Exemplo n.º 1
0
def make_whisker(dim, q0, L, rbase=100e-6, taper=1.0/15, damping_ratio=None,
        rho=1.0, E=3.3e9):
    """ 
    Assembles the whisker based on material properties and initial 
    configuration. The default material and geometric properties from 
    elastica2d are used by default. 
    """
    assert dim in [2,3], "dimension must be 2 or 3"    
    print 19*'-'+'BUILD WHISKER (%dd)'%dim+19*'-'

    print 'Getting parameters...',
    if dim==2: N = len(q0)-2
    else: N = (len(q0)-4)/2
    I = calc_inertia(N, rbase, taper)
    K = E*I/L
    M = calc_mass(L, N, rho, rbase, taper)
    if damping_ratio<0:
        damping_ratio = np.append([1.0], get_interp_damping(L,N))
    C = calc_damping(N, K, M, L, damping_ratio)
    parameters = {'L': L, 'k': K[:-1], 'c': C, 'm': M, 'N':N}
    print 'done'

    print 'Building system...',
    if dim==2:
        whisker = Whisker2D(parameters)
        whisker.reference_shape = q0
        peg_frames = [ty('py', kinematic=True),
                      [tz('pz', kinematic=True, name='peg_frame')]]
    else:
        whisker = Whisker3D(parameters, q0)
        peg_frames = [tx('px', kinematic=True), [ty('py', kinematic=True),
                      [tz('pz', kinematic=True, name='peg_frame')]]]
    whisker.world_frame.import_frames(peg_frames)
    print 'done'
    return whisker
Exemplo n.º 2
0
    def whisker_frames(self, curvature, base_pos, base_rot):
        """ Creates a list of frames that define the whisker. """
        if curvature is None:
            ref_angles = np.zeros(self.num_links)
        else:
            ref_angles = get_angles_from_curvature(self.lengths, curvature)

        frames = []
        for j in reversed(range(1, self.num_links)):
            frames = [tx(self.lengths[j], name='Link-%d' %j), frames]
            frames = [rz('theta-%d_z' %j), frames]
            frames = [ry('theta-%d_y' %j), frames]
            #frames = [rx('theta-%d_x' %j), frames]
            frames = [rz(-ref_angles[j]), frames]
        frames = [tx(self.lengths[0], name='Link-0'), frames]
        frames = [rz('theta-0_z', name='Moving Base Point'), frames]
        frames = [ry('theta-0_y'), frames]
        frames = [rx('theta-0_x'), frames]
        frames = [tz('z'), [ty('y'), [tx('x'), frames]]]

        (X, Y, Z)          = base_pos
        (theta, phi, zeta) = base_rot

        # Rotate to the correct position.
        frames = [rz(theta), [ry(phi), [rx(zeta), frames]]]

        # Place the whisker at the correct spot on the mystacial pad and add an angle
        #   that drives the whisking motion.
        frames = [tx(X), [ty(Y),[ tz(Z, name='Base Point'),
                 [rz('Driving Angle', name="Driving Angle"), frames]]]]

        frames = [ rz(0.0, name='Head'), frames]

        return frames
Exemplo n.º 3
0
 def point_mass_frames(self, num_links, masses):
     frames = [tx('x_base'), [ty('y_base'), [tz('z_base', name='Base Point')]] ]
     for j in range(num_links):
         frames += [tx('x-%d' %j), [ty('y-%d' %j), [tz('z-%d' %j,
             mass=masses[j], name='Link-%d' %j)]] ]
     frames += [rz(0.0, name='Head')]    
     return frames
Exemplo n.º 4
0
def make_skeleton(dimensions={}, joints={}):
    dim = fill_dimensions(dimensions)
    joints = fill_joints(joints)

