + [ForceInfo(4*i*30+2, .4, (0,0,80)) for i in range(8,10)]

#    Kt = 40.;       Dt = 2*(Kt**.5)
#    Ks = 3000.;    Ds = 2*(Ks**.5)
#    mu = 1.
#    c_swf_mid_offset = .04
#    K_swp_vel_sag = .0; K_swp_vel_sag_faster = .0;  
#    K_swp_pos_sag = 1.5; K_swp_pos_sag_faster = .1;
#    K_swp_vel_cor = .25;  K_swp_pos_cor = .3
#    K_stp_pos = 0.
#    K_stb_vel = .02
#    K_stb_pos = .15

    Kt = 40.;       Dt = 2*(Kt**.5)
    Ks = 3000.;    Ds = 2*(Ks**.5)
    mu = 1.5
    c_swf_mid_offset = .04
    K_swp_vel_sag = .05; K_swp_vel_sag_faster = .0;  
    K_swp_pos_sag = 1.7; K_swp_pos_sag_faster = .1;
    K_swp_vel_cor = .25;  K_swp_pos_cor = .3
#    K_stb_vel = .02
#    K_stb_pos = .15
    filename = 'wd2_WalkSameSame01_REPEATED.bvh'



    motion_ori = yf.readBvhFile(dir+filename)
    frameTime = 1/motion_ori.fps
    
    if 'REPEATED' in filename:
        REPEATED = True
        CAMERA_TRACKING = True
    else:
        REPEATED = False

    #===============================================================================
    # options
    #===============================================================================
    SEGMENT_EDITING =           True
    STANCE_FOOT_STABILIZE =     True
    MATCH_STANCE_LEG =          True
    SWING_FOOT_PLACEMENT =      True
    SWING_FOOT_HEIGHT =         True
    
    if '_FOOT' in filename:
        SWING_FOOT_ORIENTATION =    True
    else:
        SWING_FOOT_ORIENTATION =    False
    
    STANCE_FOOT_PUSH =          True
    STANCE_FOOT_BALANCING =     True
    
    stitch_func = lambda x : 1. - yfg.hermite2nd(x)
    stf_stabilize_func = yfg.concatenate([yfg.hermite2nd, yfg.one], [c_landing_duration])
    match_stl_func = yfg.hermite2nd
#    match_stl_func_y = yfg.hermite2nd
    swf_placement_func = yfg.hermite2nd
    swf_height_func = yfg.hermite2nd
    swf_height_sine_func = yfg.sine
#    stf_balancing_func = yfg.concatenate([yfg.hermite2nd, yfg.one], [c_landing_duration])
    stf_balancing_func = yfg.hermite2nd
    

    #===============================================================================
    # initialize character
    #===============================================================================
#    mcfgfile = open(dir + 'mcfg', 'r')
    mcfgfile = open('mcfg_simbicon', 'r')
    mcfg = cPickle.load(mcfgfile)
    mcfgfile.close()
    
    wcfg = ypc.WorldConfig()
    wcfg.planeHeight = 0.
    wcfg.useDefaultContactModel = False
    wcfg.lockingVel = c_locking_vel
    stepsPerFrame = 30
    wcfg.timeStep = (frameTime)/stepsPerFrame
    
    vpWorld = cvw.VpWorld(wcfg)
    motionModel = cvm.VpMotionModel(vpWorld, motion_ori[0], mcfg)
    controlModel = cvm.VpControlModel(vpWorld, motion_ori[0], mcfg)
    vpWorld.initialize()
    print controlModel
    
    motionModel.recordVelByFiniteDiff()
    controlModel.initializeHybridDynamics()
    
    #===============================================================================
    # load segment info
    #===============================================================================
    skeleton = motion_ori[0].skeleton
    
    segname = os.path.splitext(filename)[0]+'.seg'
    segfile = open(dir+segname, 'r')
    seginfo = cPickle.load(segfile)
    segfile.close()
    
    intervals = [info['interval'] for info in seginfo]
    states = [info['state'] for info in seginfo]
    temp_motion = copy.deepcopy(motion_ori)
    segments = yma.splitMotionIntoSegments(temp_motion, intervals)    
    print len(intervals), 'segments'
    for i in range(len(intervals)):
        print '%dth'%i, yba.GaitState.text[states[i]], intervals[i], ',', 
    print

    motion_seg_orig = ym.JointMotion()
    motion_seg_orig += segments[0]
    motion_seg = ym.JointMotion()
    motion_seg += segments[0]
    motion_stitch = ym.JointMotion()
    motion_stitch += segments[0]

    motion_stf_stabilize = ym.JointMotion()
    motion_match_stl = ym.JointMotion()
    motion_swf_placement = ym.JointMotion()
    motion_swf_height = ym.JointMotion()
    motion_swf_orientation = ym.JointMotion()
    motion_stf_balancing = ym.JointMotion()
    motion_stf_push = ym.JointMotion()
    motion_control = ym.JointMotion()

    motion_debug1 = ym.JointMotion()
    motion_debug2 = ym.JointMotion()
    motion_debug3 = ym.JointMotion()
    
    P = ym.JointMotion()
    P_hat = ym.JointMotion()
    M_tc = ym.JointMotion()
    M_hat_tc_1 = ym.JointMotion()
    
    #===============================================================================
    # loop variable
    #===============================================================================
    seg_index = [0]
    acc_offset = [0]
    extended = [False]
    prev_R_swp = [None]
    stl_y_limit_num = [0]
    stl_xz_limit_num = [0]
    avg_dCM = [mm.O_Vec3()]
#    avg_stf_v = [mm.O_Vec3()]
#    avg_stf_av = [mm.O_Vec3()]
    
