| Directory: | ./ |
|---|---|
| File: | include/hpp/bezier-com-traj/waypoints/waypoints_c0_dc0_ddc0_ddc1_dc1_c1.hh |
| Date: | 2025-03-18 04:20:50 |
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| 1 | /* | ||
| 2 | * Copyright 2018, LAAS-CNRS | ||
| 3 | * Author: Pierre Fernbach | ||
| 4 | */ | ||
| 5 | |||
| 6 | #ifndef BEZIER_COM_TRAJ_c0_dc0_ddc0_ddc1_dc1_c1_H | ||
| 7 | #define BEZIER_COM_TRAJ_c0_dc0_ddc0_ddc1_dc1_c1_H | ||
| 8 | |||
| 9 | #include <hpp/bezier-com-traj/data.hh> | ||
| 10 | |||
| 11 | namespace bezier_com_traj { | ||
| 12 | namespace c0_dc0_ddc0_ddc1_dc1_c1 { | ||
| 13 | |||
| 14 | static const ConstraintFlag flag = | ||
| 15 | INIT_POS | INIT_VEL | INIT_ACC | END_ACC | END_VEL | END_POS; | ||
| 16 | |||
| 17 | /// ### EQUATION FOR CONSTRAINTS ON INIT AND FINAL POSITION AND VELOCITY AND | ||
| 18 | /// ACCELERATION (DEGREE = 6) | ||
| 19 | /// | ||
| 20 | /** | ||
| 21 | * @brief evaluateCurveAtTime compute the expression of the point on the curve | ||
| 22 | * at t, defined by the waypoint pi and one free waypoint (x) | ||
| 23 | * @param pi constant waypoints of the curve, assume p0 p1 p2 x p3 p4 p5 | ||
| 24 | * @param t param (normalized !) | ||
| 25 | * @return the expression of the waypoint such that wp.first . x + wp.second = | ||
| 26 | * point on curve | ||
| 27 | */ | ||
| 28 | 80 | inline coefs_t evaluateCurveAtTime(const std::vector<point_t>& pi, double t) { | |
| 29 |
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80 | coefs_t wp; |
| 30 | 80 | double t2 = t * t; | |
| 31 | 80 | double t3 = t2 * t; | |
| 32 | 80 | double t4 = t3 * t; | |
| 33 | 80 | double t5 = t4 * t; | |
| 34 | 80 | double t6 = t5 * t; | |
| 35 | // equation found with sympy | ||
| 36 | 80 | wp.first = -20.0 * t6 + 60.0 * t5 - 60.0 * t4 + 20.0 * t3; | |
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80 | wp.second = 1.0 * pi[0] * t6 - 6.0 * pi[0] * t5 + 15.0 * pi[0] * t4 - |
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160 | 20.0 * pi[0] * t3 + 15.0 * pi[0] * t2 - 6.0 * pi[0] * t + |
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160 | 1.0 * pi[0] - 6.0 * pi[1] * t6 + 30.0 * pi[1] * t5 - |
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160 | 60.0 * pi[1] * t4 + 60.0 * pi[1] * t3 - 30.0 * pi[1] * t2 + |
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160 | 6.0 * pi[1] * t + 15.0 * pi[2] * t6 - 60.0 * pi[2] * t5 + |
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160 | 90.0 * pi[2] * t4 - 60.0 * pi[2] * t3 + 15.0 * pi[2] * t2 + |
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160 | 15.0 * pi[4] * t6 - 30.0 * pi[4] * t5 + 15.0 * pi[4] * t4 - |
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160 | 6.0 * pi[5] * t6 + 6.0 * pi[5] * t5 + 1.0 * pi[6] * t6; |
| 45 | 160 | return wp; | |
| 46 | } | ||
| 47 | |||
| 48 | 272 | inline coefs_t evaluateAccelerationCurveAtTime(const std::vector<point_t>& pi, | |
| 49 | double T, double t) { | ||
| 50 |
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272 | coefs_t wp; |
| 51 | 272 | double alpha = 1. / (T * T); | |
| 52 | 272 | double t2 = t * t; | |
| 53 | 272 | double t3 = t2 * t; | |
| 54 | 272 | double t4 = t3 * t; | |
| 55 | // equation found with sympy | ||
| 56 | 272 | wp.first = 1.0 * (-600.0 * t4 + 1200.0 * t3 - 720.0 * t2 + 120.0 * t) * alpha; | |
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272 | wp.second = 1.0 * |
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272 | (30.0 * pi[0] * t4 - 120.0 * pi[0] * t3 + 180.0 * pi[0] * t2 - |
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544 | 120.0 * pi[0] * t + 30.0 * pi[0] - 180.0 * pi[1] * t4 + |
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544 | 600.0 * pi[1] * t3 - 720.0 * pi[1] * t2 + 360.0 * pi[1] * t - |
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544 | 60.0 * pi[1] + 450.0 * pi[2] * t4 - 1200.0 * pi[2] * t3 + |
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544 | 1080.0 * pi[2] * t2 - 360.0 * pi[2] * t + 30.0 * pi[2] + |
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544 | 450.0 * pi[4] * t4 - 600.0 * pi[4] * t3 + 180.0 * pi[4] * t2 - |
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816 | 180.0 * pi[5] * t4 + 120.0 * pi[5] * t3 + 30.0 * pi[6] * t4) * |
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272 | alpha; |
