| Line | Branch | Exec | Source |
|---|---|---|---|
| 1 | /* | ||
| 2 | * Copyright 2018, LAAS-CNRS | ||
| 3 | * Author: Pierre Fernbach | ||
| 4 | */ | ||
| 5 | |||
| 6 | #ifndef BEZIER_COM_TRAJ_c0_dc0_ddc0_dc1_c1_H | ||
| 7 | #define BEZIER_COM_TRAJ_c0_dc0_ddc0_dc1_c1_H | ||
| 8 | |||
| 9 | #include <hpp/bezier-com-traj/data.hh> | ||
| 10 | |||
| 11 | namespace bezier_com_traj { | ||
| 12 | namespace c0_dc0_ddc0_dc1_c1 { | ||
| 13 | |||
| 14 | static const ConstraintFlag flag = | ||
| 15 | INIT_POS | INIT_VEL | INIT_ACC | END_VEL | END_POS; | ||
| 16 | |||
| 17 | /// ### EQUATION FOR CONSTRAINTS ON INIT AND FINAL POSITION AND VELOCITY AND | ||
| 18 | /// INIT ACCELERATION (DEGREE = 5) | ||
| 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 x p2 p3 | ||
| 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 | 64 | inline coefs_t evaluateCurveAtTime(const std::vector<point_t>& pi, double t) { | |
| 29 |
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64 | coefs_t wp; |
| 30 | 64 | double t2 = t * t; | |
| 31 | 64 | double t3 = t2 * t; | |
| 32 | 64 | double t4 = t3 * t; | |
| 33 | 64 | double t5 = t4 * t; | |
| 34 | // equation found with sympy | ||
| 35 | 64 | wp.first = 10.0 * t5 - 20.0 * t4 + 10.0 * t3; | |
| 36 |
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64 | wp.second = -1.0 * pi[0] * t5 + 5.0 * pi[0] * t4 - 10.0 * pi[0] * t3 + |
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128 | 10.0 * pi[0] * t2 - 5.0 * pi[0] * t + 1.0 * pi[0] + |
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128 | 5.0 * pi[1] * t5 - 20.0 * pi[1] * t4 + 30.0 * pi[1] * t3 - |
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128 | 20.0 * pi[1] * t2 + 5.0 * pi[1] * t - 10.0 * pi[2] * t5 + |
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128 | 30.0 * pi[2] * t4 - 30.0 * pi[2] * t3 + 10.0 * pi[2] * t2 - |
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128 | 5.0 * pi[4] * t5 + 5.0 * pi[4] * t4 + 1.0 * pi[5] * t5; |
| 42 | 128 | return wp; | |
| 43 | } | ||
| 44 | |||
| 45 | 212 | inline coefs_t evaluateAccelerationCurveAtTime(const std::vector<point_t>& pi, | |
| 46 | double T, double t) { | ||
| 47 |
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212 | coefs_t wp; |
| 48 | 212 | double alpha = 1. / (T * T); | |
| 49 | 212 | double t2 = t * t; | |
| 50 | 212 | double t3 = t2 * t; | |
| 51 | // equation found with sympy | ||
| 52 | 212 | wp.first = (200.0 * t3 - 240.0 * t2 + 60.0 * t) * alpha; | |
| 53 |
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212 | wp.second = 1.0 * |
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212 | (-20.0 * pi[0] * t3 + 60.0 * pi[0] * t2 - 60.0 * pi[0] * t + |
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424 | 20.0 * pi[0] + 100.0 * pi[1] * t3 - 240.0 * pi[1] * t2 + |
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424 | 180.0 * pi[1] * t - 40.0 * pi[1] - 200.0 * pi[2] * t3 + |
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424 | 360.0 * pi[2] * t2 - 180.0 * pi[2] * t + 20.0 * pi[2] - |
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636 | 100.0 * pi[4] * t3 + 60.0 * pi[4] * t2 + 20.0 * pi[5] * t3) * |
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212 | alpha; |
| 60 | 424 | return wp; | |
| 61 | } | ||
| 62 | |||
| 63 | 38 | inline std::vector<point_t> computeConstantWaypoints(const ProblemData& pData, | |
| 64 | double T) { | ||
| 65 | // equation for constraint on initial and final position and velocity and | ||
| 66 | // initial acceleration(degree 5, 5 constant waypoint and one free (p3)) | ||
| 67 | // first, compute the constant waypoints that only depend on pData : | ||
| 68 | 38 | double n = 5.; | |
| 69 | 38 | std::vector<point_t> pi; | |
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38 | pi.push_back(pData.c0_); // p0 |
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38 | pi.push_back((pData.dc0_ * T / n) + pData.c0_); // p1 |
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76 | pi.push_back((pData.ddc0_ * T * T / (n * (n - 1))) + |
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76 | (2. * pData.dc0_ * T / n) + pData.c0_); // p2 |
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38 | pi.push_back(point_t::Zero()); // x |
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38 | pi.push_back((-pData.dc1_ * T / n) + pData.c1_); // p4 |
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38 | pi.push_back(pData.c1_); // p5 |
| 77 | 76 | return pi; | |
| 78 | ✗ | } | |
| 79 | |||
| 80 | 10 | inline bezier_wp_t::t_point_t computeWwaypoints(const ProblemData& pData, | |
| 81 | double T) { | ||
| 82 |
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10 | bezier_wp_t::t_point_t wps; |
| 83 | 10 | const int DIM_POINT = 6; | |
| 84 | 10 | const int DIM_VAR = 3; | |
| 85 |
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10 | std::vector<point_t> pi = computeConstantWaypoints(pData, T); |
| 86 | 10 | std::vector<Matrix3> Cpi; | |
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70 | for (std::size_t i = 0; i < pi.size(); ++i) { |
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60 | Cpi.push_back(skew(pi[i])); |
| 89 | } | ||
| 90 |
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10 | const Vector3 g = pData.contacts_.front().contactPhase_->m_gravity; |
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10 | const Matrix3 Cg = skew(g); |
| 92 | 10 | const double T2 = T * T; | |
| 93 | 10 | const double alpha = 1 / (T2); | |
| 94 | |||
| 95 | // equation of waypoints for curve w found with sympy | ||
| 96 |