    frames = [
        tx(joints['torso_tx']), [ty(joints['torso_ty']), [tz(joints['torso_tz']), [
            rz(joints['torso_rz']), [ ry(joints['torso_ry']), [
                rx(joints['torso_rx'], name='pelvis',  mass=dim['pelvis_mass']), [
                    tx(-dim['lhip_width'], name='lhip'), [
                        rz(joints['lhip_rz']), [ry(joints['lhip_ry']), [rx(joints['lhip_rx'], name='lfemur'), [
                            tz(-dim['lfemur_length']/2, name='lfemur_mass', mass=dim['femur_mass']),
                            tz(-dim['lfemur_length'], name='lfemur_end'), [
                                rx(joints['lknee_rx'], name='ltibia'), [
                                    tz(-dim['ltibia_length']/2, name='ltibia_mass', mass=dim['tibia_mass']),
                                    tz(-dim['ltibia_length'], name='ltibia_end'), [
                                        rz(joints['lfoot_rz']), [ry(joints['lfoot_ry']), [
                                            rx(joints['lfoot_rx'], name='lfoot'), [
                                                ty(dim['lfoot_length'], name='lfoot_end')]]]]]]]]]],
                    tx(dim['rhip_width'], name='rhip'), [
                        rz(joints['rhip_rz']), [ry(joints['rhip_ry']), [rx(joints['rhip_rx'], name='rfemur'), [
                            tz(-dim['rfemur_length']/2, name='rfemur_mass', mass=dim['femur_mass']), 
                                tz(-dim['rfemur_length'], name='rfemur_end'), [
                                    rx(joints['rknee_rx'], name='rtibia'), [
                                        tz(-dim['rtibia_length']/2, name='rtibia_mass', mass=dim['tibia_mass']), 
                                    tz(-dim['rtibia_length'], name='rtibia_end'), [
                                        rz(joints['rfoot_rz']), [ry(joints['rfoot_ry']), [
                                            rx(joints['rfoot_rx'], name='rfoot'), [
                                                ty(dim['rfoot_length'], name='rfoot_end')]]]]]]]]]],
                    tz(dim['upper_torso_length'], name='spine_top'), [
                        tz(dim['neck_length'], name='neck'), [
                            rz(joints['neck_rz']), [ry(joints['neck_ry']), [
                                rx(joints['neck_rz'], name='neck_joint'), [
                                    tz(dim['lower_head_length'], name='head'), [
                                        tz(dim['upper_head_length'], name='head_center', mass=dim['head_mass']), [
                                            tz(dim['final_head_length'], name='head_end')]]]]]],
                        tx(-dim['lshoulder_width'], name='lshoulder'), [
                            rz(joints['lshoulder_rz']), [ry(joints['lshoulder_ry']), [
                                rx(joints['lshoulder_rx'], name='lhumerus'), [
                                    tz(-dim['lhumerus_length']/2, name='lhumerus_mass', mass=dim['humerus_mass']), 
                                    tz(-dim['lhumerus_length'], name='lhumerus_end'), [
                                        rx(joints['lelbow_rx'], name='lradius'), [
                                            tz(-dim['lradius_length']/2, name='lradius_mass', mass=dim['radius_mass']), 
                                            tz(-dim['lradius_length'], name='lradius_end'), [
                                                rz(joints['lhand_rz']), [ry(joints['lhand_ry']), [
                                                    rx(joints['lhand_rx'], name='lhand'), [
                                                        tz(-dim['lhand_length'], name='lhand_end')]]]]]]]]]],
                        tx(dim['rshoulder_width'], name='rshoulder'), [
                            rz(joints['rshoulder_rz']), [ry(joints['rshoulder_ry']), [
                                rx(joints['rshoulder_rx'], name='rhumerus'), [
                                    tz(-dim['rhumerus_length']/2, name='rhumerus_mass', mass=dim['humerus_mass']), 
                                    tz(-dim['rhumerus_length'], name='rhumerus_end'), [
                                        rx(joints['relbow_rx'], name='rradius'), [
                                            tz(-dim['rradius_length']/2, name='rradius_mass', mass=dim['radius_mass']), 
                                            tz(-dim['rradius_length'], name='rradius_end'), [
                                                rz(joints['rhand_rz']), [ry(joints['rhand_ry']), [
                                                    rx(joints['rhand_rx'], name='rhand'), [
                                                        tz(-dim['rhand_length'], name='rhand_end')]]]]]]]]]]
                    ]]]]]]]]
    return frames
Exemplo n.º 5
0
 def whisker_frames(self, L):
     """Creates a list of frames that define the whisker."""
     frames = []
     for j in reversed(range(1, self.num_links)):
         frames = [ty(L, name='Link-%d' %j), frames]
         frames = [rx('theta-%d' %j, name='f%d' %j), frames]
         frames = [rx('curvature-%d' %j, kinematic=True), frames]
     frames = [ty(L, name='Link-0'), frames]
     frames = [tz('z'), [ty('y', name='Base_Point'), frames]]
     frames = [rx('theta-0', name='f0'), frames]
     frames = [tz('z0', kinematic=True), [ty('y0', kinematic=True), frames]]
     frames = [rx('curvature-0', kinematic=True), frames]
     return frames
Exemplo n.º 6
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 def point_mass_frames(self, num_links, masses):
     frames = [
         tx('x_base'), [ty('y_base'), [tz('z_base', name='Base Point')]]
     ]
     for j in range(num_links):
         frames += [
             tx('x-%d' % j),
             [
                 ty('y-%d' % j),
                 [tz('z-%d' % j, mass=masses[j], name='Link-%d' % j)]
             ]
         ]
     frames += [rz(0.0, name='Head')]
     return frames
Exemplo n.º 7
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def MassSystem2D():
    # define system:
    system = trep.System()

    frames = [
        tx('xm', name='x-mass'), [ty('ym', name='y-mass', mass=BALL_MASS)],
        ty(1, name='robot_plane'), [tx('xr', name='x-robot', kinematic=True)]
    ]
    system.import_frames(frames)
    trep.potentials.Gravity(system, (0, -g, 0))
    trep.forces.Damping(system, 0.05)

    # add string constraint as a kinematic configuration var
    trep.constraints.Distance(system, 'y-mass', 'x-robot', 'r')
    return system
def MassSystem2D():
    # define system:
    system = trep.System()

    frames = [
        tx('xm', name='x-mass'), [
            ty('ym', name='y-mass', mass=BALL_MASS) ],
        ty(1, name='robot_plane'), [
            tx('xr', name='x-robot', kinematic=True) ]]
    system.import_frames(frames)
    trep.potentials.Gravity(system, (0, -g, 0))
    trep.forces.Damping(system, 0.05)

    # add string constraint as a kinematic configuration var
    trep.constraints.Distance(system, 'y-mass', 'x-robot','r')
    return system
Exemplo n.º 9
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    def whisker_frames(self, curvature):
        """ Creates a list of frames that define the whisker. """
        if curvature is None:
            ref_angles = np.zeros(self.num_links)
        else:
            ref_angles = get_angles_from_curvature(self.lengths, curvature)

        frames = []
        for j in reversed(range(1, self.num_links)):
            frames = [ty(self.lengths[j], name='Link-%d' %j), frames]
            frames = [rx('theta-%d' %j), frames]
            frames = [rx(ref_angles[j]), frames]
        frames = [ty(self.lengths[0], name='Link-0'), frames]
        frames = [tz('z'), [ty('y', name='Base_Point'), frames]]
        frames = [rx('theta-0'), frames]
        frames = [rx(ref_angles[0]), frames]
        return frames
Exemplo n.º 10
0
 def whisker_frames(self):
     """Creates a list of frames that define the whisker."""
     x0, y0, z0, th_x0, th_y0, th_z0 = extract_angles(self._ref)
     L = self._link_length
     frames = []
     for j in reversed(range(1, self.num_links)):
         frames = [tx(L, name='Link-%d' %j), frames]
         frames = [rz('theta_z-%d' %j), [ry('theta_y-%d' %j), frames]]
         frames = [rz(th_z0[j]),[ry(th_y0[j]),frames]]
     frames = [tx(L, name='Link-0'), frames]
     frames = [tx('xb'), [ty('yb'), [tz('zb', name='Rotated_Base_Point'), 
                frames]]]
     frames = [rz('theta_z-0'), [ry('theta_y-0'), [rx('theta_x-0'),
                frames]]]
     frames = [rz(th_z0[0]),[ry(th_y0[0]), [rx(th_x0[0]), frames]]]    
     frames = [tx(x0), [ty(y0), [tz(z0, name='Base_Point'), frames]]]
     return frames
Exemplo n.º 11
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    def whisker_frames(self, curvature):
        """ Creates a list of frames that define the whisker. """
        if curvature is None:
            ref_angles = np.zeros(self.num_links)
        else:
            ref_angles = get_angles_from_curvature(self.lengths, curvature)