| 66 | 544 | return wp; | |
| 67 | } | ||
| 68 | |||
| 69 | 50 | inline std::vector<point_t> computeConstantWaypoints(const ProblemData& pData, | |
| 70 | double T) { | ||
| 71 | // equation for constraint on initial and final position and velocity and | ||
| 72 | // initial acceleration(degree 5, 5 constant waypoint and one free (p3)) | ||
| 73 | // first, compute the constant waypoints that only depend on pData : | ||
| 74 | 50 | double n = 6.; | |
| 75 | 50 | std::vector<point_t> pi; | |
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50 | pi.push_back(pData.c0_); // p0 |
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50 | pi.push_back((pData.dc0_ * T / n) + pData.c0_); // p1 |
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100 | pi.push_back((pData.ddc0_ * T * T / (n * (n - 1))) + |
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100 | (2. * pData.dc0_ * T / n) + pData.c0_); // p2 |
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50 | pi.push_back(point_t::Zero()); // x |
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100 | pi.push_back((pData.ddc1_ * T * T / (n * (n - 1))) - |
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100 | (2 * pData.dc1_ * T / n) + pData.c1_); |
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50 | pi.push_back((-pData.dc1_ * T / n) + pData.c1_); // p4 |
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50 | pi.push_back(pData.c1_); // p5 |
| 85 | 100 | return pi; | |
| 86 | } | ||
| 87 | |||
| 88 | 13 | inline bezier_wp_t::t_point_t computeWwaypoints(const ProblemData& pData, | |
| 89 | double T) { | ||
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13 | bezier_wp_t::t_point_t wps; |
| 91 | 13 | const int DIM_POINT = 6; | |
| 92 | 13 | const int DIM_VAR = 3; | |
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13 | std::vector<point_t> pi = computeConstantWaypoints(pData, T); |
| 94 | 13 | std::vector<Matrix3> Cpi; | |
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104 | for (std::size_t i = 0; i < pi.size(); ++i) { |
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91 | Cpi.push_back(skew(pi[i])); |
| 97 | } | ||
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13 | const Vector3 g = pData.contacts_.front().contactPhase_->m_gravity; |
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13 | const Matrix3 Cg = skew(g); |
| 100 | 13 | const double T2 = T * T; | |
| 101 | 13 | const double alpha = 1 / (T2); | |
| 102 | |||
| 103 | // equation of waypoints for curve w found with sympy | ||
| 104 |
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13 | waypoint_t w0 = initwp(DIM_POINT, DIM_VAR); |
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13 | w0.second.head<3>() = (30 * pi[0] - 60 * pi[1] + 30 * pi[2]) * alpha; |
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13 | w0.second.tail<3>() = |
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13 | 1.0 * |
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26 | (1.0 * Cg * T2 * pi[0] - 60.0 * Cpi[0] * pi[1] + 30.0 * Cpi[0] * pi[2]) * |
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13 | alpha; |
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13 | wps.push_back(w0); |
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13 | waypoint_t w1 = initwp(DIM_POINT, DIM_VAR); |
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13 | w1.first.block<3, 3>(0, 0) = 13.3333333333333 * alpha * Matrix3::Identity(); |
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13 | w1.first.block<3, 3>(3, 0) = 13.3333333333333 * Cpi[0] * alpha; |
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13 | w1.second.head<3>() = |
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26 | 1.0 * (16.6666666666667 * pi[0] - 20.0 * pi[1] - 10.0 * pi[2]) * alpha; |
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26 | w1.second.tail<3>() = 1.0 * |
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13 | (0.333333333333333 * Cg * T2 * pi[0] + |
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26 | 0.666666666666667 * Cg * T2 * pi[1] - |
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39 | 30.0 * Cpi[0] * pi[2] + 20.0 * Cpi[1] * pi[2]) * |
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13 | alpha; |
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13 | wps.push_back(w1); |
