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#ifndef BEZIER_COM_TRAJ_C0_DC0_DDC0_J0_J1_DDC1_DC1_C1_HH |
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#define BEZIER_COM_TRAJ_C0_DC0_DDC0_J0_J1_DDC1_DC1_C1_HH |
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/* |
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* Copyright 2018, LAAS-CNRS |
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* Author: Pierre Fernbach |
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*/ |
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#include <hpp/bezier-com-traj/data.hh> |
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namespace bezier_com_traj { |
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namespace c0_dc0_ddc0_j0_j1_ddc1_dc1_c1 { |
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static const ConstraintFlag flag = INIT_POS | INIT_VEL | INIT_ACC | END_ACC | |
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END_VEL | END_POS | INIT_JERK | END_JERK; |
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static const size_t DIM_VAR = 3; |
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static const size_t DIM_POINT = 3; |
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/// ### EQUATION FOR CONSTRAINTS ON INIT AND FINAL POSITION AND VELOCITY AND |
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/// ACCELERATION AND JERK (DEGREE = 8) |
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/// |
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/** |
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* @brief evaluateCurveAtTime compute the expression of the point on the curve |
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* at t, defined by the waypoint pi and one free waypoint (x) |
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* @param pi constant waypoints of the curve, assume pi[8] pi[1] pi[2] pi[3] x |
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* pi[4] pi[5] pi[6] pi[7] |
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* @param t param (normalized !) |
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* @return the expression of the waypoint such that wp.first . x + wp.second = |
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* point on curve |
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*/ |
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inline coefs_t evaluateCurveAtTime(const std::vector<point_t>& pi, double t) { |
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coefs_t wp; |
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const double t2 = t * t; |
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const double t3 = t2 * t; |
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const double t4 = t3 * t; |
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const double t5 = t4 * t; |
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const double t6 = t5 * t; |
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const double t7 = t6 * t; |
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const double t8 = t7 * t; |
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// equation found with sympy |
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wp.first = 70.0 * t8 - 280.0 * t7 + 420.0 * t6 - 280.0 * t5 + 70.0 * t4; |
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wp.second = 1.0 * pi[8] * t8 - 8.0 * pi[8] * t7 + 28.0 * pi[8] * t6 - |
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56.0 * pi[8] * t5 + 70.0 * pi[8] * t4 - 56.0 * pi[8] * t3 + |
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28.0 * pi[8] * t2 - 8.0 * pi[8] * t + 1.0 * pi[8] - |
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8.0 * pi[1] * t8 + 56.0 * pi[1] * t7 - 168.0 * pi[1] * t6 + |
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280.0 * pi[1] * t5 - 280.0 * pi[1] * t4 + 168.0 * pi[1] * t3 - |
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56.0 * pi[1] * t2 + 8.0 * pi[1] * t + 28.0 * pi[2] * t8 - |
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168.0 * pi[2] * t7 + 420.0 * pi[2] * t6 - 560.0 * pi[2] * t5 + |
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420.0 * pi[2] * t4 - 168.0 * pi[2] * t3 + 28.0 * pi[2] * t2 - |
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56.0 * pi[3] * pow(t, 8) + 280.0 * pi[3] * t7 - |
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560.0 * pi[3] * t6 + 560.0 * pi[3] * t5 - 280.0 * pi[3] * t4 + |
