waypoints_c0_dc0_dc1.hh

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/*
 * Copyright 2018, LAAS-CNRS
 * Author: Pierre Fernbach
 */
 
#ifndef BEZIER_COM_TRAJ_C0DC0D1_H
#define BEZIER_COM_TRAJ_C0DC0D1_H
 
#include <hpp/bezier-com-traj/data.hh>
 
namespace bezier_com_traj {
namespace c0_dc0_dc1 {
 
static const ConstraintFlag flag = INIT_POS | INIT_VEL | END_VEL;
 
 
inline coefs_t evaluateCurveAtTime(const std::vector<point_t>& pi, double t) {
  coefs_t wp;
  double t2 = t * t;
  double t3 = t2 * t;
  // equation found with sympy
  wp.first = -2.0 * t3 + 3.0 * t2;
  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 - 6.0 * pi[1] * t2 +
              3.0 * pi[1] * t;
  return wp;
}
 
inline coefs_t evaluateAccelerationCurveAtTime(const std::vector<point_t>& pi,
                                               double T, double t) {
  coefs_t wp;
  double alpha = 1. / (T * T);
  // equation found with sympy
  wp.first = (-12.0 * t + 6.0) * alpha;
  wp.second =
      (-6.0 * pi[0] * t + 6.0 * pi[0] + 18.0 * pi[1] * t - 12.0 * pi[1]) *
      alpha;
  return wp;
}
 
inline std::vector<point_t> computeConstantWaypoints(const ProblemData& pData,
                                                     double T) {
  // equation for constraint on initial and final position and velocity (degree
  // 3, 2 constant waypoints and two free (p2 = p3)) first, compute the constant
  // waypoints that only depend on pData :
  if (pData.dc1_.norm() != 0.)
    throw std::runtime_error(
        "Capturability not implemented for spped different than 0");
  std::vector<point_t> pi;
  pi.push_back(pData.c0_);                          // p0
  pi.push_back((pData.dc0_ * T / 3.) + pData.c0_);  // p1
  pi.push_back(point_t::Zero());                    // p2 = x
  pi.push_back(point_t::Zero());                    // p3 = x
  return pi;
}
 
inline bezier_wp_t::t_point_t computeWwaypoints(const ProblemData& pData,
                                                double T) {
  bezier_wp_t::t_point_t wps;
  const int DIM_POINT = 6;
  const int DIM_VAR = 3;
  std::vector<point_t> pi = c0_dc0_dc1::computeConstantWaypoints(pData, T);
  std::vector<Matrix3> Cpi;
  for (std::size_t i = 0; i < pi.size(); ++i) {
    Cpi.push_back(skew(pi[i]));
  }
  const Vector3 g = pData.contacts_.front().contactPhase_->m_gravity;
  const Matrix3 Cg = skew(g);
  const double T2 = T * T;
  const double alpha = 1. / (T2);
  // equation of waypoints for curve w found with sympy
  // TODO Apparently sympy equations are false ...
 
  waypoint_t w0 = initwp(DIM_POINT, DIM_VAR);
  w0.first.block<3, 3>(0, 0) = 6 * alpha * Matrix3::Identity();
  w0.first.block<3, 3>(3, 0) = 6.0 * Cpi[0] * alpha;
  w0.second.head<3>() = (6 * pi[0] - 12 * pi[1]) * alpha;
  w0.second.tail<3>() = (-Cpi[0]) * (12.0 * pi[1] * alpha + g);
  wps.push_back(w0);
  waypoint_t w1 = initwp(DIM_POINT, DIM_VAR);
  w1.first.block<3, 3>(0, 0) = 3 * alpha * Matrix3::Identity();
  w1.first.block<3, 3>(3, 0) = skew(1.5 * (3 * pi[1] - pi[0])) * alpha;
  w1.second.head<3>() = 1.5 * alpha * (3 * pi[0] - 5 * pi[1]);
  w1.second.tail<3>() =
      (3 * alpha * pi[0]).cross(-pi[1]) + 0.25 * (Cg * (3 * pi[1] + pi[0]));
  wps.push_back(w1);
  waypoint_t w2 = initwp(DIM_POINT, DIM_VAR);
  w2.first.block<3, 3>(0, 0) = 0 * alpha * Matrix3::Identity();
  w2.first.block<3, 3>(3, 0) =
      skew(0.5 * g - 3 * alpha * pi[0] + 3 * alpha * pi[1]);
  w2.second.head<3>() = 3 * alpha * (pi[0] - pi[1]);
  w2.second.tail<3>() = 0.5 * Cg * pi[1];
  wps.push_back(w2);
  waypoint_t w3 = initwp(DIM_POINT, DIM_VAR);
  w3.first.block<3, 3>(0, 0) = -3 * alpha * Matrix3::Identity();
  w3.first.block<3, 3>(3, 0) = skew(g - 1.5 * alpha * (pi[1] + pi[0]));
  w3.second.head<3>() = 1.5 * alpha * (pi[1] + pi[0]);
  wps.push_back(w3);
  waypoint_t w4 = initwp(DIM_POINT, DIM_VAR);
  w4.first.block<3, 3>(0, 0) = -6 * alpha * Matrix3::Identity();
  w4.first.block<3, 3>(3, 0) = skew(g - 6 * alpha * pi[1]);
  w4.second.head<3>() = 6 * pi[1] * alpha;
  wps.push_back(w4);
  return wps;
}
 
inline coefs_t computeFinalVelocityPoint(const ProblemData& pData, double T) {
  coefs_t v;
  std::vector<point_t> pi = c0_dc0_dc1::computeConstantWaypoints(pData, T);
  // equation found with sympy
  v.first = 0.;
  v.second = point3_t::Zero();
  return v;
}
 
}  // namespace c0_dc0_dc1
}  // namespace bezier_com_traj
 
#endif