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13 | waypoint_t w2 = initwp(DIM_POINT, DIM_VAR); |
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13 | w2.first.block<3, 3>(0, 0) = 6.66666666666667 * alpha * Matrix3::Identity(); |
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13 | w2.first.block<3, 3>(3, 0) = |
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26 | 1.0 * (-13.3333333333333 * Cpi[0] + 20.0 * Cpi[1]) * alpha; |
| 126 |
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13 | w2.second.head<3>() = |
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26 | 1.0 * (8.33333333333333 * pi[0] - 20.0 * pi[2] + 5.0 * pi[4]) * alpha; |
| 128 |
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13 | w2.second.tail<3>() = |
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13 | 1.0 * |
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13 | (0.0833333333333334 * Cg * T2 * pi[0] + 0.5 * Cg * T2 * pi[1] + |
| 131 |
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26 | 0.416666666666667 * Cg * T2 * pi[2] + 5.0 * Cpi[0] * pi[4] - |
| 132 |
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26 | 20.0 * Cpi[1] * pi[2]) * |
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13 | alpha; |
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13 | wps.push_back(w2); |
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13 | waypoint_t w3 = initwp(DIM_POINT, DIM_VAR); |
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13 | w3.first.block<3, 3>(0, 0) = -5.71428571428572 * alpha * Matrix3::Identity(); |
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26 | w3.first.block<3, 3>(3, 0) = 1.0 * |
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13 | (0.238095238095238 * Cg * T2 - 20.0 * Cpi[1] + |
| 139 |
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26 | 14.2857142857143 * Cpi[2]) * |
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13 | alpha; |
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26 | w3.second.head<3>() = 1.0 * |
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13 | (3.57142857142857 * pi[0] + 7.14285714285714 * pi[1] - |
| 143 |
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26 | 14.2857142857143 * pi[2] + 7.85714285714286 * pi[4] + |
| 144 |
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26 | 1.42857142857143 * pi[5]) * |
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13 | alpha; |
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13 | w3.second.tail<3>() = |
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13 | 1.0 * |
| 148 |
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13 | (0.0119047619047619 * Cg * T2 * pi[0] + |
| 149 |
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26 | 0.214285714285714 * Cg * T2 * pi[1] + |
| 150 |
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26 | 0.535714285714286 * Cg * T2 * pi[2] - 5.0 * Cpi[0] * pi[4] + |
| 151 |
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39 | 1.42857142857143 * Cpi[0] * pi[5] + 12.8571428571429 * Cpi[1] * pi[4]) * |
| 152 |
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13 | alpha; |
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13 | wps.push_back(w3); |
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13 | waypoint_t w4 = initwp(DIM_POINT, DIM_VAR); |
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13 | w4.first.block<3, 3>(0, 0) = -14.2857142857143 * alpha * Matrix3::Identity(); |
| 156 |
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13 | w4.first.block<3, 3>(3, 0) = |
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26 | 1.0 * (0.476190476190476 * Cg * T2 - 14.2857142857143 * Cpi[2]) * alpha; |
| 158 |
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26 | w4.second.head<3>() = 1.0 * |
| 159 |
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13 | (1.19047619047619 * pi[0] + 7.14285714285714 * pi[1] - |
| 160 |
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26 | 3.57142857142857 * pi[2] + 5.0 * pi[4] + |
| 161 |
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39 | 4.28571428571429 * pi[5] + 0.238095238095238 * pi[6]) * |
| 162 |
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13 | alpha; |
| 163 |
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13 | w4.second.tail<3>() = |
| 164 |
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13 | 1.0 * |