#    stf_push_func = [yfg.zero]
    step_length_cur = [0.]

    step_length_tar = [0.]
    step_axis = [mm.O_Vec3()]
            
    #===============================================================================
    # information
    #===============================================================================
    bodyIDsToCheck = range(vpWorld.getBodyNum())
    mus = [mu]*len(bodyIDsToCheck)
    
    bodyMasses = controlModel.getBodyMasses()
    totalMass = controlModel.getTotalMass()

    lID = controlModel.name2id('LeftFoot');      rID = controlModel.name2id('RightFoot')
    lUpLeg = skeleton.getJointIndex('LeftUpLeg');rUpLeg = skeleton.getJointIndex('RightUpLeg')
    lKnee = skeleton.getJointIndex('LeftLeg');   rKnee = skeleton.getJointIndex('RightLeg')
    lFoot = skeleton.getJointIndex('LeftFoot');  rFoot = skeleton.getJointIndex('RightFoot')
    spine = skeleton.getJointIndex('Spine')
    
    uppers = [skeleton.getJointIndex(name) for name in ['Hips', 'Spine', 'Spine1', 'LeftArm', 'LeftForeArm', 'RightArm', 'RightForeArm']]
    upperMass = sum([bodyMasses[i] for i in uppers])
    lLegs = [skeleton.getJointIndex(name) for name in ['LeftUpLeg', 'LeftLeg', 'LeftFoot']]
    rLegs = [skeleton.getJointIndex(name) for name in ['RightUpLeg', 'RightLeg', 'RightFoot']]
    allJoints = set(range(skeleton.getJointNum()))
    
    halfFootHeight = controlModel.getBodyShape(lFoot)[1] / 2.
    
    for fi in forceInfos:
        fi.targetBody = spine
        
    #===========================================================================
    # data collection
    #===========================================================================
    rhip_torques = []
    rknee_torques = []
    rankle_torques = []

    #===============================================================================
    # rendering
    #===============================================================================
    rd_CM = [None]; rd_CP = [None]; rd_CMP = [None]
    rd_forces = [None]; rd_force_points = [None]
    rd_torques = []; rd_joint_positions = []
    
    rd_point1 = [None]
    rd_point2 = [None]
    rd_vec1 = [None];   rd_vecori1 = [None] 
    rd_vec2 = [None];   rd_vecori2 = [None]
    rd_frame1 = [None]
    rd_frame2 = [None]
    
    if MULTI_VIEWER:
        viewer = ymv.MultiViewer(800, 655, True, wheelWork=True)
#        viewer = ymv.MultiViewer(1600, 1255)
        viewer.setRenderers1([cvr.VpModelRenderer(motionModel, MOTION_COLOR, yr.POLYGON_FILL)])
        viewer.setRenderers2([cvr.VpModelRenderer(controlModel, CHARACTER_COLOR, yr.POLYGON_FILL), 
                              yr.ForcesRenderer(rd_forces, rd_force_points, (255,0,0), ratio=.01, lineWidth=.04, fromPoint=False)])
#        viewer.glWindow2.groundOffset[0] -= 10
        viewer.glWindow2.groundSize = 100
    else:
        viewer = ysv.SimpleViewer()
    #    viewer.record(False)
    
#        viewer.doc.addRenderer('motionModel', cvr.VpModelRenderer(motionModel, (0,150,255), yr.POLYGON_LINE))
        viewer.doc.addRenderer('controlModel', cvr.VpModelRenderer(controlModel, (200,200,200), yr.POLYGON_LINE))
        
    #    viewer.doc.addObject('motion_ori', motion_ori)
    #    viewer.doc.addRenderer('motion_ori', yr.JointMotionRenderer(motion_ori, (0,100,255), yr.LINK_BONE))
#        viewer.doc.addRenderer('motion_seg_orig', yr.JointMotionRenderer(motion_seg_orig, (0,100,255), yr.LINK_BONE))
#        viewer.doc.addRenderer('motion_seg', yr.JointMotionRenderer(motion_seg, (0,150,255), yr.LINK_BONE))
#        viewer.doc.addRenderer('motion_stitch', yr.JointMotionRenderer(motion_stitch, (0,255,200), yr.LINK_BONE))
#        viewer.doc.addRenderer('motion_stf_stabilize', yr.JointMotionRenderer(motion_stf_stabilize, (255,0,0), yr.LINK_BONE))
#        viewer.doc.addRenderer('motion_match_stl', yr.JointMotionRenderer(motion_match_stl, (255,200,0), yr.LINK_BONE))
#        viewer.doc.addRenderer('motion_swf_placement', yr.JointMotionRenderer(motion_swf_placement, (255,100,255), yr.LINK_BONE))
#        viewer.doc.addRenderer('motion_swf_height', yr.JointMotionRenderer(motion_swf_height, (50,255,255), yr.LINK_BONE))
#        viewer.doc.addRenderer('motion_swf_orientation', yr.JointMotionRenderer(motion_swf_orientation, (255,100,0), yr.LINK_BONE))
#        viewer.doc.addRenderer('motion_stf_push', yr.JointMotionRenderer(motion_stf_push, (50,255,200), yr.LINK_BONE))
    #    viewer.doc.addRenderer('motion_stf_balancing', yr.JointMotionRenderer(motion_stf_balancing, (255,100,255), yr.LINK_BONE))
#        viewer.doc.addRenderer('motion_control', yr.JointMotionRenderer(motion_control, (255,0,0), yr.LINK_BONE))
    