        frames = []
        for j in reversed(range(1, self.num_links)):
            frames = [ty(self.lengths[j], name='Link-%d' % j), frames]
            frames = [rx('theta-%d' % j), frames]
            frames = [rx(ref_angles[j]), frames]
        frames = [ty(self.lengths[0], name='Link-0'), frames]
        frames = [tz('z'), [ty('y', name='Base_Point'), frames]]
        frames = [rx('theta-0'), frames]
        frames = [rx(ref_angles[0]), frames]
        return frames
def build_system():
    system = trep.System()
    frames = [
        tx('xs', name='x-stylus', kinematic=True), [
            ty('ys', name='y-stylus', kinematic=True), [
                tz('zs', name='z-stylus', kinematic=True)]],
        tx('xm', name='x-mass'), [
            ty('ym', name='y-mass'), [
                tz('zm', name=MASSFRAME, mass=M)]]]
    system.import_frames(frames)#### adds children frame to the world frame system
    trep.constraints.Distance(system, MASSFRAME, 'z-stylus', L, name="Link") ###enforces constraint between between the mass frame and the end of the stylus
    
###use two PointOnPlane constraints to constrain point to a line

###trep.constraints.PointOnPlane(system, MASSFRAME, 'z-stylus', L, name="Link") ###enforces constraint between between the mass frame and the end of the stylus
    trep.potentials.Gravity(system, (0,0,-g))
    trep.forces.Damping(system, B)
    return system
    def create_system(self):
        # define system:
        system = trep.System()

        frames = [
            tx('xm', name='x-mass'), [
                ty('ym', name='y-mass'), [
                    tz('zm', name='z-mass', mass=self.mass) ]],
            ty(h0, name='robot_plane'), [
                tx('xr', name='x-robot', kinematic=True), [
                    tz('zr', name='z-robot', kinematic=True) ]]]
        system.import_frames(frames)
        trep.potentials.Gravity(system, (0, -g, 0))
        trep.forces.Damping(system, 0.05)

        # add string constraint as a kinematic configuration var
        trep.constraints.Distance(system, 'z-mass', 'z-robot','r')

        return system
Exemplo n.º 14
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    def whisker_frames(self, curvature, base_pos, base_rot):
        """ Creates a list of frames that define the whisker. """
        if curvature is None:
            ref_angles = np.zeros(self.num_links)
        else:
            ref_angles = get_angles_from_curvature(self.lengths, curvature)

        frames = []
        for j in reversed(range(1, self.num_links)):
            frames = [tx(self.lengths[j], name='Link-%d' % j), frames]
            frames = [rz('theta-%d_z' % j), frames]
            frames = [ry('theta-%d_y' % j), frames]
            #frames = [rx('theta-%d_x' %j), frames]
            frames = [rz(-ref_angles[j]), frames]
        frames = [tx(self.lengths[0], name='Link-0'), frames]
        frames = [rz('theta-0_z', name='Moving Base Point'), frames]
        frames = [ry('theta-0_y'), frames]
        frames = [rx('theta-0_x'), frames]
        frames = [tz('z'), [ty('y'), [tx('x'), frames]]]

        (X, Y, Z) = base_pos
        (theta, phi, zeta) = base_rot

        # Rotate to the correct position.
        frames = [rz(theta), [ry(phi), [rx(zeta), frames]]]

        # Place the whisker at the correct spot on the mystacial pad and add an angle
        #   that drives the whisking motion.
        frames = [
            tx(X),
            [
                ty(Y),
                [
                    tz(Z, name='Base Point'),
                    [rz('Driving Angle', name="Driving Angle"), frames]
                ]
            ]
        ]

        frames = [rz(0.0, name='Head'), frames]

        return frames
Exemplo n.º 15
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def build_system():
    sys = trep.System()
    frames = [
        ty('yc',name=CARTFRAME, mass=M), [ 
            rx('theta', name="pendulumShoulder"), [
                tz(L, name=MASSFRAME, mass=M)]]]
    sys.import_frames(frames)
    trep.potentials.Gravity(sys, (0,0,-g))
    trep.forces.Damping(sys, B)
    trep.forces.ConfigForce(sys,'yc','cart-force')
    return sys
Exemplo n.º 16
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def build_system(torque_force=False):
    sys = trep.System()
    frames = [
        tx('xs', name=XCARTFRAME, kinematic=True), [
            ty('yc',name=CARTFRAME, mass=M,kinematic=True), [ 
                rx('theta', name="Shoulder1"), [
                    ry('phi',name="shoulder2"),[
                        tz(L, name=MASSFRAME, mass=M)]]]]]
    sys.import_frames(frames)
    trep.potentials.Gravity(sys, (0,0,-g))
    trep.forces.Damping(sys, B)
    if torque_force:
        trep.forces.ConfigForce(sys, 'theta', 'theta-force')
    return sys
Exemplo n.º 17
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def build_system(torque_force=False):
    cart_mass = 10.0
    pendulum_length = 1.0
    pendulum_mass = 1.0

    system = trep.System()
    frames = [
        tx('x', name='Cart', mass=cart_mass), [
            rz('theta', name="PendulumBase"), [
                ty(-pendulum_length, name="Pendulum", mass=pendulum_mass)]]]
    system.import_frames(frames)
    trep.potentials.Gravity(system, (0, -9.8, 0))
    trep.forces.Damping(system, 0.01)
    trep.forces.ConfigForce(system, 'x', 'x-force')
    if torque_force:
        trep.forces.ConfigForce(system, 'theta', 'theta-force')
    return system
Exemplo n.º 18
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def build_system(torque_force=False):
    cart_mass = 10.0
    pendulum_length = 1.0
    pendulum_mass = 1.0