| 165 |
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13 | (0.0476190476190471 * Cg * T2 * pi[1] + |
| 166 |
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26 | 0.357142857142857 * Cg * T2 * pi[2] + |
| 167 |
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26 | 0.119047619047619 * Cg * T2 * pi[4] - 1.42857142857143 * Cpi[0] * pi[5] + |
| 168 |
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26 | 0.238095238095238 * Cpi[0] * pi[6] - 12.8571428571429 * Cpi[1] * pi[4] + |
| 169 |
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39 | 5.71428571428571 * Cpi[1] * pi[5] + 17.8571428571429 * Cpi[2] * pi[4]) * |
| 170 |
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13 | alpha; |
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13 | wps.push_back(w4); |
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13 | waypoint_t w5 = initwp(DIM_POINT, DIM_VAR); |
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13 | w5.first.block<3, 3>(0, 0) = -14.2857142857143 * alpha * Matrix3::Identity(); |
| 174 |
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13 | w5.first.block<3, 3>(3, 0) = |
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26 | 1.0 * (0.476190476190476 * Cg * T2 - 14.2857142857143 * Cpi[4]) * alpha; |
| 176 |
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26 | w5.second.head<3>() = 1.0 * |
| 177 |
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13 | (0.238095238095238 * pi[0] + 4.28571428571429 * pi[1] + |
| 178 |
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26 | 5.0 * pi[2] - 3.57142857142857 * pi[4] + |
| 179 |
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39 | 7.14285714285714 * pi[5] + 1.19047619047619 * pi[6]) * |
| 180 |
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13 | alpha; |
| 181 |
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13 | w5.second.tail<3>() = |
| 182 |
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13 | 1.0 * |
| 183 |
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13 | (+0.11904761904762 * Cg * T2 * pi[2] + |
| 184 |
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26 | 0.357142857142857 * Cg * T2 * pi[4] + |
| 185 |
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26 | 0.0476190476190476 * Cg * T2 * pi[5] - |
| 186 |
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26 | 0.238095238095238 * Cpi[0] * pi[6] - 5.71428571428572 * Cpi[1] * pi[5] + |
| 187 |
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26 | 1.42857142857143 * Cpi[1] * pi[6] - 17.8571428571429 * Cpi[2] * pi[4] + |
| 188 |
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26 | 12.8571428571429 * Cpi[2] * pi[5]) * |
| 189 |
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13 | alpha; |
| 190 |
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13 | wps.push_back(w5); |
| 191 |
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13 | waypoint_t w6 = initwp(DIM_POINT, DIM_VAR); |
| 192 |
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13 | w6.first.block<3, 3>(0, 0) = -5.71428571428571 * alpha * Matrix3::Identity(); |
| 193 |
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26 | w6.first.block<3, 3>(3, 0) = 1.0 * |
| 194 |
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13 | (0.238095238095238 * Cg * T2 + |
| 195 |
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39 | 14.2857142857143 * Cpi[4] - 20.0 * Cpi[5]) * |
| 196 |
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13 | alpha; |
| 197 |
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26 | w6.second.head<3>() = 1.0 * |
| 198 |
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13 | (1.42857142857143 * pi[1] + 7.85714285714286 * pi[2] - |
| 199 |
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26 | 14.2857142857143 * pi[4] + 7.14285714285715 * pi[5] + |
| 200 |
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26 | 3.57142857142857 * pi[6]) * |
| 201 |
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13 | alpha; |
| 202 |
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13 | w6.second.tail<3>() = |
| 203 |
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13 | 1.0 * |
| 204 |
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13 | (0.535714285714286 * Cg * T2 * pi[4] + |
| 205 |