#        viewer.doc.addRenderer('motion_debug1', yr.JointMotionRenderer(motion_debug1, (0,255,0), yr.LINK_BONE))
#        viewer.doc.addRenderer('motion_debug2', yr.JointMotionRenderer(motion_debug2, (255,0,255), yr.LINK_BONE))
#        viewer.doc.addRenderer('motion_debug3', yr.JointMotionRenderer(motion_debug3, (255,255,0), yr.LINK_BONE))

#        viewer.doc.addRenderer('M_tc', yr.JointMotionRenderer(M_tc, (255,255,0), yr.LINK_BONE))
#        viewer.doc.addRenderer('P_hat', yr.JointMotionRenderer(P_hat, (255,255,0), yr.LINK_BONE))
#        viewer.doc.addRenderer('P', yr.JointMotionRenderer(P, (255,255,0), yr.LINK_BONE))
#        viewer.doc.addRenderer('M_hat_tc_1', yr.JointMotionRenderer(M_hat_tc_1, (255,255,0), yr.LINK_BONE))
    
    #    viewer.doc.addRenderer('rd_CM', yr.PointsRenderer(rd_CM, (255,255,0)))
    #    viewer.doc.addRenderer('rd_CP', yr.PointsRenderer(rd_CP, (255,0,0)))
    #    viewer.doc.addRenderer('rd_CMP', yr.PointsRenderer(rd_CMP, (0,255,0)))
        viewer.doc.addRenderer('forces', yr.ForcesRenderer(rd_forces, rd_force_points, (255,0,0), ratio=.01, lineWidth=.04, fromPoint=False))
#        viewer.doc.addRenderer('torques', yr.VectorsRenderer(rd_torques, rd_joint_positions, (255,0,0)))
    
    #    viewer.doc.addRenderer('rd_point1', yr.PointsRenderer(rd_point1, (0,255,0)))
    #    viewer.doc.addRenderer('rd_point2', yr.PointsRenderer(rd_point2, (255,0,0)))
#        viewer.doc.addRenderer('rd_vec1', yr.VectorsRenderer(rd_vec1, rd_vecori1, (255,0,0)))
    #    viewer.doc.addRenderer('rd_vec2', yr.VectorsRenderer(rd_vec2, rd_vecori2, (0,255,0)))
    #    viewer.doc.addRenderer('rd_frame1', yr.FramesRenderer(rd_frame1, (0,200,200)))
    #    viewer.doc.addRenderer('rd_frame2', yr.FramesRenderer(rd_frame2, (200,200,0)))
    #    viewer.setMaxFrame(len(motion_ori)-1)

    if not REPEATED:
        viewer.setMaxFrame(len(motion_ori)-1)
    else:
        viewer.setMaxFrame(1440)
        
    if CAMERA_TRACKING:
        if MULTI_VIEWER:
            cameraTargets1 = [None] * (viewer.getMaxFrame()+1)
            cameraTargets2 = [None] * (viewer.getMaxFrame()+1)
        else:
            cameraTargets = [None] * (viewer.getMaxFrame()+1)
            
    if TORQUE_PLOT:
        rhip_torques = [0.]*viewer.getMaxFrame()
        rknee_torques = [0.]*viewer.getMaxFrame()
        rankle_torques = [0.]*viewer.getMaxFrame()
        
    pt = [0.]
    def postFrameCallback_Always(frame):
        if frame==1: pt[0] = time.time()
        if frame==31: print 'elapsed time for 30 frames:', time.time()-pt[0]
        if CAMERA_TRACKING:
            if MULTI_VIEWER:
                if cameraTargets1[frame]==None:
                    cameraTargets1[frame] = motionModel.getBodyPositionGlobal(0)
#                    cameraTargets1[frame] = motion_ori[frame].getJointPositionGlobal(0)
                viewer.setCameraTarget1(cameraTargets1[frame])
                
                if cameraTargets2[frame]==None:
                    cameraTargets2[frame] = controlModel.getJointPositionGlobal(0)
                viewer.setCameraTarget2(cameraTargets2[frame])
                
            else:
                if cameraTargets[frame]==None:
                    cameraTargets[frame] = controlModel.getJointPositionGlobal(0)
                viewer.setCameraTarget(cameraTargets[frame])
        if plot!=None:
            plot.updateVline(frame)
    viewer.setPostFrameCallback_Always(postFrameCallback_Always)

    plot = None
#    plot = ymp.InteractivePlot()
    if plot!=None:
        plot.setXlimit(0, len(motion_ori))
        plot.setYlimit(0., 1.)
        plot.addDataSet('zero')
        plot.addDataSet('diff')
        plot.addDataSet('debug1')
        plot.addDataSet('debug2')

    def viewer_onClose(data):
        if plot!=None:
            plot.close()
        viewer.onClose(data)
    viewer.callback(viewer_onClose)
         
    def simulateCallback(frame):
        # seginfo
        segIndex = seg_index[0]
        curState = seginfo[segIndex]['state']
        curInterval = yma.offsetInterval(acc_offset[0], seginfo[segIndex]['interval'])
        stanceLegs = seginfo[segIndex]['stanceHips']
        swingLegs = seginfo[segIndex]['swingHips']
        stanceFoots = seginfo[segIndex]['stanceFoots']
        swingFoots = seginfo[segIndex]['swingFoots']
        swingKnees = seginfo[segIndex]['swingKnees']
        groundHeight = seginfo[segIndex]['ground_height']
#        maxStfPushFrame = seginfo[segIndex]['max_stf_push_frame']
        