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56.0 * pi[3] * t3 - 56.0 * pi[5] * t8 + 168.0 * pi[5] * t7 - |
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168.0 * pi[5] * t6 + 56.0 * pi[5] * pow(t, 5) + |
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28.0 * pi[6] * t8 - 56.0 * pi[6] * t7 + 28.0 * pi[6] * t6 - |
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8.0 * pi[7] * t8 + 8.0 * pi[7] * t7 + 1.0 * pi[8] * t8; |
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return wp; |
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} |
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inline coefs_t evaluateVelocityCurveAtTime(const std::vector<point_t>& pi, |
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double T, double t) { |
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coefs_t wp; |
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const double alpha = 1. / (T); |
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const double t2 = t * t; |
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const double t3 = t2 * t; |
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const double t4 = t3 * t; |
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const double t5 = t4 * t; |
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const double t6 = t5 * t; |
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const double t7 = t6 * t; |
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// equation found with sympy |
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wp.first = |
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(560.0 * t7 - 1960.0 * t6 + 2520.0 * t5 - 1400.0 * t4 + 280.0 * t3) * |
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alpha; |
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wp.second = (8.0 * pi[8] * t7 - 56.0 * pi[8] * t6 + 168.0 * pi[8] * t5 - |
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280.0 * pi[8] * t4 + 280.0 * pi[8] * t3 - 168.0 * pi[8] * t2 + |
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56.0 * pi[8] * t - 8.0 * pi[8] - 64.0 * pi[1] * t7 + |
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392.0 * pi[1] * t6 - 1008.0 * pi[1] * t5 + 1400.0 * pi[1] * t4 - |
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1120.0 * pi[1] * t3 + 504.0 * pi[1] * t2 - 112.0 * pi[1] * t + |
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8.0 * pi[1] + 224.0 * pi[2] * t7 - 1176.0 * pi[2] * t6 + |
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2520.0 * pi[2] * t5 - 2800.0 * pi[2] * t4 + 1680.0 * pi[2] * t3 - |
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504.0 * pi[2] * t2 + 56.0 * pi[2] * t - 448.0 * pi[3] * t7 + |
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1960.0 * pi[3] * t6 - 3360.0 * pi[3] * t5 + 2800.0 * pi[3] * t4 - |
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1120.0 * pi[3] * t3 + 168.0 * pi[3] * t2 - 448.0 * pi[5] * t7 + |
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1176.0 * pi[5] * t6 - 1008.0 * pi[5] * t5 + 280.0 * pi[5] * t4 + |
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224.0 * pi[6] * t7 - 392.0 * pi[6] * t6 + 168.0 * pi[6] * t5 - |
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64.0 * pi[7] * t7 + 56.0 * pi[7] * t6 + 8.0 * pi[8] * t7) * |
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alpha; |
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return wp; |
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} |
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inline coefs_t evaluateAccelerationCurveAtTime(const std::vector<point_t>& pi, |
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double T, double t) { |
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coefs_t wp; |
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const double alpha = 1. / (T * T); |
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const double t2 = t * t; |
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const double t3 = t2 * t; |
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const double t4 = t3 * t; |
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const double t5 = t4 * t; |
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const double t6 = t5 * t; |
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// equation found with sympy |
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wp.first = |
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((3920.0 * t6 - 11760.0 * t5 + 12600.0 * t4 - 5600.0 * t3 + 840.0 * t2)) * |
