hpp-bezier-com-traj  4.10.0
Multi contact trajectory generation for the COM using Bezier curves
waypoints_c0_dc0_c1.hh
Go to the documentation of this file.
1 /*
2  * Copyright 2018, LAAS-CNRS
3  * Author: Pierre Fernbach
4  */
5 
6 #ifndef BEZIER_COM_TRAJ_C0DC0C1_H
7 #define BEZIER_COM_TRAJ_C0DC0C1_H
8 
10 
11 namespace bezier_com_traj {
12 namespace c0_dc0_c1 {
13 
14 static const ConstraintFlag flag = INIT_POS | INIT_VEL | END_POS;
15 
17 
23 inline coefs_t evaluateCurveAtTime(const std::vector<point_t>& pi, double t) {
24  coefs_t wp;
25  double t2 = t * t;
26  double t3 = t2 * t;
27  // equation found with sympy
28  wp.first = -3.0 * t3 + 3.0 * t2;
29  wp.second = -1.0 * pi[0] * t3 + 3.0 * pi[0] * t2 - 3.0 * pi[0] * t + 1.0 * pi[0] + 3.0 * pi[1] * t3 -
30  6.0 * pi[1] * t2 + 3.0 * pi[1] * t + 1.0 * pi[3] * t3;
31  return wp;
32 }
33 
34 inline coefs_t evaluateAccelerationCurveAtTime(const std::vector<point_t>& pi, double T, double t) {
35  coefs_t wp;
36  double alpha = 1. / (T * T);
37  // equation found with sympy
38  wp.first = (-18.0 * t + 6.0) * alpha;
39  wp.second = (-6.0 * pi[0] * t + 6.0 * pi[0] + 18.0 * pi[1] * t - 12.0 * pi[1] + 6.0 * pi[3] * t) * alpha;
40  return wp;
41 }
42 
43 inline std::vector<point_t> computeConstantWaypoints(const ProblemData& pData, double T) {
44  // equation for constraint on initial and final position and velocity (degree 4, 4 constant waypoint and one free
45  // (p2)) first, compute the constant waypoints that only depend on pData :
46  int n = 3;
47  std::vector<point_t> pi;
48  pi.push_back(pData.c0_); // p0
49  pi.push_back((pData.dc0_ * T / n) + pData.c0_); // p1
50  pi.push_back(point_t::Zero()); // p2 = x
51  pi.push_back(pData.c1_); // p3
52 
53  return pi;
54 }
55 
56 inline bezier_wp_t::t_point_t computeWwaypoints(const ProblemData& pData, double T) {
57  bezier_wp_t::t_point_t wps;
58  const int DIM_POINT = 6;
59  const int DIM_VAR = 3;
60  std::vector<point_t> pi = computeConstantWaypoints(pData, T);
61  std::vector<Matrix3> Cpi;
62  for (std::size_t i = 0; i < pi.size(); ++i) {
63  Cpi.push_back(skew(pi[i]));
64  }
65  const Vector3 g = pData.contacts_.front().contactPhase_->m_gravity;
66  const Matrix3 Cg = skew(g);
67  const double T2 = T * T;
68  const double alpha = 1 / (T2);
69  // equation of waypoints for curve w found with sympy
70  waypoint_t w0 = initwp(DIM_POINT, DIM_VAR);
71  w0.first.block<3, 3>(0, 0) = 6 * alpha * Matrix3::Identity();
72  w0.first.block<3, 3>(3, 0) = 6.0 * Cpi[0] * alpha;
73  w0.second.head<3>() = (6 * pi[0] - 12 * pi[1]) * alpha;
74  w0.second.tail<3>() = 1.0 * (1.0 * Cg * T2 * pi[0] - 12.0 * Cpi[0] * pi[1]) * alpha;
75  wps.push_back(w0);
76  waypoint_t w1 = initwp(DIM_POINT, DIM_VAR);
77  w1.first.block<3, 3>(3, 0) = 1.0 * (-6.0 * Cpi[0] + 6.0 * Cpi[1]) * alpha;
78  w1.second.head<3>() = 1.0 * (4.0 * pi[0] - 6.0 * pi[1] + 2.0 * pi[3]) * alpha;
79  w1.second.tail<3>() = 1.0 * (1.0 * Cg * T2 * pi[1] + 2.0 * Cpi[0] * pi[3]) * alpha;
80  wps.push_back(w1);
81  waypoint_t w2 = initwp(DIM_POINT, DIM_VAR);
82  w2.first.block<3, 3>(0, 0) = -6.0 * alpha * Matrix3::Identity();
83  w2.first.block<3, 3>(3, 0) = 1.0 * (1.0 * Cg * T2 - 6.0 * Cpi[1]) * alpha;
84  w2.second.head<3>() = 1.0 * (2.0 * pi[0] + 4.0 * pi[3]) * alpha;
85  w2.second.tail<3>() = 1.0 * (-2.0 * Cpi[0] * pi[3] + 6.0 * Cpi[1] * pi[3]) * alpha;
86  wps.push_back(w2);
87  waypoint_t w3 = initwp(DIM_POINT, DIM_VAR);
88  w3.first.block<3, 3>(0, 0) = -12 * alpha * Matrix3::Identity();