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10 | waypoint_t w0 = initwp(DIM_POINT, DIM_VAR); |
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10 | w0.second.head<3>() = (20 * pi[0] - 40 * pi[1] + 20 * pi[2]) * alpha; |
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10 | w0.second.tail<3>() = |
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10 | 1.0 * |
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20 | (1.0 * Cg * T2 * pi[0] - 40.0 * Cpi[0] * pi[1] + 20.0 * Cpi[0] * pi[2]) * |
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10 | alpha; |
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10 | wps.push_back(w0); |
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10 | waypoint_t w1 = initwp(DIM_POINT, DIM_VAR); |
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10 | w1.first.block<3, 3>(0, 0) = 8.57142857142857 * alpha * Matrix3::Identity(); |
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10 | w1.first.block<3, 3>(3, 0) = 8.57142857142857 * Cpi[0] * alpha; |
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20 | w1.second.head<3>() = 1.0 * |
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10 | (11.4285714285714 * pi[0] - 14.2857142857143 * pi[1] - |
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20 | 5.71428571428572 * pi[2]) * |
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10 | alpha; |
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10 | w1.second.tail<3>() = |
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10 | 1.0 * |
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10 | (0.285714285714286 * Cg * T2 * pi[0] + |
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20 | 0.714285714285714 * Cg * T2 * pi[1] - 20.0 * Cpi[0] * pi[2] + |
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20 | 14.2857142857143 * Cpi[1] * pi[2]) * |
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10 | alpha; |
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10 | wps.push_back(w1); |
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10 | waypoint_t w2 = initwp(DIM_POINT, DIM_VAR); |
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10 | w2.first.block<3, 3>(0, 0) = 5.71428571428571 * alpha * Matrix3::Identity(); |
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10 | w2.first.block<3, 3>(3, 0) = |
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20 | 1.0 * (-8.57142857142857 * Cpi[0] + 14.2857142857143 * Cpi[1]) * alpha; |
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20 | w2.second.head<3>() = 1.0 * |
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10 | (5.71428571428571 * pi[0] - 14.2857142857143 * pi[2] + |
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20 | 2.85714285714286 * pi[4]) * |
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10 | alpha; |
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10 | w2.second.tail<3>() = |
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10 | 1.0 * |
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10 | (0.0476190476190479 * Cg * T2 * pi[0] + |
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20 | 0.476190476190476 * Cg * T2 * pi[1] + |
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20 | 0.476190476190476 * Cg * T2 * pi[2] + 2.85714285714286 * Cpi[0] * pi[4] - |
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20 | 14.2857142857143 * Cpi[1] * pi[2]) * |
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10 | alpha; |
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10 | wps.push_back(w2); |
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10 | waypoint_t w3 = initwp(DIM_POINT, DIM_VAR); |
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10 | w3.first.block<3, 3>(0, 0) = -2.85714285714286 * alpha * Matrix3::Identity(); |
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10 | w3.first.block<3, 3>(3, 0) = |
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10 | 1.0 * |
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10 | (0.285714285714286 * Cg * T2 - 14.2857142857143 * Cpi[1] + |
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20 | 11.4285714285714 * Cpi[2]) * |
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10 | alpha; |
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20 | w3.second.head<3>() = 1.0 * |
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10 | (2.28571428571429 * pi[0] + 5.71428571428571 * pi[1] - |
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20 | 11.4285714285714 * pi[2] + 5.71428571428571 * pi[4] + |
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20 | 0.571428571428571 * pi[5]) * |
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10 | alpha; |
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10 | w3.second.tail<3>() = |
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10 | 1.0 * |
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10 | (0.142857142857143 * Cg * T2 * pi[1] + |
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20 | 0.571428571428571 * Cg * T2 * pi[2] - 2.85714285714286 * Cpi[0] * pi[4] + |
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30 | 0.571428571428571 * Cpi[0] * pi[5] + 8.57142857142857 * Cpi[1] * pi[4]) * |
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10 | alpha; |
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10 | wps.push_back(w3); |
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10 | waypoint_t w4 = initwp(DIM_POINT, DIM_VAR); |
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10 | w4.first.block<3, 3>(0, 0) = -11.4285714285714 * alpha * Matrix3::Identity(); |
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10 | w4.first.block<3, 3>(3, 0) = |