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alpha; |
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wp.second = (56.0 * pi[8] * t6 - 336.0 * pi[8] * t5 + 840.0 * pi[8] * t4 - |
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1120.0 * pi[8] * t3 + 840.0 * pi[8] * t2 - 336.0 * pi[8] * t + |
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56.0 * pi[8] - 448.0 * pi[1] * t6 + 2352.0 * pi[1] * t5 - |
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5040.0 * pi[1] * t4 + 5600.0 * pi[1] * t3 - 3360.0 * pi[1] * t2 + |
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1008.0 * pi[1] * t - 112.0 * pi[1] + 1568.0 * pi[2] * t6 - |
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7056.0 * pi[2] * t5 + 12600.0 * pi[2] * t4 - |
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11200.0 * pi[2] * t3 + 5040.0 * pi[2] * t2 - 1008.0 * pi[2] * t + |
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56.0 * pi[2] - 3136.0 * pi[3] * t6 + 11760.0 * pi[3] * t5 - |
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16800.0 * pi[3] * t4 + 11200.0 * pi[3] * t3 - |
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3360.0 * pi[3] * t2 + 336.0 * pi[3] * t - 3136.0 * pi[5] * t6 + |
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7056.0 * pi[5] * t5 - 5040.0 * pi[5] * t4 + 1120.0 * pi[5] * t3 + |
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1568.0 * pi[6] * t6 - 2352.0 * pi[6] * t5 + 840.0 * pi[6] * t4 - |
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448.0 * pi[7] * t6 + 336.0 * pi[7] * t5 + 56.0 * pi[8] * t6) * |
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alpha; |
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return wp; |
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} |
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inline coefs_t evaluateJerkCurveAtTime(const std::vector<point_t>& pi, double T, |
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double t) { |
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coefs_t wp; |
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const double alpha = 1. / (T * T * T); |
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const double t2 = t * t; |
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const double t3 = t2 * t; |
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const double t4 = t3 * t; |
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const double t5 = t4 * t; |
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// equation found with sympy |
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wp.first = |
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(23520.0 * t5 - 58800.0 * t4 + 50400.0 * t3 - 16800.0 * t2 + 1680.0 * t) * |
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alpha; |
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wp.second = |
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1.0 * |
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(336.0 * pi[0] * t5 - 1680.0 * pi[0] * t4 + 3360.0 * pi[0] * t3 - |
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3360.0 * pi[0] * t2 + 1680.0 * pi[0] * t - 336.0 * pi[0] - |
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2688.0 * pi[1] * t5 + 11760.0 * pi[1] * t4 - 20160.0 * pi[1] * t3 + |
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16800.0 * pi[1] * t2 - 6720.0 * pi[1] * t + 1008.0 * pi[1] + |
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9408.0 * pi[2] * t5 - 35280.0 * pi[2] * t4 + 50400.0 * pi[2] * t3 - |
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33600.0 * pi[2] * t2 + 10080.0 * pi[2] * t - 1008.0 * pi[2] - |
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18816.0 * pi[3] * t5 + 58800.0 * pi[3] * t4 - 67200.0 * pi[3] * t3 + |
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33600.0 * pi[3] * t2 - 6720.0 * pi[3] * t + 336.0 * pi[3] - |
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18816.0 * pi[5] * t5 + 35280.0 * pi[5] * t4 - 20160.0 * pi[5] * t3 + |
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3360.0 * pi[5] * t2 + 9408.0 * pi[6] * t5 - 11760.0 * pi[6] * t4 + |
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3360.0 * pi[6] * t3 - 2688.0 * pi[7] * t5 + 1680.0 * pi[7] * t4 + |
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336.0 * pi[8] * t5) * |
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alpha; |
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return wp; |