89  w3.first.block<3, 3>(3, 0) = -12.0 * Cpi[3] * alpha;
90  w3.second.head<3>() = (6 * pi[1] + 6 * pi[3]) * alpha;
91  w3.second.tail<3>() = 1.0 * (1.0 * Cg * T2 * pi[3] - 6.0 * Cpi[1] * pi[3]) * alpha;
92  wps.push_back(w3);
93  return wps;
94 }
95 
96 inline coefs_t computeFinalVelocityPoint(const ProblemData& pData, double T) {
97  coefs_t v;
98  // equation found with sympy
99  v.first = -3. / T;
100  v.second = 3. * pData.c1_ / T;
101  return v;
102 }
103 
104 } // namespace c0_dc0_c1
105 } // namespace bezier_com_traj
106 
107 #endif
bezier_com_traj::initwp
T initwp()
bezier_com_traj::waypoint_t
Definition: utils.hh:27
bezier_com_traj::c0_dc0_c1::evaluateAccelerationCurveAtTime
coefs_t evaluateAccelerationCurveAtTime(const std::vector< point_t > &pi, double T, double t)
Definition: waypoints_c0_dc0_c1.hh:34
bezier_com_traj::w1
waypoint6_t w1(point_t_tC p0, point_t_tC p1, point_t_tC, const Matrix3 &, const Matrix3 &, const Matrix3 &gX, const double alpha)
Definition: solve_0_step.cpp:22
bezier_com_traj::coefs_t
std::pair< double, point3_t > coefs_t
Definition: definitions.hh:61
bezier_com_traj::c0_dc0_c1::computeConstantWaypoints
std::vector< point_t > computeConstantWaypoints(const ProblemData &pData, double T)
Definition: waypoints_c0_dc0_c1.hh:43
END_POS
END_POS
Definition: flags.hh:23
bezier_com_traj::ProblemData::dc0_
point_t dc0_
Definition: data.hh:103
bezier_com_traj::Vector3
centroidal_dynamics::Vector3 Vector3
Definition: definitions.hh:21
bezier_com_traj::Matrix3
Eigen::Matrix< value_type, 3, 3 > Matrix3
Definition: definitions.hh:16
bezier_com_traj::c0_dc0_c1::evaluateCurveAtTime
coefs_t evaluateCurveAtTime(const std::vector< point_t > &pi, double t)
evaluateCurveAtTime compute the expression of the point on the curve at t, defined by the waypoint pi...
Definition: waypoints_c0_dc0_c1.hh:23
bezier_com_traj::c0_dc0_c1::computeWwaypoints
bezier_wp_t::t_point_t computeWwaypoints(const ProblemData &pData, double T)
Definition: waypoints_c0_dc0_c1.hh:56
INIT_VEL
INIT_VEL
Definition: flags.hh:21
bezier_com_traj::ProblemData::c0_
point_t c0_
Definition: data.hh:103
bezier_com_traj::w3
waypoint6_t w3(point_t_tC p0, point_t_tC p1, point_t_tC g, const Matrix3 &, const Matrix3 &, const Matrix3 &, const double alpha)
Definition: solve_0_step.cpp:42
bezier_com_traj::ProblemData::c1_
point_t c1_
Definition: data.hh:103
bezier_com_traj::DIM_POINT
const int DIM_POINT
Definition: solve_end_effector.hh:15
bezier_com_traj::w2
waypoint6_t w2(point_t_tC p0, point_t_tC p1, point_t_tC g, const Matrix3 &, const Matrix3 &, const Matrix3 &gX, const double alpha)
Definition: solve_0_step.cpp:32
bezier_com_traj::c0_dc0_c1::computeFinalVelocityPoint
coefs_t computeFinalVelocityPoint(const ProblemData &pData, double T)
Definition: waypoints_c0_dc0_c1.hh:96
bezier_com_traj::skew
BEZIER_COM_TRAJ_DLLAPI Matrix3 skew(point_t_tC x)
skew symmetric matrix
Definition: utils.cpp:56
data.hh
bezier_com_traj::w0
waypoint6_t w0(point_t_tC p0, point_t_tC p1, point_t_tC g, const Matrix3 &p0X, const Matrix3 &, const Matrix3 &, const double alpha)
Definition: solve_0_step.cpp:12
bezier_com_traj
Definition: common_solve_methods.hh:16
bezier_com_traj::ProblemData
Defines all the inputs of the problem: Initial and terminal constraints, as well as selected cost fun...
Definition: data.hh:88
bezier_com_traj::ProblemData::contacts_
std::vector< ContactData > contacts_
Definition: data.hh:102
INIT_POS
INIT_POS
Definition: flags.hh:20