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20 | 1.0 * (0.571428571428571 * Cg * T2 - 11.4285714285714 * Cpi[2]) * alpha; |
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20 | w4.second.head<3>() = 1.0 * |
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10 | (0.571428571428571 * pi[0] + 5.71428571428571 * pi[1] - |
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20 | 2.85714285714286 * pi[2] + 5.71428571428571 * pi[4] + |
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20 | 2.28571428571429 * pi[5]) * |
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10 | alpha; |
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10 | w4.second.tail<3>() = |
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10 | 1.0 * |
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10 | (0.285714285714286 * Cg * T2 * pi[2] + |
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20 | 0.142857142857143 * Cg * T2 * pi[4] - |
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20 | 0.571428571428572 * Cpi[0] * pi[5] - 8.57142857142857 * Cpi[1] * pi[4] + |
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30 | 2.85714285714286 * Cpi[1] * pi[5] + 14.2857142857143 * Cpi[2] * pi[4]) * |
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10 | alpha; |
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10 | wps.push_back(w4); |
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10 | waypoint_t w5 = initwp(DIM_POINT, DIM_VAR); |
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10 | w5.first.block<3, 3>(0, 0) = -14.2857142857143 * alpha * Matrix3::Identity(); |
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10 | w5.first.block<3, 3>(3, 0) = |
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20 | 1.0 * (0.476190476190476 * Cg * T2 - 14.2857142857143 * Cpi[4]) * alpha; |
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20 | w5.second.head<3>() = 1.0 * |
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10 | (2.85714285714286 * pi[1] + 5.71428571428571 * pi[2] + |
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20 | 5.71428571428571 * pi[5]) * |
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10 | alpha; |
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10 | w5.second.tail<3>() = |
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10 | 1.0 * |
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10 | (0.476190476190476 * Cg * T2 * pi[4] + |
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20 | 0.0476190476190476 * Cg * T2 * pi[5] - |
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20 | 2.85714285714286 * Cpi[1] * pi[5] - 14.2857142857143 * Cpi[2] * pi[4] + |
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20 | 8.57142857142857 * Cpi[2] * pi[5]) * |
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10 | alpha; |
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10 | wps.push_back(w5); |
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10 | waypoint_t w6 = initwp(DIM_POINT, DIM_VAR); |
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10 | w6.first.block<3, 3>(0, 0) = -5.71428571428572 * alpha * Matrix3::Identity(); |
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10 | w6.first.block<3, 3>(3, 0) = |
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20 | 1.0 * (14.2857142857143 * Cpi[4] - 20.0 * Cpi[5]) * alpha; |
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20 | w6.second.head<3>() = 1.0 * |
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10 | (8.57142857142857 * pi[2] - 14.2857142857143 * pi[4] + |
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20 | 11.4285714285714 * pi[5]) * |
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10 | alpha; |
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20 | w6.second.tail<3>() = 1.0 * |
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10 | (0.714285714285714 * Cg * T2 * pi[4] + |
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20 | 0.285714285714286 * Cg * T2 * pi[5] - |
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20 | 8.57142857142858 * Cpi[2] * pi[5]) * |
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10 | alpha; |
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10 | wps.push_back(w6); |
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10 | waypoint_t w7 = initwp(DIM_POINT, DIM_VAR); |
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10 | w7.first.block<3, 3>(0, 0) = 20 * alpha * Matrix3::Identity(); |
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10 | w7.first.block<3, 3>(3, 0) = 1.0 * (20.0 * Cpi[5]) * alpha; |
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10 | w7.second.head<3>() = (-40 * pi[4] + 20 * pi[5]) * alpha; |
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10 | w7.second.tail<3>() = |
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20 | 1.0 * (1.0 * Cg * T2 * pi[5] + 40.0 * Cpi[4] * pi[5]) * alpha; |
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10 | wps.push_back(w7); |
| 206 | 20 | return wps; | |
| 207 | 10 | } | |
| 208 | |||
| 209 | ✗ | inline coefs_t computeFinalVelocityPoint(const ProblemData& pData, double T) { | |
| 210 | ✗ | coefs_t v; | |
| 211 | ✗ | std::vector<point_t> pi = computeConstantWaypoints(pData, T); | |
| 212 | // equation found with sympy | ||
| 213 | ✗ | v.first = 0.; | |
| 214 | ✗ | v.second = (-5.0 * pi[4] + 5.0 * pi[5]) / T; | |
| 215 | ✗ | return v; | |
| 216 | ✗ | } | |
| 217 | |||
| 218 | } // namespace c0_dc0_ddc0_dc1_c1 | ||
| 219 | } // namespace bezier_com_traj | ||
| 220 | |||
| 221 | #endif | ||
| 222 |