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} |
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inline waypoint_t evaluateCurveWaypointAtTime(const std::vector<point_t>& pi, |
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double t) { |
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coefs_t coef = evaluateCurveAtTime(pi, t); |
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waypoint_t wp; |
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wp.first = Matrix3::Identity() * coef.first; |
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wp.second = coef.second; |
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return wp; |
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} |
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inline waypoint_t evaluateVelocityCurveWaypointAtTime( |
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const std::vector<point_t>& pi, double T, double t) { |
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coefs_t coef = evaluateVelocityCurveAtTime(pi, T, t); |
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waypoint_t wp; |
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wp.first = Matrix3::Identity() * coef.first; |
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wp.second = coef.second; |
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return wp; |
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} |
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inline waypoint_t evaluateAccelerationCurveWaypointAtTime( |
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const std::vector<point_t>& pi, double T, double t) { |
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coefs_t coef = evaluateAccelerationCurveAtTime(pi, T, t); |
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waypoint_t wp; |
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wp.first = Matrix3::Identity() * coef.first; |
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wp.second = coef.second; |
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return wp; |
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} |
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inline waypoint_t evaluateJerkCurveWaypointAtTime( |
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const std::vector<point_t>& pi, double T, double t) { |
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coefs_t coef = evaluateJerkCurveAtTime(pi, T, t); |
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waypoint_t wp; |
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wp.first = Matrix3::Identity() * coef.first; |
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wp.second = coef.second; |
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return wp; |
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} |
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inline std::vector<point_t> computeConstantWaypoints(const ProblemData& pData, |
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double T) { |
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// equation for constraint on initial and final position and velocity and |
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// initial acceleration(degree 5, 5 constant waypoint and one free (pi[3])) |
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// first, compute the constant waypoints that only depend on pData : |
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double n = 8.; |
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std::vector<point_t> pi; |
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pi.push_back(pData.c0_); |
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pi.push_back((pData.dc0_ * T / n) + pData.c0_); |
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pi.push_back((pData.ddc0_ * T * T / (n * (n - 1))) + |
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(2 * pData.dc0_ * T / n) + |
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pData.c0_); // * T because derivation make a T appear |
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pi.push_back((pData.j0_ * T * T * T / (n * (n - 1) * (n - 2))) + |
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(3 * pData.ddc0_ * T * T / (n * (n - 1))) + |
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(3 * pData.dc0_ * T / n) + pData.c0_); |
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pi.push_back(point_t::Zero()); |