    system = trep.System()
    frames = [
        tx('x', name='Cart', mass=cart_mass), [
            rz('theta', name="PendulumBase"), [
                ty(-pendulum_length, name="Pendulum", mass=pendulum_mass)]]]
    system.import_frames(frames)
    trep.potentials.Gravity(system, (0, -9.8, 0))
    trep.forces.Damping(system, 0.01)
    trep.forces.ConfigForce(system, 'x', 'x-force')
    if torque_force:
        trep.forces.ConfigForce(system, 'theta', 'theta-force')
    return system
Exemplo n.º 19
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 def make_string_constraints(self):
     for name, hook_point in self.string_hooks.iteritems():
         info = {
             'name' : name,
             'x' : name + '-x',            # Name of X kinematic config variable
             'y' : name + '-y',            # Name of Y kinematic config variable
             'length' : name + '-length',  # Name of length kinematic config variable
             # Name of the frames connected by the strings
             'control_hook' : name + '_control',
             'hook' : hook_point
             }
         # Add frames from the control_hook
         self.string_plane.import_frames([
             tx(info['x'], kinematic=True), [
                 ty(info['y'], kinematic=True, name=info['control_hook'])
                 ]])
         trep.constraints.Distance(self, info['hook'],
                                   info['control_hook'], info['length'],
                                   name=name)
         self.string_constraints[name] = info
Exemplo n.º 20
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 def make_string_constraints(self):
     for name, hook_point in self.string_hooks.iteritems():
         info = {
             'name': name,
             'x': name + '-x',  # Name of X kinematic config variable
             'y': name + '-y',  # Name of Y kinematic config variable
             'length':
             name + '-length',  # Name of length kinematic config variable
             # Name of the frames connected by the strings
             'control_hook': name + '_control',
             'hook': hook_point
         }
         # Add frames from the control_hook
         self.string_plane.import_frames([
             tx(info['x'], kinematic=True),
             [ty(info['y'], kinematic=True, name=info['control_hook'])]
         ])
         trep.constraints.Distance(self,
                                   info['hook'],
                                   info['control_hook'],
                                   info['length'],
                                   name=name)
         self.string_constraints[name] = info
Exemplo n.º 21
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        if q1 == self.config and q2 == self.config:
            return self.k
        else:
            return 0.0

    def V_dqdqdq(self, q1, q2, q3):
        return 0.0

    
tf = 10.0
dt = 0.01

# Here we define the mechanical system
system = trep.System()
frames = [
    ty(3), # Provided as an angle reference
    rx("theta"), [ty(3, mass=1)]
    ]
system.import_frames(frames)
#trep.potentials.Gravity(system, (0, 0, -9.8))
PyConfigSpring(system, 'theta', x0=0.7, k=20)
trep.forces.Damping(system, 1.2)

# These are the initial conditions for the variational integrator.
q0 = [0]
q1 = [0]

# Now we create and initialize a variational integrator for the system.
mvi = trep.MidpointVI(system)
mvi.initialize_from_configs(0.0, q0, dt, q1)
Exemplo n.º 22
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D = 3.0 * 0.0254  # wheel diamater in meters
# transform from center of geometry of the cover out to the string hooks.  The
# base frame has x forward, y out the left side of the robot, and z out the top
# (all in the robot's pov).
cover_to_left_string = [-0.010, 0.039, 0.041]
cover_to_right_string = [-0.010, -0.039, 0.041]

################################################################################
# Now we are ready to define the system
################################################################################
system = trep.System()
frames = [
    ###### PUPPET ######
    tx('TorsoX'),
    [
        ty('TorsoY'),
        [
            tz('TorsoZ'),
            [
                rz('TorsoPsi'),
                [
                    ry('TorsoTheta'),
                    [
                        rx('TorsoPhi', name='Torso'),
                        [
                            tz(-torso_height_2 / 2, mass=torso_mass),
                            tx(-torso_width_1 / 2),
                            [tz(torso_height_3, name='RightShoulderHook')],
                            tx(torso_width_1 / 2),
                            [tz(torso_height_3, name='LeftShoulderHook')],
                            tz(torso_height_4, name='Head'),
Exemplo n.º 23
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d = 0.01 #m
dw = 0.1 #m
LEFTWHISK = "Left whisker"
RIGHTWHISK = "Right whisker"
Aw = math.pi/3
An = math.pi/3 #(math.pi/2.0)

q0= np.array([0,0,0]) #
dq0 = np.array([0,0,0])


system = trep.System()
frames = [#1
    rx('theta', name ="neck",kinematic=True),[#2
        tz(Hp, name = 'head', mass = MH),[#3
            ty(-d,name = "Lcheek"),[
                rx('phiL',name = LEFTWHISK, kinematic = True),[
                    ty(-dw, name = "Lwhisk", mass = MW)]],
            ty(d,name = "Rcheek"),[
                rx('phiR',name = RIGHTWHISK, kinematic = True),[
                    ty(dw, name = "Rwhisk", mass = MW)]]]]]
system.import_frames(frames)

trep.potentials.Gravity(system,(0,0,-g))
trep.forces.Damping(system,B)

print "configs",system.configs

def proj_func(x):
    x[0] = np.fmod(x[0]+np.pi, 2.0*np.pi)
    if(x[0] < 0):
Exemplo n.º 24
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# define initial config and velocity
q0 = np.array([0, np.pi])  # q = [x_cart, theta]
dq0 = np.array([0, 0])  # dq = [xdot, thetadot]

# define time parameters:
dt = 0.0167
tf = 10.0

# create system
system = trep.System()
# define frames
frames = [
    trep.tx("x_cart", name="CartFrame", mass=mc),
    [
        trep.rz("theta", name="PendulumBase"),
        [trep.ty(l, name="Pendulum", mass=m)]
    ]
]
# add frames to system
system.import_frames(frames)
# add gravity potential
trep.potentials.Gravity(system, (0, -g, 0))
# add a horizontal force on the cart
trep.forces.ConfigForce(system, "x_cart", "cart_force")

#############
# SAC STUFF #
#############


def proj_func(x):
Exemplo n.º 25
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        if q1 == self.config and q2 == self.config:
            return self.k
        else:
            return 0.0

    def V_dqdqdq(self, q1, q2, q3):
        return 0.0


tf = 10.0
dt = 0.01

# Here we define the mechanical system
system = trep.System()
frames = [
    ty(3),  # Provided as an angle reference
    rx("theta"),
    [ty(3, mass=1)]
]
system.import_frames(frames)
#trep.potentials.Gravity(system, (0, 0, -9.8))
PyConfigSpring(system, 'theta', x0=0.7, k=20)
trep.forces.Damping(system, 1.2)