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26 | 0.214285714285714 * Cg * T2 * pi[5] + |
| 206 |
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26 | 0.0119047619047619 * Cg * T2 * pi[6] - |
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26 | 1.42857142857143 * Cpi[1] * pi[6] - 12.8571428571429 * Cpi[2] * pi[5] + |
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26 | 5.0 * Cpi[2] * pi[6]) * |
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13 | alpha; |
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13 | wps.push_back(w6); |
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13 | waypoint_t w7 = initwp(DIM_POINT, DIM_VAR); |
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13 | w7.first.block<3, 3>(0, 0) = 6.66666666666667 * alpha * Matrix3::Identity(); |
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13 | w7.first.block<3, 3>(3, 0) = |
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26 | 1.0 * (20.0 * Cpi[5] - 13.3333333333333 * Cpi[6]) * alpha; |
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13 | w7.second.head<3>() = |
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26 | 1.0 * (5.0 * pi[2] - 20.0 * pi[4] + 8.33333333333333 * pi[6]) * alpha; |
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13 | w7.second.tail<3>() = |
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13 | 1.0 * |
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13 | (0.416666666666667 * Cg * T2 * pi[4] + 0.5 * Cg * T2 * pi[5] + |
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26 | 0.0833333333333333 * Cg * T2 * pi[6] - 5.0 * Cpi[2] * pi[6] + |
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26 | 20.0 * Cpi[4] * pi[5]) * |
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13 | alpha; |
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13 | wps.push_back(w7); |
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13 | waypoint_t w8 = initwp(DIM_POINT, DIM_VAR); |
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13 | w8.first.block<3, 3>(0, 0) = 13.3333333333333 * alpha * Matrix3::Identity(); |
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13 | w8.first.block<3, 3>(3, 0) = 1.0 * (13.3333333333333 * Cpi[6]) * alpha; |
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13 | w8.second.head<3>() = |
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13 | 1.0 * |
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26 | (-9.99999999999999 * pi[4] - 20.0 * pi[5] + 16.6666666666667 * pi[6]) * |
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13 | alpha; |
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26 | w8.second.tail<3>() = 1.0 * |
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13 | (0.666666666666667 * Cg * T2 * pi[5] + |
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26 | 0.333333333333333 * Cg * T2 * pi[6] - |
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39 | 20.0 * Cpi[4] * pi[5] + 30.0 * Cpi[4] * pi[6]) * |
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13 | alpha; |
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13 | wps.push_back(w8); |
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13 | waypoint_t w9 = initwp(DIM_POINT, DIM_VAR); |
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13 | w9.second.head<3>() = (30 * pi[4] - 60 * pi[5] + 30 * pi[6]) * alpha; |
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13 | w9.second.tail<3>() = |
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13 | 1.0 * |
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26 | (1.0 * Cg * T2 * pi[6] - 30.0 * Cpi[4] * pi[6] + 60.0 * Cpi[5] * pi[6]) * |
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13 | alpha; |
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13 | wps.push_back(w9); |
| 244 | 26 | return wps; | |
| 245 | 13 | } | |
| 246 | |||
| 247 | ✗ | inline coefs_t computeFinalVelocityPoint(const ProblemData& pData, double T) { | |
| 248 | ✗ | coefs_t v; | |
| 249 | ✗ | std::vector<point_t> pi = computeConstantWaypoints(pData, T); | |
| 250 | // equation found with sympy | ||
| 251 | ✗ | v.first = 0.; | |
| 252 | ✗ | v.second = (-6.0 * pi[5] + 6.0 * pi[6]) / T; | |
| 253 | ✗ | return v; | |
| 254 | } | ||
| 255 | |||
| 256 | } // namespace c0_dc0_ddc0_ddc1_dc1_c1 | ||
| 257 | |||
| 258 | } // namespace bezier_com_traj | ||
| 259 | |||
| 260 | #endif | ||
| 261 |