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pi.push_back((-pData.j1_ * T * T * T / (n * (n - 1) * (n - 2))) + |
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(3 * pData.ddc1_ * T * T / (n * (n - 1))) - |
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(3 * pData.dc1_ * T / n) + pData.c1_); // * T ?? |
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pi.push_back((pData.ddc1_ * T * T / (n * (n - 1))) - |
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(2 * pData.dc1_ * T / n) + pData.c1_); // * T ?? |
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pi.push_back((-pData.dc1_ * T / n) + pData.c1_); // * T ? |
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pi.push_back(pData.c1_); |
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return pi; |
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} |
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inline bezier_wp_t::t_point_t computeWwaypoints(const ProblemData& pData, |
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double T) { |
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bezier_wp_t::t_point_t wps; |
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const int DIM_POINT = 6; |
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const int DIM_VAR = 3; |
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std::vector<point_t> pi = computeConstantWaypoints(pData, T); |
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std::vector<Matrix3> Cpi; |
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for (std::size_t i = 0; i < pi.size(); ++i) { |
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Cpi.push_back(skew(pi[i])); |
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} |
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const Vector3 g = pData.contacts_.front().contactPhase_->m_gravity; |
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const Matrix3 Cg = skew(g); |
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const double T2 = T * T; |
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const double alpha = 1 / (T2); |
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// equation of waypoints for curve w found with sympy |
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waypoint_t w0 = initwp(DIM_POINT, DIM_VAR); |
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w0.second.head<3>() = (30 * pi[0] - 60 * pi[1] + 30 * pi[2]) * alpha; |
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w0.second.tail<3>() = |
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1.0 * |
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(1.0 * Cg * T2 * pi[0] - 60.0 * Cpi[0] * pi[1] + 30.0 * Cpi[0] * pi[2]) * |
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alpha; |
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wps.push_back(w0); |
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waypoint_t w1 = initwp(DIM_POINT, DIM_VAR); |
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w1.first.block<3, 3>(0, 0) = 13.3333333333333 * alpha * Matrix3::Identity(); |
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w1.first.block<3, 3>(3, 0) = 13.3333333333333 * Cpi[0] * alpha; |
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w1.second.head<3>() = |
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1.0 * (16.6666666666667 * pi[0] - 20.0 * pi[1] - 10.0 * pi[2]) * alpha; |
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w1.second.tail<3>() = 1.0 * |
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(0.333333333333333 * Cg * T2 * pi[0] + |
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0.666666666666667 * Cg * T2 * pi[1] - |
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30.0 * Cpi[0] * pi[2] + 20.0 * Cpi[1] * pi[2]) * |
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alpha; |
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wps.push_back(w1); |
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waypoint_t w2 = initwp(DIM_POINT, DIM_VAR); |
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|
✗ |
w2.first.block<3, 3>(0, 0) = 6.66666666666667 * alpha * Matrix3::Identity(); |
| 244 |
|
✗ |
w2.first.block<3, 3>(3, 0) = |
| 245 |
|
✗ |
1.0 * (-13.3333333333333 * Cpi[0] + 20.0 * Cpi[1]) * alpha; |
| 246 |
|
✗ |
w2.second.head<3>() = |
| 247 |
|
✗ |
1.0 * (8.33333333333333 * pi[0] - 20.0 * pi[2] + 5.0 * pi[4]) * alpha; |
| 248 |
|
✗ |
w2.second.tail<3>() = |
| 249 |
|
✗ |
1.0 * |
| 250 |
|
✗ |