        prev_frame = frame-1 if frame>0 else 0
#        prev_frame = frame
        
        # information
#        dCM_tar = yrp.getCM(motion_seg.getJointVelocitiesGlobal(frame), bodyMasses, upperMass, uppers)
#        CM_tar = yrp.getCM(motion_seg.getJointPositionsGlobal(frame), bodyMasses, upperMass, uppers)
##        dCM_tar = yrp.getCM(motion_seg.getJointVelocitiesGlobal(frame), bodyMasses, totalMass)
##        CM_tar = yrp.getCM(motion_seg.getJointPositionsGlobal(frame), bodyMasses, totalMass)
#        stf_tar = motion_seg.getJointPositionGlobal(stanceFoots[0], frame)
#        CMr_tar = CM_tar - stf_tar

        dCM_tar = motion_seg.getJointVelocityGlobal(0, prev_frame)
        CM_tar = motion_seg.getJointPositionGlobal(0, prev_frame)
#        dCM_tar = yrp.getCM(motion_seg.getJointVelocitiesGlobal(prev_frame), bodyMasses, upperMass, uppers)
#        CM_tar = yrp.getCM(motion_seg.getJointPositionsGlobal(prev_frame), bodyMasses, upperMass, uppers)
#        dCM_tar = yrp.getCM(motion_seg.getJointVelocitiesGlobal(prev_frame), bodyMasses, totalMass)
#        CM_tar = yrp.getCM(motion_seg.getJointPositionsGlobal(prev_frame), bodyMasses, totalMass)
        stf_tar = motion_seg.getJointPositionGlobal(stanceFoots[0], prev_frame)
        CMr_tar = CM_tar - stf_tar
            
        dCM = avg_dCM[0]
        CM = controlModel.getJointPositionGlobal(0)
#        CM = yrp.getCM(controlModel.getJointPositionsGlobal(), bodyMasses, upperMass, uppers)
#        CM = yrp.getCM(controlModel.getJointPositionsGlobal(), bodyMasses, totalMass)
        CMreal = yrp.getCM(controlModel.getJointPositionsGlobal(), bodyMasses, totalMass)
        stf = controlModel.getJointPositionGlobal(stanceFoots[0])
        CMr = CM - stf
        
        diff_dCM = mm.projectionOnPlane(dCM-dCM_tar, (1,0,0), (0,0,1))
        diff_dCM_axis = np.cross((0,1,0), diff_dCM)
        rd_vec1[0] = diff_dCM; rd_vecori1[0] = CM_tar
        
        diff_CMr = mm.projectionOnPlane(CMr-CMr_tar, (1,0,0), (0,0,1))
#        rd_vec1[0] = diff_CMr; rd_vecori1[0] = stf_tar
        diff_CMr_axis = np.cross((0,1,0), diff_CMr)
        
        direction = mm.normalize2(mm.projectionOnPlane(dCM_tar, (1,0,0), (0,0,1)))
#        direction = mm.normalize2(mm.projectionOnPlane(dCM, (1,0,0), (0,0,1)))
        directionAxis = np.cross((0,1,0), direction)
        
        diff_dCM_sag, diff_dCM_cor = mm.projectionOnVector2(diff_dCM, direction)
#        rd_vec1[0] = diff_dCM_sag; rd_vecori1[0] = CM_tar
        diff_dCM_sag_axis = np.cross((0,1,0), diff_dCM_sag)
        diff_dCM_cor_axis = np.cross((0,1,0), diff_dCM_cor)
            
        diff_CMr_sag, diff_CMr_cor = mm.projectionOnVector2(diff_CMr, direction)
        diff_CMr_sag_axis = np.cross((0,1,0), diff_CMr_sag)
        diff_CMr_cor_axis = np.cross((0,1,0), diff_CMr_cor)
            
        t = (frame-curInterval[0])/float(curInterval[1]-curInterval[0])
        t_raw = t
        if t>1.: t=1.
        
        
        p_root = motion_stitch[frame].getJointPositionGlobal(0)
        R_root = motion_stitch[frame].getJointOrientationGlobal(0)

        motion_seg_orig.goToFrame(frame)
        motion_seg.goToFrame(frame)
        motion_stitch.goToFrame(frame)
        
        motion_debug1.append(motion_stitch[frame].copy())
        motion_debug1.goToFrame(frame)
        motion_debug2.append(motion_stitch[frame].copy())
        motion_debug2.goToFrame(frame)
        motion_debug3.append(motion_stitch[frame].copy())
        motion_debug3.goToFrame(frame)
        
        # paper implementation
        M_tc.append(motion_stitch[prev_frame])
        M_tc.goToFrame(frame)
        P_hat.append(M_tc[frame].copy())
        P_hat.goToFrame(frame)
        
        p_temp = ym.JointPosture(skeleton)
        p_temp.rootPos = controlModel.getJointPositionGlobal(0)
        p_temp.setJointOrientationsLocal(controlModel.getJointOrientationsLocal())
        P.append(p_temp)
        P.goToFrame(frame)
        