# These are the initial conditions for the variational integrator.
q0 = [0]
q1 = [0]

# Now we create and initialize a variational integrator for the system.
mvi = trep.MidpointVI(system)
mvi.initialize_from_configs(0.0, q0, dt, q1)
Exemplo n.º 26
0
# This script simulates a damped pendulum with a single link.

import sys
import trep
from trep import tx,ty,tz,rx,ry,rz
import trep.constraints
import trep.visual as visual

tf = 10.0
dt = 0.01

# Here we define the mechanical system
system = trep.System()
frames = [
    ty(3), # Provided as an angle reference
    rx("theta"), [tz(-3, mass=1)]
    ]
system.import_frames(frames)
trep.potentials.Gravity(system, (0, 0, -9.8))
trep.forces.Damping(system, 1.2)

# These are the initial conditions for the variational integrator.
q0 = (0.23,)   # Note the comma, this is how you create a tuple with 
q1 = (0.24,)   # a single element

# Now we create and initialize a variational integrator for the system.
mvi = trep.MidpointVI(system)
mvi.initialize_from_configs(0.0, q0, dt, q1)

# This is the actual simulation loop.  We will store the results in
# two lists.
Exemplo n.º 27
0
    # This is our simulation loop.  We save the results in two lists.
    q = [mvi.q2]
    t = [mvi.t2]
    while mvi.t1 < tf:
        mvi.step(mvi.t2 + dt)
        q.append(mvi.q2)
        t.append(mvi.t2)

    return (t, q)


system = trep.System()
system.import_frames([
    rx('theta1'), [tz(2, mass=1, name='pend1')],
    ty(1), [rx('theta2'), [tz(2, mass=1, name='pend2')]]
])

trep.potentials.LinearSpring(system, 'pend1', 'pend2', k=20, x0=1)
trep.forces.LinearDamper(system, 'pend1', 'pend2', c=1)
trep.potentials.Gravity(system, name="Gravity")

system.q = [3, -3]

# Simulate
start = time.clock()
(t, q) = simulate_system(system)
finish = time.clock()

# Display
print "Simulation: dt=%f, tf=%f, runtime=%f s" % (dt, tf, finish - start)
Exemplo n.º 28
0
import trep.visual as visual

tf = 10.0
dt = 0.01


# Define the mechanical system
system = trep.System()
frames = [
    rx('J', name='J'), [
        tz(-0.5, name='I', mass=1),
        tz(-1), [
            rx('H', name='H'), [
                tz(-1, name='G', mass=1),
                tz(-2, name='O2')]]],
    ty(1.5), [
        rx('K', name='K'), [
            tz(-1, name='L', mass=1),
            tz(-2), [
                rx('M', name='M'), [
                    tz(-0.5, name='N', mass=1),
                    tz(-1.0, name='O')]]]],
    ty(-1.5), [
        rx('A', name='A'), [
            tz(-1, name='B', mass=1),
            tz(-2), [
                rx('C', name='C'), [
                    tz(-0.375, name='D', mass=1),
                    tz(-0.75), [
                        rx('E', name='E'), [
                            tz(-0.5, name='F', mass=1),
Exemplo n.º 29
0
# set mass, length, and gravity:
m = 1.0; l = 1.0; g = 9.8;

# set state and step conditions:
pk = 0.5 # discrete generalized momentum
qk = 0.2 # theta config
uk = 0.8 # input torque
dt = 0.1 # timestep

# create system
system = trep.System()
# define frames
frames = [
        trep.rz("theta_1", name="PendAngle"), [
            trep.ty(-l, name="PendMass", mass=m)]]
# add frames to system
system.import_frames(frames)
# add gravity potential
trep.potentials.Gravity(system, (0,-g,0))
# add a torque at the base
trep.forces.ConfigForce(system, "theta_1", "tau")

# create and initialize variational integrator
mvi = trep.MidpointVI(system)
mvi.initialize_from_state(0, np.array([qk]), np.array([pk]))

# take single step with VI:
mvi.step(mvi.t1+dt, np.array([uk])) # args are t2, u1

# calc derivatives of discrete Lagrangian:
Exemplo n.º 30
0
def make_skeleton(dimensions={}, joints={}):
    dim = fill_dimensions(dimensions)
    joints = fill_joints(joints)