(0.0833333333333334 * Cg * T2 * pi[0] + 0.5 * Cg * T2 * pi[1] + |
| 251 |
|
✗ |
0.416666666666667 * Cg * T2 * pi[2] + 5.0 * Cpi[0] * pi[4] - |
| 252 |
|
✗ |
20.0 * Cpi[1] * pi[2]) * |
| 253 |
|
✗ |
alpha; |
| 254 |
|
✗ |
wps.push_back(w2); |
| 255 |
|
✗ |
waypoint_t w3 = initwp(DIM_POINT, DIM_VAR); |
| 256 |
|
✗ |
w3.first.block<3, 3>(0, 0) = -5.71428571428572 * alpha * Matrix3::Identity(); |
| 257 |
|
✗ |
w3.first.block<3, 3>(3, 0) = 1.0 * |
| 258 |
|
✗ |
(0.238095238095238 * Cg * T2 - 20.0 * Cpi[1] + |
| 259 |
|
✗ |
14.2857142857143 * Cpi[2]) * |
| 260 |
|
✗ |
alpha; |
| 261 |
|
✗ |
w3.second.head<3>() = 1.0 * |
| 262 |
|
✗ |
(3.57142857142857 * pi[0] + 7.14285714285714 * pi[1] - |
| 263 |
|
✗ |
14.2857142857143 * pi[2] + 7.85714285714286 * pi[4] + |
| 264 |
|
✗ |
1.42857142857143 * pi[5]) * |
| 265 |
|
✗ |
alpha; |
| 266 |
|
✗ |
w3.second.tail<3>() = |
| 267 |
|
✗ |
1.0 * |
| 268 |
|
✗ |
(0.0119047619047619 * Cg * T2 * pi[0] + |
| 269 |
|
✗ |
0.214285714285714 * Cg * T2 * pi[1] + |
| 270 |
|
✗ |
0.535714285714286 * Cg * T2 * pi[2] - 5.0 * Cpi[0] * pi[4] + |
| 271 |
|
✗ |
1.42857142857143 * Cpi[0] * pi[5] + 12.8571428571429 * Cpi[1] * pi[4]) * |
| 272 |
|
✗ |
alpha; |
| 273 |
|
✗ |
wps.push_back(w3); |
| 274 |
|
✗ |
waypoint_t w4 = initwp(DIM_POINT, DIM_VAR); |
| 275 |
|
✗ |
w4.first.block<3, 3>(0, 0) = -14.2857142857143 * alpha * Matrix3::Identity(); |
| 276 |
|
✗ |
w4.first.block<3, 3>(3, 0) = |
| 277 |
|
✗ |
1.0 * (0.476190476190476 * Cg * T2 - 14.2857142857143 * Cpi[2]) * alpha; |
| 278 |
|
✗ |
w4.second.head<3>() = 1.0 * |
| 279 |
|
✗ |
(1.19047619047619 * pi[0] + 7.14285714285714 * pi[1] - |
| 280 |
|
✗ |
3.57142857142857 * pi[2] + 5.0 * pi[4] + |
| 281 |
|
✗ |
4.28571428571429 * pi[5] + 0.238095238095238 * pi[6]) * |
| 282 |
|
✗ |
alpha; |
| 283 |
|
✗ |
w4.second.tail<3>() = |
| 284 |
|
✗ |
1.0 * |
| 285 |
|
✗ |
(0.0476190476190471 * Cg * T2 * pi[1] + |
| 286 |
|
✗ |
0.357142857142857 * Cg * T2 * pi[2] + |
| 287 |
|
✗ |
0.119047619047619 * Cg * T2 * pi[4] - 1.42857142857143 * Cpi[0] * pi[5] + |
| 288 |
|
✗ |
0.238095238095238 * Cpi[0] * pi[6] - 12.8571428571429 * Cpi[1] * pi[4] + |
| 289 |
|
✗ |
5.71428571428571 * Cpi[1] * pi[5] + 17.8571428571429 * Cpi[2] * pi[4]) * |
| 290 |
|
✗ |
alpha; |
| 291 |
|
✗ |
wps.push_back(w4); |
| 292 |
|
✗ |
waypoint_t w5 = initwp(DIM_POINT, DIM_VAR); |
| 293 |
|
✗ |
w5.first.block<3, 3>(0, 0) = -14.2857142857143 * alpha * Matrix3::Identity(); |
| 294 |
|
✗ |
w5.first.block<3, 3>(3, 0) = |
| 295 |
|
✗ |
1.0 * (0.476190476190476 * Cg * T2 - 14.2857142857143 * Cpi[4]) * alpha; |
| 296 |
|
✗ |
w5.second.head<3>() = 1.0 * |
| 297 |
|
✗ |
(0.238095238095238 * pi[0] + 4.28571428571429 * pi[1] + |
| 298 |
|
✗ |
5.0 * pi[2] - 3.57142857142857 * pi[4] + |
| 299 |
|
✗ |
7.14285714285714 * pi[5] + 1.19047619047619 * pi[6]) * |
| 300 |
|
✗ |
alpha; |
| 301 |
|
✗ |
w5.second.tail<3>() = |
| 302 |
|
✗ |
1.0 * |
| 303 |
|
✗ |
(+0.11904761904762 * Cg * T2 * pi[2] + |
| 304 |
|
✗ |
0.357142857142857 * Cg * T2 * pi[4] + |
| 305 |
|
✗ |
0.0476190476190476 * Cg * T2 * pi[5] - |
| 306 |
|
✗ |
0.238095238095238 * Cpi[0] * pi[6] - 5.71428571428572 * Cpi[1] * pi[5] + |
| 307 |
|
✗ |
1.42857142857143 * Cpi[1] * pi[6] - 17.8571428571429 * Cpi[2] * pi[4] + |
| 308 |
|
✗ |
12.8571428571429 * Cpi[2] * pi[5]) * |
| 309 |
|
✗ |
alpha; |
| 310 |
|
✗ |
wps.push_back(w5); |
| 311 |
|
✗ |
waypoint_t w6 = initwp(DIM_POINT, DIM_VAR); |
| 312 |
|
✗ |
w6.first.block<3, 3>(0, 0) = -5.71428571428571 * alpha * Matrix3::Identity(); |
| 313 |
|
✗ |
w6.first.block<3, 3>(3, 0) = 1.0 * |
| 314 |
|
✗ |
(0.238095238095238 * Cg * T2 + |
| 315 |
|
✗ |
14.2857142857143 * Cpi[4] - 20.0 * Cpi[5]) * |
| 316 |
|
✗ |
alpha; |
| 317 |
|
✗ |
w6.second.head<3>() = 1.0 * |
| 318 |
|
✗ |
(1.42857142857143 * pi[1] + 7.85714285714286 * pi[2] - |
| 319 |
|
✗ |
14.2857142857143 * pi[4] + 7.14285714285715 * pi[5] + |
| 320 |
|
✗ |
3.57142857142857 * pi[6]) * |
| 321 |
|
✗ |
alpha; |
| 322 |
|
✗ |
w6.second.tail<3>() = |
| 323 |
|
✗ |
1.0 * |
| 324 |
|
✗ |
(0.535714285714286 * Cg * T2 * pi[4] + |
| 325 |
|
✗ |
0.214285714285714 * Cg * T2 * pi[5] + |
| 326 |
|
✗ |
0.0119047619047619 * Cg * T2 * pi[6] - |
| 327 |
|
✗ |
1.42857142857143 * Cpi[1] * pi[6] - 12.8571428571429 * Cpi[2] * pi[5] + |
| 328 |
|
✗ |
5.0 * Cpi[2] * pi[6]) * |
| 329 |
|
✗ |
alpha; |
| 330 |
|
✗ |
wps.push_back(w6); |
| 331 |
|
✗ |
waypoint_t w7 = initwp(DIM_POINT, DIM_VAR); |
| 332 |
|
✗ |
w7.first.block<3, 3>(0, 0) = 6.66666666666667 * alpha * Matrix3::Identity(); |
| 333 |