        # stance foot stabilize
        motion_stf_stabilize.append(motion_stitch[frame].copy())
        motion_stf_stabilize.goToFrame(frame)
        if STANCE_FOOT_STABILIZE:
            for stanceFoot in stanceFoots:
                R_target_foot = motion_seg[frame].getJointOrientationGlobal(stanceFoot)
                R_current_foot = motion_stf_stabilize[frame].getJointOrientationGlobal(stanceFoot)
                motion_stf_stabilize[frame].setJointOrientationGlobal(stanceFoot, cm.slerp(R_current_foot, R_target_foot , stf_stabilize_func(t)))
#                R_target_foot = motion_seg[frame].getJointOrientationLocal(stanceFoot)
#                R_current_foot = motion_stf_stabilize[frame].getJointOrientationLocal(stanceFoot)
#                motion_stf_stabilize[frame].setJointOrientationLocal(stanceFoot, cm.slerp(R_current_foot, R_target_foot , stf_stabilize_func(t)))

        # match stance leg 
        motion_match_stl.append(motion_stf_stabilize[frame].copy())
        motion_match_stl.goToFrame(frame)
        if MATCH_STANCE_LEG:
            if curState!=yba.GaitState.STOP:
                for i in range(len(stanceLegs)):
                    stanceLeg = stanceLegs[i]
                    stanceFoot = stanceFoots[i]
                    
#                    # motion stance leg -> character stance leg as time goes
                    R_motion = motion_match_stl[frame].getJointOrientationGlobal(stanceLeg)
                    R_character = controlModel.getJointOrientationGlobal(stanceLeg)
                    motion_match_stl[frame].setJointOrientationGlobal(stanceLeg, cm.slerp(R_motion, R_character, match_stl_func(t)))

#                    t_y = match_stl_func_y(t)
#                    t_xz = match_stl_func(t)
#                    
#                    R_motion = motion_match_stl[frame].getJointOrientationGlobal(stanceLeg)
#                    R_character = controlModel.getJointOrientationGlobal(stanceLeg)
#                    R = np.dot(R_character, R_motion.T)
#                    R_y, R_xz = mm.projectRotation((0,1,0), R)
#                    motion_match_stl[frame].mulJointOrientationGlobal(stanceLeg, mm.scaleSO3(R_xz, t_xz))
#                    motion_match_stl[frame].mulJointOrientationGlobal(stanceLeg, mm.scaleSO3(R_y, t_y))

        # swing foot placement
        motion_swf_placement.append(motion_match_stl[frame].copy())
        motion_swf_placement.goToFrame(frame)
        if SWING_FOOT_PLACEMENT:
            t_swing_foot_placement = swf_placement_func(t);
            
            if extended[0]:
                R_swp_sag = prev_R_swp[0][0]
                R_swp_cor = prev_R_swp[0][1]
            else:
                R_swp_sag = mm.I_SO3(); R_swp_cor = mm.I_SO3()
                R_swp_cor = np.dot(R_swp_cor, mm.exp(diff_dCM_cor_axis * K_swp_vel_cor * -t_swing_foot_placement))
                if np.dot(direction, diff_CMr_sag) < 0:
                    R_swp_sag = np.dot(R_swp_sag, mm.exp(diff_dCM_sag_axis * K_swp_vel_sag * -t_swing_foot_placement))
                    R_swp_sag = np.dot(R_swp_sag, mm.exp(diff_CMr_sag_axis * K_swp_pos_sag * -t_swing_foot_placement))
                else:
                    R_swp_sag = np.dot(R_swp_sag, mm.exp(diff_dCM_sag_axis * K_swp_vel_sag_faster * -t_swing_foot_placement))
                    R_swp_sag = np.dot(R_swp_sag, mm.exp(diff_CMr_sag_axis * K_swp_pos_sag_faster * -t_swing_foot_placement))
                R_swp_cor = np.dot(R_swp_cor, mm.exp(diff_CMr_cor_axis * K_swp_pos_cor * -t_swing_foot_placement))

            for i in range(len(swingLegs)):
                swingLeg = swingLegs[i]
                swingFoot = swingFoots[i] 
                
                # save swing foot global orientation
#                R_swf = motion_swf_placement[frame].getJointOrientationGlobal(swingFoot)
                
                # rotate swing leg
                motion_swf_placement[frame].mulJointOrientationGlobal(swingLeg, R_swp_sag)
                motion_swf_placement[frame].mulJointOrientationGlobal(swingLeg, R_swp_cor)
                
                # restore swing foot global orientation
#                motion_swf_placement[frame].setJointOrientationGlobal(swingFoot, R_swf)
                
                prev_R_swp[0] = (R_swp_sag, R_swp_cor)

        # swing foot height
        motion_swf_height.append(motion_swf_placement[frame].copy())
        motion_swf_height.goToFrame(frame)
        if SWING_FOOT_HEIGHT:
            for swingFoot in swingFoots:
                stanceFoot = stanceFoots[0]

                # save foot global orientation
                R_foot = motion_swf_height[frame].getJointOrientationGlobal(swingFoot)
                R_stance_foot = motion_swf_height[frame].getJointOrientationGlobal(stanceFoot)

                if OLD_SWING_HEIGHT:
                    height_tar = motion_swf_height[frame].getJointPositionGlobal(swingFoot)[1] - motion_swf_height[frame].getJointPositionGlobal(stanceFoot)[1]
                else:
                    height_tar = motion_swf_height[prev_frame].getJointPositionGlobal(swingFoot)[1] - groundHeight
                    d_height_tar = motion_swf_height.getJointVelocityGlobal(swingFoot, prev_frame)[1]
#                    height_tar += c_swf_mid_offset * swf_height_sine_func(t)
#                motion_debug1[frame] = motion_swf_height[frame].copy()