    frames = [
        tx(joints['torso_tx']),
        [
            ty(joints['torso_ty']),
            [
                tz(joints['torso_tz']),
                [
                    rz(joints['torso_rz']),
                    [
                        ry(joints['torso_ry']),
                        [
                            rx(joints['torso_rx'],
                               name='pelvis',
                               mass=dim['pelvis_mass']),
                            [
                                tx(-dim['lhip_width'], name='lhip'),
                                [
                                    rz(joints['lhip_rz']),
                                    [
                                        ry(joints['lhip_ry']),
                                        [
                                            rx(joints['lhip_rx'],
                                               name='lfemur'),
                                            [
                                                tz(-dim['lfemur_length'] / 2,
                                                   name='lfemur_mass',
                                                   mass=dim['femur_mass']),
                                                tz(-dim['lfemur_length'],
                                                   name='lfemur_end'),
                                                [
                                                    rx(joints['lknee_rx'],
                                                       name='ltibia'),
                                                    [
                                                        tz(-dim['ltibia_length']
                                                           / 2,
                                                           name='ltibia_mass',
                                                           mass=dim[
                                                               'tibia_mass']),
                                                        tz(-dim[
                                                            'ltibia_length'],
                                                           name='ltibia_end'),
                                                        [
                                                            rz(joints[
                                                                'lfoot_rz']),
                                                            [
                                                                ry(joints[
                                                                    'lfoot_ry']
                                                                   ),
                                                                [
                                                                    rx(joints[
                                                                        'lfoot_rx'],
                                                                       name=
                                                                       'lfoot'
                                                                       ),
                                                                    [
                                                                        ty(dim[
                                                                            'lfoot_length'],
                                                                           name=
                                                                           'lfoot_end'
                                                                           )
                                                                    ]
                                                                ]
                                                            ]
                                                        ]
                                                    ]
                                                ]
                                            ]
                                        ]
                                    ]
                                ],
                                tx(dim['rhip_width'], name='rhip'),
                                [
                                    rz(joints['rhip_rz']),
                                    [
                                        ry(joints['rhip_ry']),
                                        [
                                            rx(joints['rhip_rx'],
                                               name='rfemur'),
                                            [
                                                tz(-dim['rfemur_length'] / 2,
                                                   name='rfemur_mass',
                                                   mass=dim['femur_mass']),
                                                tz(-dim['rfemur_length'],
                                                   name='rfemur_end'),
                                                [
                                                    rx(joints['rknee_rx'],
                                                       name='rtibia'),
                                                    [
                                                        tz(-dim['rtibia_length']
                                                           / 2,
                                                           name='rtibia_mass',
                                                           mass=dim[
                                                               'tibia_mass']),
                                                        tz(-dim[
                                                            'rtibia_length'],
                                                           name='rtibia_end'),
                                                        [
                                                            rz(joints[
                                                                'rfoot_rz']),
                                                            [
                                                                ry(joints[
                                                                    'rfoot_ry']
                                                                   ),
                                                                [
                                                                    rx(joints[
                                                                        'rfoot_rx'],
                                                                       name=
                                                                       'r_foot'
                                                                       ),
                                                                    [
                                                                        ty(dim[
                                                                            'rfoot_length'],
                                                                           name=
                                                                           'rfoot_end'
                                                                           )
                                                                    ]
                                                                ]
                                                            ]
                                                        ]
                                                    ]
                                                ]
                                            ]
                                        ]
                                    ]
                                ],
                                tz(dim['upper_torso_length'],
                                   name='spine_top'),
                                [
                                    tz(dim['neck_length'], name='neck'),
                                    [
                                        rz(joints['neck_rz']),
                                        [
                                            ry(joints['neck_ry']),
                                            [
                                                rx(joints['neck_rz'],
                                                   name='neck_joint'),
                                                [
                                                    tz(dim[
                                                        'lower_head_length'],
                                                       name='head'),
                                                    [
                                                        tz(dim[
                                                            'upper_head_length'],
                                                           name='head_center',
                                                           mass=dim[
                                                               'head_mass']),
                                                        [
                                                            tz(dim[
                                                                'final_head_length'],
                                                               name='head_end')
                                                        ]
                                                    ]
                                                ]
                                            ]
                                        ]
                                    ],
                                    tx(-dim['lshoulder_width'],
                                       name='lshoulder'),
                                    [
                                        rz(joints['lshoulder_rz']),
                                        [
                                            ry(joints['lshoulder_ry']),
                                            [
                                                rx(joints['lshoulder_rx'],
                                                   name='lhumerus'),
                                                [
                                                    tz(-dim['lhumerus_length']
                                                       / 2,
                                                       name='lhumerus_mass',
                                                       mass=dim['humerus_mass']
                                                       ),
                                                    tz(-dim['lhumerus_length'],
                                                       name='lhumerus_end'),
                                                    [
                                                        rx(joints['lelbow_rx'],
                                                           name='lradius'),
                                                        [
                                                            tz(-dim[
                                                                'lradius_length']
                                                               / 2,
                                                               name=
                                                               'lradius_mass',
                                                               mass=dim[
                                                                   'radius_mass']
                                                               ),
                                                            tz(-dim[
                                                                'lradius_length'],
                                                               name=
                                                               'lradius_end'),
                                                            [
                                                                rz(joints[
                                                                    'lhand_rz']
                                                                   ),
                                                                [
                                                                    ry(joints[
                                                                        'lhand_ry']
                                                                       ),
                                                                    [
                                                                        rx(joints[
                                                                            'lhand_rx'],
                                                                           name=
                                                                           'lhand'
                                                                           ),
                                                                        [
                                                                            tz(-dim[
                                                                                'lhand_length'],
                                                                               name
                                                                               ='lhand_end'
                                                                               )
                                                                        ]
                                                                    ]
                                                                ]
                                                            ]
                                                        ]
                                                    ]
                                                ]
                                            ]
                                        ]
                                    ],
                                    tx(dim['rshoulder_width'],
                                       name='rshoulder'),
                                    [
                                        rz(joints['rshoulder_rz']),
                                        [
                                            ry(joints['rshoulder_ry']),
                                            [
                                                rx(joints['rshoulder_rx'],
                                                   name='right_humerus'),
                                                [
                                                    tz(-dim['rhumerus_length']
                                                       / 2,
                                                       name='rhumerus_mass',
                                                       mass=dim['humerus_mass']
                                                       ),
                                                    tz(-dim['rhumerus_length'],
                                                       name='rhumerus_end'),
                                                    [
                                                        rx(joints['relbow_rx'],
                                                           name='rradius'),
                                                        [
                                                            tz(-dim[
                                                                'rradius_length']
                                                               / 2,
                                                               name=
                                                               'rradius_mass',
                                                               mass=dim[
                                                                   'radius_mass']
                                                               ),
                                                            tz(-dim[
                                                                'rradius_length'],
                                                               name=
                                                               'rradius_end'),
                                                            [
                                                                rz(joints[
                                                                    'rhand_rz']
                                                                   ),
                                                                [
                                                                    ry(joints[
                                                                        'rhand_ry']
                                                                       ),
                                                                    [
                                                                        rx(joints[
                                                                            'rhand_rx'],
                                                                           name=
                                                                           'right_hand'
                                                                           ),
                                                                        [
                                                                            tz(-dim[
                                                                                'rhand_length'],
                                                                               name
                                                                               ='right_hand_end'
                                                                               )
                                                                        ]
                                                                    ]
                                                                ]
                                                            ]
                                                        ]
                                                    ]
                                                ]
                                            ]
                                        ]
                                    ]
                                ]
                            ]
                        ]
                    ]
                ]
            ]
        ]
    ]
    return frames
Exemplo n.º 31
0
""" Not working because cosine surface not rewritten yet.
"""

import trep
from trep import ty, tz, rx
from trep.visual import *
import numpy as np

import trep_collisions as tc

# Create the system.
ball = trep.System()
ball.import_frames([ty('y'), [tz('z', mass=1.0)]])
trep.potentials.Gravity(ball)

# Create the surface.
surface = tc.surfaces.Cosine(ball, 1, 1)

# Initialize the integrator.
mvi = tc.CollisionMVI(ball, surface)

# Give the initial condition.
ball.get_config('z').q = 7.0
ball.get_config('y').q = 0.5
mvi.initialize_state(0.0, ball.q, tc.util.D2L2(mvi))