|
✗ |
w7.first.block<3, 3>(3, 0) = |
| 334 |
|
✗ |
1.0 * (20.0 * Cpi[5] - 13.3333333333333 * Cpi[6]) * alpha; |
| 335 |
|
✗ |
w7.second.head<3>() = |
| 336 |
|
✗ |
1.0 * (5.0 * pi[2] - 20.0 * pi[4] + 8.33333333333333 * pi[6]) * alpha; |
| 337 |
|
✗ |
w7.second.tail<3>() = |
| 338 |
|
✗ |
1.0 * |
| 339 |
|
✗ |
(0.416666666666667 * Cg * T2 * pi[4] + 0.5 * Cg * T2 * pi[5] + |
| 340 |
|
✗ |
0.0833333333333333 * Cg * T2 * pi[6] - 5.0 * Cpi[2] * pi[6] + |
| 341 |
|
✗ |
20.0 * Cpi[4] * pi[5]) * |
| 342 |
|
✗ |
alpha; |
| 343 |
|
✗ |
wps.push_back(w7); |
| 344 |
|
✗ |
waypoint_t w8 = initwp(DIM_POINT, DIM_VAR); |
| 345 |
|
✗ |
w8.first.block<3, 3>(0, 0) = 13.3333333333333 * alpha * Matrix3::Identity(); |
| 346 |
|
✗ |
w8.first.block<3, 3>(3, 0) = 1.0 * (13.3333333333333 * Cpi[6]) * alpha; |
| 347 |
|
✗ |
w8.second.head<3>() = |
| 348 |
|
✗ |
1.0 * |
| 349 |
|
✗ |
(-9.99999999999999 * pi[4] - 20.0 * pi[5] + 16.6666666666667 * pi[6]) * |
| 350 |
|
✗ |
alpha; |
| 351 |
|
✗ |
w8.second.tail<3>() = 1.0 * |
| 352 |
|
✗ |
(0.666666666666667 * Cg * T2 * pi[5] + |
| 353 |
|
✗ |
0.333333333333333 * Cg * T2 * pi[6] - |
| 354 |
|
✗ |
20.0 * Cpi[4] * pi[5] + 30.0 * Cpi[4] * pi[6]) * |
| 355 |
|
✗ |
alpha; |
| 356 |
|
✗ |
wps.push_back(w8); |
| 357 |
|
✗ |
waypoint_t w9 = initwp(DIM_POINT, DIM_VAR); |
| 358 |
|
✗ |
w9.second.head<3>() = (30 * pi[4] - 60 * pi[5] + 30 * pi[6]) * alpha; |
| 359 |
|
✗ |
w9.second.tail<3>() = |
| 360 |
|
✗ |
1.0 * |
| 361 |
|
✗ |
(1.0 * Cg * T2 * pi[6] - 30.0 * Cpi[4] * pi[6] + 60.0 * Cpi[5] * pi[6]) * |
| 362 |
|
✗ |
alpha; |
| 363 |
|
✗ |
wps.push_back(w9); |
| 364 |
|
✗ |
return wps; |
| 365 |
|
|
} |
| 366 |
|
|
|
| 367 |
|
✗ |
std::vector<waypoint_t> computeVelocityWaypoints( |
| 368 |
|
|
const ProblemData& pData, const double T, |
| 369 |
|
|
std::vector<bezier_t::point_t> pi = std::vector<bezier_t::point_t>()) { |
| 370 |
|
✗ |
if (pi.size() == 0) pi = computeConstantWaypoints(pData, T); |
| 371 |
|
|
|
| 372 |
|
✗ |
std::vector<waypoint_t> wps; |
| 373 |
|
✗ |
assert(pi.size() == 9); |
| 374 |
|
|
|
| 375 |
|
✗ |
double alpha = 1. / (T); |
| 376 |
|
✗ |
waypoint_t w = initwp(DIM_POINT, DIM_VAR); |
| 377 |
|
|
// assign w0: |
| 378 |
|
✗ |
w.second = alpha * 8 * (-pi[0] + pi[1]); |
| 379 |
|
✗ |
wps.push_back(w); |
| 380 |
|
✗ |
w = initwp(DIM_POINT, DIM_VAR); |
| 381 |
|
|
// assign w1: |
| 382 |
|
✗ |
w.second = alpha * 8 * (-pi[1] + pi[2]); |
| 383 |
|
✗ |
wps.push_back(w); |
| 384 |
|
✗ |
w = initwp(DIM_POINT, DIM_VAR); |
| 385 |
|
|
// assign w2: |
| 386 |
|
✗ |
w.second = alpha * 8 * (-pi[2] + pi[3]); |
| 387 |
|
✗ |
wps.push_back(w); |
| 388 |
|
✗ |
w = initwp(DIM_POINT, DIM_VAR); |
| 389 |
|
|
// assign w3: |
| 390 |
|
✗ |
w.first = 8 * alpha * Matrix3::Identity(); |
| 391 |
|
✗ |
w.second = alpha * -8 * pi[3]; |
| 392 |
|
✗ |
wps.push_back(w); |
| 393 |
|
✗ |
w = initwp(DIM_POINT, DIM_VAR); |
| 394 |
|
|
// assign w4: |
| 395 |
|
✗ |
w.first = -8 * alpha * Matrix3::Identity(); |
| 396 |
|
✗ |
w.second = alpha * 8 * pi[5]; |
| 397 |
|
✗ |
wps.push_back(w); |
| 398 |
|
✗ |
w = initwp(DIM_POINT, DIM_VAR); |
| 399 |
|
|
// assign w5: |
| 400 |
|
✗ |
w.second = alpha * 8 * (-pi[5] + pi[6]); |
| 401 |
|
✗ |
wps.push_back(w); |
| 402 |
|
✗ |
w = initwp(DIM_POINT, DIM_VAR); |
| 403 |
|
|
// assign w6: |
| 404 |
|
✗ |
w.second = alpha * 8 * (-pi[6] + pi[7]); |
| 405 |
|
✗ |
wps.push_back(w); |
| 406 |
|
✗ |
w = initwp(DIM_POINT, DIM_VAR); |
| 407 |
|
|
// assign w7: |
| 408 |
|
✗ |
w.second = alpha * 8 * (-pi[7] + pi[8]); |
| 409 |
|
✗ |
wps.push_back(w); |
| 410 |
|
✗ |
return wps; |
| 411 |
|
|
} |
| 412 |
|
|
|
| 413 |
|
✗ |
std::vector<waypoint_t> computeAccelerationWaypoints( |
| 414 |
|
|
const ProblemData& pData, const double T, |
| 415 |
|
|
std::vector<bezier_t::point_t> pi = std::vector<bezier_t::point_t>()) { |
| 416 |
|
✗ |
if (pi.size() == 0) pi = computeConstantWaypoints(pData, T); |
| 417 |
|
|
|
| 418 |
|
✗ |
std::vector<waypoint_t> wps; |
| 419 |
|
✗ |
assert(pi.size() == 9); |
| 420 |
|
✗ |
double alpha = 1. / (T * T); |
| 421 |
|
|
|
| 422 |
|
✗ |
waypoint_t w = initwp(DIM_POINT, DIM_VAR); |
| 423 |
|
|
|
| 424 |
|
|
// assign w0: |
| 425 |
|
✗ |
w.second = 56 * alpha * (pi[0] - 2 * pi[1] + pi[2]); |
| 426 |
|
✗ |
wps.push_back(w); |
| 427 |
|
✗ |
w = initwp(DIM_POINT, DIM_VAR); |
| 428 |
|
|
// assign w1: |
| 429 |
|
✗ |
w.second = 56 * alpha * (pi[1] - 2 * pi[2] + pi[3]); |
| 430 |
|
✗ |
wps.push_back(w); |
| 431 |
|
✗ |
w = initwp(DIM_POINT, DIM_VAR); |