                # rotate
                motion_swf_height[frame].rotateByTarget(controlModel.getJointOrientationGlobal(0))
#                motion_debug2[frame] = motion_swf_height[frame].copy()
#                motion_debug2[frame].translateByTarget(controlModel.getJointPositionGlobal(0))

                if OLD_SWING_HEIGHT:
                    height_cur = motion_swf_height[frame].getJointPositionGlobal(swingFoot)[1] - motion_swf_height[frame].getJointPositionGlobal(stanceFoot)[1]
                else:
                    height_cur = controlModel.getJointPositionGlobal(swingFoot)[1] - halfFootHeight - c_swf_offset
                    d_height_cur = controlModel.getJointVelocityGlobal(swingFoot)[1]

                if OLD_SWING_HEIGHT:
                    offset_height = (height_tar - height_cur) * swf_height_func(t) * c5
                else:
                    offset_height = ((height_tar - height_cur) * c5
                                     + (d_height_tar - d_height_cur) * c6) * swf_height_func(t)

                offset_sine = c_swf_mid_offset * swf_height_sine_func(t)
#                offset_sine = 0.
                
                offset = 0.
                offset += offset_height
                offset += offset_sine

                if offset > 0.:
                    newPosition =  motion_swf_height[frame].getJointPositionGlobal(swingFoot)
                    newPosition[1] += offset
                    aik.ik_analytic(motion_swf_height[frame], swingFoot, newPosition)
                else:
                    if HIGHER_OFFSET:
                        newPosition =  motion_swf_height[frame].getJointPositionGlobal(stanceFoot)
                        newPosition[1] -= offset
                        aik.ik_analytic(motion_swf_height[frame], stanceFoot, newPosition)

                # return
#                motion_debug3[frame] = motion_swf_height[frame].copy()
#                motion_debug3[frame].translateByTarget(controlModel.getJointPositionGlobal(0))
                motion_swf_height[frame].rotateByTarget(R_root)
                
                # restore foot global orientation
                motion_swf_height[frame].setJointOrientationGlobal(swingFoot, R_foot)
                motion_swf_height[frame].setJointOrientationGlobal(stanceFoot, R_stance_foot)

                if plot!=None:
                    plot.addDataPoint('debug1', frame, offset_height)
                    plot.addDataPoint('debug2', frame, height_tar - height_cur)
#                    plot.addDataPoint('diff', frame, diff)


        # swing foot orientation
        motion_swf_orientation.append(motion_swf_height[frame].copy())
        motion_swf_orientation.goToFrame(frame)
        if SWING_FOOT_ORIENTATION:
            swf_orientation_func = yfg.concatenate([yfg.zero, yfg.hermite2nd, yfg.one], [.25, .75])
            for swingFoot in swingFoots:
                R_target_foot = motion_seg[curInterval[1]].getJointOrientationGlobal(swingFoot)
                R_current_foot = motion_swf_orientation[frame].getJointOrientationGlobal(swingFoot)
                motion_swf_orientation[frame].setJointOrientationGlobal(swingFoot, cm.slerp(R_current_foot, R_target_foot, swf_orientation_func(t)))
#    swf_stabilize_func = yfg.concatenate([yfg.hermite2nd, yfg.one], [c_taking_duration])
            # push orientation
#            for swingFoot in swingFoots:
#                R_target_foot = motion_seg[frame].getJointOrientationGlobal(swingFoot)
#                R_current_foot = motion_swf_orientation[frame].getJointOrientationGlobal(swingFoot)
#                motion_swf_orientation[frame].setJointOrientationGlobal(swingFoot, cm.slerp(R_current_foot, R_target_foot , swf_stabilize_func(t)))
            
        # stance foot push                
        motion_stf_push.append(motion_swf_orientation[frame].copy())
        motion_stf_push.goToFrame(frame)
        if STANCE_FOOT_PUSH:
            for swingFoot in swingFoots:
#                max_t = (maxStfPushFrame)/float(curInterval[1]-curInterval[0])
#                stf_push_func = yfg.concatenate([yfg.sine, yfg.zero], [max_t*2])
                stf_push_func = yfg.concatenate([yfg.sine, yfg.zero], [c_taking_duration*2])
                
                R_swp_sag = mm.I_SO3()
#                R_swp_sag = np.dot(R_swp_sag, mm.exp(diff_dCM_sag_axis * K_stp_vel * -stf_push_func(t)))
                
#                if step_length_cur[0] < step_length_tar[0]:
#                    ratio = step_length_cur[0] / step_length_tar[0]
#                    R_max = maxmaxStfPushFrame
#                    R_zero = 
                R_swp_sag = np.dot(R_swp_sag, mm.exp((step_length_tar[0] - step_length_cur[0])*step_axis[0] * K_stp_pos * -stf_push_func(t)))
                    
                motion_stf_push[frame].mulJointOrientationGlobal(swingFoot, R_swp_sag)
                
        # stance foot balancing 
        motion_stf_balancing.append(motion_stf_push[frame].copy())
        motion_stf_balancing.goToFrame(frame)
        if STANCE_FOOT_BALANCING:
            R_stb = mm.exp(diff_dCM_axis * K_stb_vel * stf_balancing_func(t))
            R_stb = np.dot(R_stb, mm.exp(diff_CMr_axis * K_stb_pos * stf_balancing_func(t)))
            for stanceFoot in stanceFoots:
                if frame < 5: continue
                motion_stf_balancing[frame].mulJointOrientationGlobal(stanceFoot, R_stb)
                    
        # control trajectory
        motion_control.append(motion_stf_balancing[frame].copy())
        motion_control.goToFrame(frame)
        
        #=======================================================================
        # tracking with inverse dynamics
        #=======================================================================
        th_r = motion_control.getDOFPositions(frame)
        th = controlModel.getDOFPositions()
        dth_r = motion_control.getDOFVelocities(frame)
        dth = controlModel.getDOFVelocities()
        ddth_r = motion_control.getDOFAccelerations(frame)
        ddth_des = yct.getDesiredDOFAccelerations(th_r, th, dth_r, dth, ddth_r, Kt, Dt)

        #=======================================================================
        # simulation
        #=======================================================================
        CP = mm.v3(0.,0.,0.)
        F = mm.v3(0.,0.,0.)
        avg_dCM[0] = mm.v3(0.,0.,0.)
        