# Simulate.
tf = 5.0
dt = 0.01
(t, q, lam) = tc.simulate(mvi, tf, dt)
D = 3.0*0.0254 # wheel diamater in meters
# transform from center of geometry of the cover out to the string hooks.  The
# base frame has x forward, y out the left side of the robot, and z out the top
# (all in the robot's pov).
cover_to_left_string = [-0.010, 0.039, 0.041]
cover_to_right_string = [-0.010, -0.039, 0.041]



################################################################################
# Now we are ready to define the system
################################################################################
system = trep.System()
frames = [
    ###### PUPPET ######
    tx('TorsoX'), [ty('TorsoY'), [tz('TorsoZ'), [
        rz('TorsoPsi'), [ry('TorsoTheta'), [rx('TorsoPhi',name='Torso'), [
            tz(-torso_height_2/2, mass=torso_mass),
            tx(-torso_width_1/2), [tz(torso_height_3, name='RightShoulderHook')],
            tx( torso_width_1/2), [tz(torso_height_3, name= 'LeftShoulderHook')],
            tz(torso_height_4, name='Head'), [tz(head_length/2, mass=head_mass)],
            # Define the left arm
            tx(torso_width/2), [tz(torso_height_1), [
                rz('LShoulderPsi'), [ry('LShoulderTheta'), [rx('LShoulderPhi', name='LeftShoulder'), [
                    tz(-humerus_length/2, name='LeftHumerus', mass=humerus_mass),
                    tz(-humerus_length), [
                        rx('LElbowPhi', name='LeftElbow'), [
                            tz(-radius_length/2, name='LeftRadius', mass=radius_mass),
                            tz(-radius_length), [
                                tz(-hand_length/2, mass=hand_mass),
                                tz(-hand_length, name='LeftFinger')]]]]]]]],
Exemplo n.º 33
0
    # This is our simulation loop.  We save the results in two lists.
    q = [mvi.q2]
    t = [mvi.t2]
    while mvi.t1 < tf:
        mvi.step(mvi.t2+dt)
        q.append(mvi.q2)
        t.append(mvi.t2)

    return (t,q)

system = trep.System()
system.import_frames([
    rx('theta1'), [
        tz(2, mass=1, name='pend1')
        ],
    ty(1), [
        rx('theta2'), [
            tz(2, mass=1, name='pend2')
            ]]
    ])

trep.potentials.LinearSpring(system, 'pend1', 'pend2', k=20, x0=1)
trep.forces.LinearDamper(system, 'pend1', 'pend2', c=1)
trep.potentials.Gravity(system, name="Gravity")

system.q = [3,-3]

# Simulate
start = time.clock()
(t, q) = simulate_system(system)
finish = time.clock()
Exemplo n.º 34
0
dt = 0.01
tf = 10.0
# Set up the system frames
system = trep.System()
system.import_frames([
    # Define the 3 Center Links
    rx('theta1', kinematic=True),[
        tz(-0.75, name='pend1'),[
            rx('theta2'),[
                tz(-0.75, name='pend2'),[
                    rx('theta3'),[
                        tz(-0.5, name='legConnection'),[
                            tz(-0.5, mass=1, name='COMLeg'),[
                                tz(-1, name='pend3')]]]]]]],
    # Define the 2 Right Links
    ty(1), [
        rx('theta4', kinematic=True),[
            tz(-0.5, mass=1, name='COM4'),[
                tz(-0.5),[
                    rx('theta5'),[
                        tz(-1, name='pend5')]]]]],
    # Define the 2 Left Links
    ty(-1), [
        rx('theta6', kinematic=True),[
            tz(-0.5, mass=1, name='COM6'),[
                tz(-0.5, name='pend6'),[
                    rx('theta7'),[
                        tz(-1, name='pend7')
                    ]
                ]
            ]
Exemplo n.º 35
0
             tz(-0.7, name='pend2'),
             [
                 rx('theta3'),
                 [
                     tz(-0.5, name='legConnection'),
                     [
                         tz(-0.5, mass=1, name='COMLeg'),
                         [tz(-1, name='pend3')]
                     ]
                 ]
             ]
         ]
     ]
 ],
 # Define the 2 Right Links
 ty(1),
 [
     rx('theta4', kinematic=True),
     [
         tz(-0.5, mass=1, name='COM4'),
         [tz(-0.5), [rx('theta5'), [tz(-1, name='pend5')]]]
     ]
 ],
 # Define the 2 Left Links
 ty(-1),
 [
     rx('theta6', kinematic=True),
     [
         tz(-0.5, mass=1, name='COM6'),
         [tz(-0.5, name='pend6'), [rx('theta7'), [tz(-1, name='pend7')]]]
     ]
Exemplo n.º 36
0
             tz(-L4, name='pend2'),
             [
                 rx('theta3'),
                 [
                     tz(-L7, name='legConnection'),
                     [
                         tz(-(((L7 + L8) / 2) - L7), mass=1, name='COMLeg'),
                         [tz(-((L7 + L8) / 2), name='pend3')]
                     ]
                 ]
             ]
         ]
     ]
 ],
 # Define the 2 Right Links
 ty(B1x),
 [
     tz(B1y),
     [
         rx('theta4'),
         [
             tz(-L5 / 2, mass=1, name='COM4'),
             [tz(-L5 / 2), [rx('theta5'), [tz(-L6, name='pend5')]]]
         ]
     ]
 ],
 # Define the 2 Left Links
 ty(-B2x),
 [
     tz(B2y),
     [
Exemplo n.º 37
0
 def make_frames(self, m, a):
     return [ty('y'), [tz('z', mass=0.2*m, name='center'), 
             [rx('theta', mass=(0, m*a**2/6, 0, 0)), 
              [rx(0.0), [tz(a, mass=0.2*m)],
               rx(np.radians(120)), [tz(a, mass=0.2*m)],
               rx(np.radians(240)), [tz(a, mass=0.2*m)]]]]]
Exemplo n.º 38
0
             rx('center_theta1'),
             [
                 tz(-0.0856, name='center_link2'),
                 [
                     rx('center_theta2'),
                     [
                         tz(-0.0691, mass=0, name='center_attach'),
                         [tz(-0.1016, name='foot', mass=0)]
                     ]
                 ]
             ]
         ]
     ]
 ],
 # right links
 ty(0.0573),
 [
     tz(-0.0918),
     [
         rx('motor2', name='motor2'),
         [
             tz(-0.0657, name='right_link'),
             [rx('right_theta'), [tz(-0.1517, name='right_attach')]]
         ]
     ]
 ],
 # left links
 ty(-0.0573),
 [
     tz(-0.0918),
     [
Exemplo n.º 39
0
import numpy as np
from numpy import matrix, array
import scipy
from scipy.integrate import odeint