| 432 |
|
|
// assign w2: |
| 433 |
|
✗ |
w.first = 56 * alpha * Matrix3::Identity(); |
| 434 |
|
✗ |
w.second = (56 * pi[2] - 112 * pi[3]) * alpha; |
| 435 |
|
✗ |
wps.push_back(w); |
| 436 |
|
✗ |
w = initwp(DIM_POINT, DIM_VAR); |
| 437 |
|
|
// assign w3: |
| 438 |
|
✗ |
w.first = -112 * alpha * Matrix3::Identity(); |
| 439 |
|
✗ |
w.second = (56 * pi[3] + 56 * pi[8]) * alpha; |
| 440 |
|
✗ |
wps.push_back(w); |
| 441 |
|
✗ |
w = initwp(DIM_POINT, DIM_VAR); |
| 442 |
|
|
// assign w4: |
| 443 |
|
✗ |
w.first = 56 * alpha * Matrix3::Identity(); |
| 444 |
|
✗ |
w.second = (-112 * pi[5] + 56 * pi[6]) * alpha; |
| 445 |
|
✗ |
wps.push_back(w); |
| 446 |
|
✗ |
w = initwp(DIM_POINT, DIM_VAR); |
| 447 |
|
|
// assign w5: |
| 448 |
|
✗ |
w.second = 56 * alpha * (pi[5] - 2 * pi[6] + pi[7]); |
| 449 |
|
✗ |
wps.push_back(w); |
| 450 |
|
✗ |
w = initwp(DIM_POINT, DIM_VAR); |
| 451 |
|
|
// assign w5: |
| 452 |
|
✗ |
w.second = 56 * alpha * (pi[6] - 2 * pi[7] + pi[8]); |
| 453 |
|
✗ |
wps.push_back(w); |
| 454 |
|
✗ |
return wps; |
| 455 |
|
|
} |
| 456 |
|
|
|
| 457 |
|
✗ |
std::vector<waypoint_t> computeJerkWaypoints( |
| 458 |
|
|
const ProblemData& pData, const double T, |
| 459 |
|
|
std::vector<bezier_t::point_t> pi = std::vector<bezier_t::point_t>()) { |
| 460 |
|
✗ |
if (pi.size() == 0) pi = computeConstantWaypoints(pData, T); |
| 461 |
|
|
|
| 462 |
|
✗ |
std::vector<waypoint_t> wps; |
| 463 |
|
✗ |
assert(pi.size() == 9); |
| 464 |
|
|
|
| 465 |
|
✗ |
double alpha = 1. / (T * T * T); |
| 466 |
|
|
|
| 467 |
|
✗ |
waypoint_t w = initwp(DIM_POINT, DIM_VAR); |
| 468 |
|
|
|
| 469 |
|
|
// assign w0: |
| 470 |
|
✗ |
w.second = 336 * (-pi[0] + 3 * pi[1] - 3 * pi[2] + pi[3]) * alpha; |
| 471 |
|
✗ |
wps.push_back(w); |
| 472 |
|
✗ |
w = initwp(DIM_POINT, DIM_VAR); |
| 473 |
|
|
// assign w1: |
| 474 |
|
✗ |
w.first = 336 * alpha * Matrix3::Identity(); |
| 475 |
|
✗ |
w.second = 336 * (-pi[1] + 3 * pi[2] - 3 * pi[3]) * alpha; |
| 476 |
|
✗ |
wps.push_back(w); |
| 477 |
|
✗ |
w = initwp(DIM_POINT, DIM_VAR); |
| 478 |
|
|
// assign w2: |
| 479 |
|
✗ |
w.first = -3 * 336 * alpha * Matrix3::Identity(); |
| 480 |
|
✗ |
w.second = 336 * (-pi[2] + 3 * pi[3] + pi[5]) * alpha; |
| 481 |
|
✗ |
wps.push_back(w); |
| 482 |
|
✗ |
w = initwp(DIM_POINT, DIM_VAR); |
| 483 |
|
|
// assign w3: |
| 484 |
|
✗ |
w.first = 3 * 336 * alpha * Matrix3::Identity(); |
| 485 |
|
✗ |
w.second = 336 * (-pi[3] - 3 * pi[5] + pi[6]) * alpha; |
| 486 |
|
✗ |
wps.push_back(w); |
| 487 |
|
✗ |
w = initwp(DIM_POINT, DIM_VAR); |
| 488 |
|
|
// assign w4: |
| 489 |
|
✗ |
w.first = -336 * alpha * Matrix3::Identity(); |
| 490 |
|
✗ |
w.second = 336 * (3 * pi[5] - 3 * pi[6] + pi[7]) * alpha; |
| 491 |
|
✗ |
wps.push_back(w); |
| 492 |
|
✗ |
w = initwp(DIM_POINT, DIM_VAR); |
| 493 |
|
|
// assign w5: |
| 494 |
|
✗ |
w.second = 336 * (-pi[5] + 3 * pi[6] - 3 * pi[7] + pi[8]) * alpha; |
| 495 |
|
✗ |
wps.push_back(w); |
| 496 |
|
✗ |
return wps; |
| 497 |
|
|
} |
| 498 |
|
|
|
| 499 |
|
|
inline coefs_t computeFinalVelocityPoint(const ProblemData& pData, double T) { |
| 500 |
|
|
coefs_t v; |
| 501 |
|
|
std::vector<point_t> pi = computeConstantWaypoints(pData, T); |
| 502 |
|
|
// equation found with sympy |
| 503 |
|
|
v.first = 0.; |
| 504 |
|
|
v.second = (-6.0 * pi[5] + 6.0 * pi[6]) / T; |
| 505 |
|
|
return v; |
| 506 |
|
|
} |
| 507 |
|
|
|
| 508 |
|
✗ |
inline std::pair<MatrixXX, VectorX> computeVelocityCost( |
| 509 |
|
|
const ProblemData& pData, double T, |
| 510 |
|
|
std::vector<bezier_t::point_t> pi = std::vector<bezier_t::point_t>()) { |
| 511 |
|
✗ |
MatrixXX H = MatrixXX::Zero(3, 3); |
| 512 |
|
✗ |
VectorX g = VectorX::Zero(3); |
| 513 |
|
✗ |
if (pi.size() == 0) pi = computeConstantWaypoints(pData, T); |
| 514 |
|
|
|
| 515 |
|
✗ |
g = (-7.8321678321748 * pi[0] - 7.83216783237586 * pi[1] + |
| 516 |
|
✗ |
9.13752913728184 * pi[3] + 9.13752913758454 * pi[5] - |
| 517 |
|
✗ |
7.83216783216697 * pi[7] - 7.83216783216777 * pi[8]) / |
| 518 |
|
✗ |
(2 * T); |
| 519 |
|
✗ |
H = Matrix3::Identity() * 6.52680652684107 / (T); |
| 520 |
|
|
|
| 521 |
|
✗ |
double norm = H.norm(); |
| 522 |
|
✗ |
H /= norm; |
| 523 |
|
✗ |
g /= norm; |
| 524 |
|
|
|
| 525 |
|
✗ |
return std::make_pair(H, g); |
| 526 |
|
|
} |
| 527 |
|
|
|
| 528 |
|
|
} // namespace c0_dc0_ddc0_j0_j1_ddc1_dc1_c1 |
| 529 |
|
|
|
| 530 |
|
|
} // namespace bezier_com_traj |
| 531 |
|
|
|
| 532 |
|
|
#endif // WAYPOINTS_C0_DC0_DDC0_J0_J1_DDC1_DC1_C1_HH |
| 533 |
|
|
|