        # external force rendering info
        del rd_forces[:]; del rd_force_points[:]
        for fi in forceInfos:
            if fi.startFrame <= frame and frame < fi.startFrame + fi.duration*(1/frameTime):
                rd_forces.append(fi.force)
                rd_force_points.append(controlModel.getBodyPositionGlobal(fi.targetBody)  + -mm.normalize2(fi.force)*.2)
                    
        for i in range(stepsPerFrame):
            
            bodyIDs, contactPositions, contactPositionLocals, contactForces = vpWorld.calcPenaltyForce(bodyIDsToCheck, mus, Ks, Ds)
            vpWorld.applyPenaltyForce(bodyIDs, contactPositionLocals, contactForces)
            
            # apply external force
            for fi in forceInfos:
                if fi.startFrame <= frame and frame < fi.startFrame + fi.duration*(1/frameTime):
                    controlModel.applyBodyForceGlobal(fi.targetBody, fi.force)
                                
            controlModel.setDOFAccelerations(ddth_des)
            controlModel.solveHybridDynamics()
            
#            # apply external force
#            for fi in forceInfos:
#                if fi.startFrame <= frame and frame < fi.startFrame + fi.duration*(1/frameTime):
#                    controlModel.applyBodyForceGlobal(fi.targetBody, fi.force)
            
            vpWorld.step()
#            yvu.align2D(controlModel)

            if len(contactForces) > 0:
                CP += yrp.getCP(contactPositions, contactForces)
                F += sum(contactForces)
            avg_dCM[0] += controlModel.getJointVelocityGlobal(0)
#            avg_dCM[0] += yrp.getCM(controlModel.getJointVelocitiesGlobal(), bodyMasses, upperMass, uppers)
#            avg_dCM[0] += yrp.getCM(controlModel.getJointVelocitiesGlobal(), bodyMasses, totalMass)

#            if len(stanceFoots)>0:
#                avg_stf_v[0] += controlModel.getJointVelocityGlobal(stanceFoots[0])
#                avg_stf_av[0] += controlModel.getJointAngVelocityGlobal(stanceFoots[0])
        
        CP /= stepsPerFrame
        F /= stepsPerFrame
        avg_dCM[0] /= stepsPerFrame
        
#        if len(stanceFoots)>0:
#            avg_stf_v[0] /= stepsPerFrame
#            avg_stf_av[0] /= stepsPerFrame
#            rd_vec1[0] = avg_stf_av[0]; rd_vec1[0][0] = 0.; rd_vec1[0][2] = 0.
#            rd_vecori1[0]= controlModel.getJointPositionGlobal(stanceFoots[0])

        #=======================================================================
        # segment editing
        #=======================================================================
        lastFrame = False
        
        if SEGMENT_EDITING:
            if curState==yba.GaitState.STOP:
                if frame == len(motion_seg)-1:
                    lastFrame = True
                    
            elif (curState==yba.GaitState.LSWING or curState==yba.GaitState.RSWING) and t>c_min_contact_time:
                swingID = lID if curState==yba.GaitState.LSWING else rID

                contact = False
                if swingID in bodyIDs:
                    minContactVel = 1000.
                    for i in range(len(bodyIDs)):
                        if bodyIDs[i]==swingID:
                            vel = controlModel.getBodyVelocityGlobal(swingID, contactPositionLocals[i])
                            vel[1] = 0
                            contactVel = mm.length(vel)
                            if contactVel < minContactVel: minContactVel = contactVel 
                    if minContactVel < c_min_contact_vel: contact = True
                
                extended[0] = False
                
                if contact:
#                    print frame, 'foot touch'
                    lastFrame = True
                    acc_offset[0] += frame - curInterval[1]
                    
                elif frame == len(motion_seg)-1:
                    print frame, 'extend frame', frame+1
                    
                    preserveJoints = []
#                    preserveJoints = [lFoot, rFoot]
#                    preserveJoints = [lFoot, rFoot, lKnee, rKnee]
#                    preserveJoints = [lFoot, rFoot, lKnee, rKnee, lUpLeg, rUpLeg]
                    stanceKnees = [rKnee] if curState==yba.GaitState.LSWING else [lKnee]   
                    preserveJoints = [stanceFoots[0], stanceKnees[0], stanceLegs[0]]
   
                    diff = 3
                    motion_seg_orig.extend([motion_seg_orig[-1]])
                    motion_seg.extend(ymt.extendByIntegration_root(motion_seg, 1, diff))
                    
                    motion_stitch.extend(ymt.extendByIntegration_constant(motion_stitch, 1, preserveJoints, diff))