import trep.visual as visual

# Define the length of the simulation and the time step.
tf = 10.0
dt = 0.01

system = trep.System()
frames = [
    tx('TorsoX'),
    [
        ty('TorsoY'),
        [
            tz('TorsoZ'),
            [
                rz('TorsoPsi'),
                [
                    ry('TorsoTheta'),
                    [
                        rx('TorsoPhi', name='Torso'),
                        [
                            tz(-1.5, mass=50),
                            tx(-1.011),
                            [tz(0.658, name='Right Torso Hook')],
                            tx(1.011),
                            [tz(0.658, name='Left Torso Hook')],
                            tz(0.9, name='Head'),
Exemplo n.º 40
0
# This is a basic humanoid puppet with a fixed head.  It has no
# inputs.  

import sys
import trep
from trep import tx, ty, tz, rx, ry, rz
import trep.visual as visual

# Set the length of simulation and the time step.
tf = 10.0
dt = 0.01

# Define the puppet's mechanical structure
system = trep.System()
frames = [
    tx('TorsoX'), [ty('TorsoY'), [tz('TorsoZ'), [
        rz('TorsoPsi'), [ry('TorsoTheta'), [rx('TorsoPhi',name='Torso'), [
            tz(-1.5, mass=50),
            tx(-1.011), [tz(0.658, name='Right Torso Hook')],
            tx( 1.011), [tz(0.658, name= 'Left Torso Hook')],
            tz(0.9, name='Head'), [tz(0.5, mass=(10,1,1,1))],
            # Define the left arm
            tx(1.3), [tz(0.4), [
                rz('LShoulderPsi'), [ry('LShoulderTheta'), [rx('LShoulderPhi', name='Left Shoulder'), [
                    tz(-0.95, name='Left Humerus', mass=(5,1,1,1)),
                    tz(-1.9), [
                        rx('LElbowTheta', name='Left Elbow'), [
                            tz(-1, name='Left Radius', mass=(4,1,1,1)),
                            tz(-2.001), [tx(0.14), [ty(-0.173, name='Left Finger')]]]]]]]]],
            # Define the right arm
            tx(-1.3), [tz(0.4), [
Exemplo n.º 41
0
import numpy as np
import trep

# set mass, length, and gravity:
m = 1.0; l = 1.0; g = 9.8;

# create system
system = trep.System()

# define frames
frames = [
    trep.rz("theta_1", name="Link1"), [
        trep.ty(-l, name="Mass1", mass=m), [
            trep.rz("theta_2", name="Link2"), [
                trep.ty(-l, name="Mass2", mass=m)]]],
    trep.tx(2*l, name="Link3Anchor")]

# add frames to system
system.import_frames(frames)

# add link 3 as a distance constraint
trep.constraints.Distance(system, "Mass2", "Link3Anchor", l)

# set gravity
trep.potentials.Gravity(system, (0, -g, 0))

# add and set torque input on theta_1
trep.forces.ConfigForce(system, "theta_1", "torque1")
system.get_input('torque1').u = 2.0

# solve for equilibrium configuration
Exemplo n.º 42
0
B=0.002 #damping

MH = 0.5 #kg
MUL =0.2 #kg
MLL = 0.1 #kg
UL = 0.25 #m
LL = 0.25 #m
HIP = "hip joint"
ULEG = "UpperLeg"
LLEG = "LowerLeg"



system = trep.System()
frames = [#1
    ty('yb', name ="body", mass = MH),[#2
        rx('theta1', name = HIP,),[#3
            tz(-UL ,name = ULEG, mass = MUL),[
                rx('theta2', name = 'knee'),[
                    tz(-LL, name = LLEG, mass = MLL)]]]]]
system.import_frames(frames)

trep.potentials.Gravity(system,(0,0,-g))
trep.forces.Damping(system,B)
trep.forces.ConfigForce(system, 'theta1','hip-torque')


print "configs",system.nu

q0= np.array([0,-np.pi/2,0]) #
dq0 = np.array([0,0,0])
Exemplo n.º 43
0
import trep.visual as visual

tf = 10.0
dt = 0.01

# Define the mechanical system
system = trep.System()
frames = [
    rx('J', name='J'),
    [
        tz(-0.5, name='I', mass=1),
        tz(-1),
        [rx('H', name='H'), [tz(-1, name='G', mass=1),
                             tz(-2, name='O2')]]
    ],
    ty(1.5),
    [
        rx('K', name='K'),
        [
            tz(-1, name='L', mass=1),
            tz(-2),
            [
                rx('M', name='M'),
                [tz(-0.5, name='N', mass=1),
                 tz(-1.0, name='O')]
            ]
        ]
    ],
    ty(-1.5),
    [
        rx('A', name='A'),
Exemplo n.º 44
0
# This script simulates a pendulum with a single link driven by
# a torsional spring instead of gravity.

import sys
import trep
from trep import tx,ty,tz,rx,ry,rz
import trep.constraints
import trep.visual as visual

tf = 10.0
dt = 0.01

# Here we define the mechanical system
system = trep.System()
frames = [
    ty(3), # Provided as an angle reference
    rx("theta"), [ty(3, mass=1)]
    ]
system.import_frames(frames)
trep.potentials.ConfigSpring(system, 'theta', k=20, q0=0.6)

# These are the initial conditions for the variational integrator.
q0 = (0,)   # Note the comma, this is how you create a tuple with 
q1 = (0,)   # a single element

# Now we create and initialize a variational integrator for the system.
mvi = trep.MidpointVI(system)
mvi.initialize_from_configs(0.0, q0, dt, q1)

# This is the actual simulation loop.  We will store the results in
# two lists.