q = (_g * 2.).flatten() # solve the QP : solved = False try: res = quadprog_solve_qp(P, q, G, h) solved = True except ValueError, e: print "Quadprog error : " print e.message raise ValueError( "Quadprog failed to solve QP for optimized limb-RRT end-effector trajectory, for try number " + str(numTry)) # build a bezier curve from the result of quadprog : vars = np.split(res, numVars) wps = bezier_com.computeEndEffectorConstantWaypoints( pData, t_middle) # one wp per column id_firstVar = 4 # depend on the flag defined above, but for end effector we always use this ones ... i = id_firstVar for x in vars: wps[:, i] = x i += 1 bezier_middle = bezier(wps, t_middle) # create concatenation with takeoff/landing curves = predef_curves.curves[::] curves[id_middle] = bezier_middle pBezier = PolyBezier(curves) if VERBOSE: print "time interval = ", time_interval[1] - time_interval[0] print "polybezier length = ", pBezier.max() ref_traj = trajectories.BezierTrajectory(pBezier, placement_init, placement_end, time_interval)
def generate_effector_trajectory_limb_rrt_optimized(cfg, time_interval, placement_init, placement_end, numTry, q_t=None, phase_previous=None, phase=None, phase_next=None, fullBody=None, eeName=None, viewer=None): if numTry == 0: return generateSmoothBezierTraj(cfg, time_interval, placement_init, placement_end) else: if q_t is None or phase_previous is None or phase is None or phase_next is None or not fullBody or not eeName: raise ValueError( "Cannot compute LimbRRTOptimizedTraj for try >= 1 without optionnal arguments" ) if cfg.EFF_T_PREDEF > 0: predef_curves = generatePredefBeziers(cfg, time_interval, placement_init, placement_end) else: predef_curves = generateSmoothBezierTraj(cfg, time_interval, placement_init, placement_end) id_middle = int(math.floor(predef_curves.num_curves() / 2.)) predef_middle = predef_curves.curve_at_index(id_middle).translation_curve() pos_init = predef_middle(predef_middle.min()) pos_end = predef_middle(predef_middle.max()) logger.warning("generateLimbRRTOptimizedTraj, try number %d", numTry) logger.info("bezier takeoff end : %s", pos_init) logger.info("bezier landing init : %s", pos_end) t_begin = predef_middle.min() t_end = predef_middle.max() t_middle = t_end - t_begin logger.info("t begin : %f", t_begin) logger.info("t end : %f", t_end) q_init = q_t(t_begin) q_end = q_t(t_end) global current_limbRRT_id # compute new limb-rrt path if needed: if not current_limbRRT_id or (numTry in recompute_rrt_at_tries): logger.warning("Compute new limb-rrt path ...") current_limbRRT_id = generateLimbRRTPath(q_init, q_end, phase_previous, phase, phase_next, fullBody) if viewer and cfg.DISPLAY_FEET_TRAJ and DISPLAY_RRT_PATH: from hpp.gepetto import PathPlayer pp = PathPlayer(viewer) pp.displayPath(current_limbRRT_id, jointName=fullBody.getLinkNames(eeName)[0]) # find weight and number of variable to use from the numTry : for offset in reversed(recompute_rrt_at_tries): if numTry >= offset: id = numTry - offset break logger.info("weights_var id = %d", id) if id >= len(weights_vars): raise ValueError( "Max number of try allow to find a collision-end effector trajectory reached." ) weight = weights_vars[id][0] varFlag = weights_vars[id][1] numVars = weights_vars[id][2] logger.warning("use weight %f with num free var = %d", weight, numVars) # compute constraints for the end effector trajectories : pData = bezier_com.ProblemData() pData.c0_ = predef_middle(predef_middle.min()) pData.dc0_ = predef_middle.derivate(predef_middle.min(), 1) pData.ddc0_ = predef_middle.derivate(predef_middle.min(), 2) pData.j0_ = predef_middle.derivate(predef_middle.min(), 3) pData.c1_ = predef_middle(predef_middle.max()) pData.dc1_ = predef_middle.derivate(predef_middle.max(), 1) pData.ddc1_ = predef_middle.derivate(predef_middle.max(), 2) pData.j1_ = predef_middle.derivate(predef_middle.max(), 3) pData.constraints_.flag_ = bezier_com.ConstraintFlag.INIT_POS \ | bezier_com.ConstraintFlag.INIT_VEL \ | bezier_com.ConstraintFlag.INIT_ACC \ | bezier_com.ConstraintFlag.END_ACC \ | bezier_com.ConstraintFlag.END_VEL \ | bezier_com.ConstraintFlag.END_POS \ | bezier_com.ConstraintFlag.INIT_JERK \ | bezier_com.ConstraintFlag.END_JERK \ | varFlag Constraints = bezier_com.computeEndEffectorConstraints(pData, t_middle) Cost_smooth = bezier_com.computeEndEffectorVelocityCost(pData, t_middle) Cost_distance = computeDistanceCostMatrices(fullBody, current_limbRRT_id, pData, t_middle, eeName) # formulate QP matrices : # _ prefix = previous notation (in bezier_com_traj) # min x' H x + 2 g' x # subject to A*x <= b _A = Constraints.A _b = Constraints.b _H = ((1. - weight) * Cost_smooth.A + weight * Cost_distance.A) _g = ((1. - weight) * Cost_smooth.b + weight * Cost_distance.b) logger.debug("A = %s", _A) logger.debug("b = %s", _b) logger.debug("H = %s", _H) logger.debug("h = %s", _g) """ _A = np.array(_A) _b = np.array(_b) _H = np.array(_H) _g = np.array(_g) """ # quadprog notation : #min (1/2)x' P x + q' x #subject to G x <= h #subject to C x = d G = _A h = _b.flatten() # remove the transpose when working with array P = _H * 2. q = (_g * 2.).flatten() logger.debug("G = %s", G) logger.debug("h = %s", h) logger.debug("P = %s", P) logger.debug("q = %s", q) logger.debug("Shapes : ") logger.debug("G : %s", G.shape) logger.debug("h : %s", h.shape) logger.debug("P : %s", P.shape) logger.debug("q : %s", q.shape) # solve the QP : solved = False try: res = quadprog_solve_qp(P, q, G, h) solved = True except ValueError as e: logger.error("Quadprog error : ", exc_info=e) raise ValueError( "Quadprog failed to solve QP for optimized limb-RRT end-effector trajectory, for try number " + str(numTry)) logger.info("Quadprog solved.") # build a bezier curve from the result of quadprog : vars = np.split(res, numVars) wps = bezier_com.computeEndEffectorConstantWaypoints( pData, t_middle) # one wp per column logger.debug("Constant waypoints computed.") id_firstVar = 4 # depend on the flag defined above, but for end effector we always use this ones ... i = id_firstVar for x in vars: wps[:, i] = np.array(x) logger.debug("waypoint number %d : %s", i, wps[:, i]) i += 1 logger.debug("Variables waypoints replaced by quadprog results.") bezier_middle = bezier(wps, t_begin, t_end) # create concatenation with takeoff/landing pBezier = piecewise_SE3() for ci in range(predef_curves.num_curves()): if ci == id_middle: pBezier.append( SE3Curve(bezier_middle, placement_init.rotation, placement_end.rotation)) else: pBezier.append(predef_curves.curve_at_index(ci)) logger.info("time interval = [%f ; %f]", pBezier.min(), pBezier.max()) return pBezier