#                    # extend for swing foot ground speed matching & swing foot height lower
##                    extendedPostures = ymt.extendByIntegration(motion_stitch, 1, preserveJoints, diff)
##                    extendedPostures = [motion_stitch[-1]] 
##
#                    extendFrameNum = frame - curInterval[1] + 1
#                    k = 1.-extendFrameNum/5.
#                    if k<0.: k=0.
#                    extendedPostures = ymt.extendByIntegrationAttenuation(motion_stitch, 1, preserveJoints, diff, k)
#
##                    if len(swingFoots)>0 and np.inner(dCM_tar, dCM)>0.:
##                        print frame, 'speed matching'
##                        R_swf = motion_stitch[-1].getJointOrientationGlobal(swingFoots[0])
##                        
##                        p_swf = motion_stitch[-1].getJointPositionGlobal(swingFoots[0])
##                        v_swf = motion_stitch.getJointVelocityGlobal(swingFoots[0], frame-diff, frame)
##                        a_swf = motion_stitch.getJointAccelerationGlobal(swingFoots[0], frame-diff, frame)
##                        p_swf += v_swf * (frameTime) + a_swf * (frameTime)*(frameTime)
##                        aik.ik_analytic(extendedPostures[0], swingFoots[0], p_swf)
##                        
##                        extendedPostures[0].setJointOrientationGlobal(swingFoots[0], R_swf)
#
#                    motion_stitch.extend(extendedPostures)
                    
                    extended[0] = True
        else:
            if frame == len(motion_seg)-1: lastFrame = True
                    
        if lastFrame:
            if segIndex < len(segments)-1:
                print '%d (%d): end of %dth seg (%s, %s)'%(frame, frame-curInterval[1],segIndex, yba.GaitState.text[curState], curInterval)
                if plot!=None: plot.addDataPoint('diff', frame, (frame-curInterval[1])*.01)
                
                if len(stanceFoots)>0 and len(swingFoots)>0:
#                    step_cur = controlModel.getJointPositionGlobal(swingFoots[0]) - controlModel.getJointPositionGlobal(stanceFoots[0])
#                    step_tar = motion_seg[curInterval[1]].getJointPositionGlobal(swingFoots[0]) - motion_seg[curInterval[1]].getJointPositionGlobal(stanceFoots[0])
                    step_cur = controlModel.getJointPositionGlobal(0) - controlModel.getJointPositionGlobal(stanceFoots[0])
                    step_tar = motion_seg[curInterval[1]].getJointPositionGlobal(0) - motion_seg[curInterval[1]].getJointPositionGlobal(stanceFoots[0])
                    
                    step_cur = mm.projectionOnPlane(step_cur, (1,0,0), (0,0,1))
                    step_tar = mm.projectionOnPlane(step_tar, (1,0,0), (0,0,1))
                    
                    step_cur_sag, step_cur_cor = mm.projectionOnVector2(step_cur, direction)
                    step_tar_sag, step_tar_cor = mm.projectionOnVector2(step_tar, direction)
                    
                    step_length_tar[0] = mm.length(step_tar_sag)
                    if np.inner(step_tar_sag, step_cur_sag) > 0:
                        step_length_cur[0] = mm.length(step_cur_sag)
                    else:
                        step_length_cur[0] = -mm.length(step_cur_sag)
                    
                    step_axis[0] = directionAxis
                    
#                    rd_vec1[0] = step_tar_sag
#                    rd_vecori1[0] = motion_seg[curInterval[1]].getJointPositionGlobal(stanceFoots[0])
#                    rd_vec2[0] = step_cur_sag
#                    rd_vecori2[0] = controlModel.getJointPositionGlobal(stanceFoots[0])

                seg_index[0] += 1
                curSeg = segments[seg_index[0]]
                stl_y_limit_num[0] = 0
                stl_xz_limit_num[0] = 0
                
                del motion_seg_orig[frame+1:]
                motion_seg_orig.extend(ymb.getAttachedNextMotion(curSeg, motion_seg_orig[-1], False, False))
                
                del motion_seg[frame+1:]
                del motion_stitch[frame+1:]
                transitionLength = len(curSeg)-1

#                motion_seg.extend(ymb.getAttachedNextMotion(curSeg, motion_seg[-1], False, False))
#                motion_stitch.extend(ymb.getStitchedNextMotion(curSeg, motion_control[-1], transitionLength, stitch_func, True, False))

                d = motion_seg[-1] - curSeg[0]
                d.rootPos[1] = 0.
                motion_seg.extend(ymb.getAttachedNextMotion(curSeg, d, True, False))
                d = motion_control[-1] - curSeg[0]
                d.rootPos[1] = 0.
                motion_stitch.extend(ymb.getStitchedNextMotion(curSeg, d, transitionLength, stitch_func, True, False))
                
#                motion_seg.extend(ymb.getAttachedNextMotion(curSeg, motion_seg[-1], False, True))
#                motion_stitch.extend(ymb.getStitchedNextMotion(curSeg, motion_control[-1], transitionLength, stitch_func, True, True))
            else:
                motion_seg_orig.append(motion_seg_orig[-1])
                motion_seg.append(motion_seg[-1])
                motion_stitch.append(motion_control[-1])
                
                
        # rendering
        motionModel.update(motion_ori[frame])
#        motionModel.update(motion_seg[frame])
        
        rd_CP[0] = CP
        rd_CMP[0] = (CMreal[0] - (F[0]/F[1])*CMreal[1], 0, CMreal[2] - (F[2]/F[1])*CMreal[1])
        
        if plot!=None:
            plot.addDataPoint('zero', frame, 0)
            plot.updatePoints()
        
        
    viewer.setSimulateCallback(simulateCallback)
    
    if MULTI_VIEWER:
        viewer.startTimer(frameTime / 1.4)
    else:
        viewer.startTimer(frameTime * .1)
    viewer.show()
    
    Fl.run()