polynomial.cc

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#include <towr/variables/polynomial.h>

#include <cassert>
#include <cmath>


namespace towr {

Polynomial::Polynomial (int order, int dim)
{
  int n_coeff = order+1;
  for (int c=A; c<n_coeff; ++c) {
    coeff_ids_.push_back(static_cast<Coefficients>(c));
    coeff_.push_back(VectorXd::Zero(dim));
  }
}

State Polynomial::GetPoint(double t_local) const
{
  // sanity checks
  if (t_local < 0.0)
    assert(false);//("spliner.cc called with dt<0")

  int n_dim = coeff_.front().size();
  State out(n_dim, 3);

  for (auto d : {kPos, kVel, kAcc})
    for (Coefficients c : coeff_ids_)
      out.at(d) += GetDerivativeWrtCoeff(t_local, d, c)*coeff_.at(c);

  return out;
}

double
Polynomial::GetDerivativeWrtCoeff (double t, Dx deriv, Coefficients c) const
{
  switch (deriv) {
    case kPos:   return               std::pow(t,c);         break;
    case kVel:   return c>=B? c*      std::pow(t,c-1) : 0.0; break;
    case kAcc:   return c>=C? c*(c-1)*std::pow(t,c-2) : 0.0; break;
    default: assert(false); // derivative not defined
  }
}



CubicHermitePolynomial::CubicHermitePolynomial (int dim)
    : Polynomial(3,dim),
      n0_(dim),
      n1_(dim)
{
  T_ = 0.0;
}

void
CubicHermitePolynomial::SetNodes (const Node& n0, const Node& n1)
{
  n0_ = n0;
  n1_ = n1;
}

void
CubicHermitePolynomial::SetDuration(double duration)
{
  T_ = duration;
}

void
CubicHermitePolynomial::UpdateCoeff()
{
  coeff_[A] =  n0_.p();
  coeff_[B] =  n0_.v();
  coeff_[C] = -( 3*(n0_.p() - n1_.p()) +  T_*(2*n0_.v() + n1_.v()) ) / std::pow(T_,2);
  coeff_[D] =  ( 2*(n0_.p() - n1_.p()) +  T_*(  n0_.v() + n1_.v()) ) / std::pow(T_,3);
}

double
CubicHermitePolynomial::GetDerivativeWrtStartNode (Dx dfdt,
                                             Dx node_derivative, // pos or velocity node
                                             double t_local) const
{
  switch (dfdt) {
    case kPos:
      return GetDerivativeOfPosWrtStartNode(node_derivative, t_local);
    case kVel:
      return GetDerivativeOfVelWrtStartNode(node_derivative, t_local);
    case kAcc:
      return GetDerivativeOfAccWrtStartNode(node_derivative, t_local);
    default:
      assert(false); // derivative not yet implemented
  }
}

double
CubicHermitePolynomial::GetDerivativeWrtEndNode (Dx dfdt,
                                           Dx node_derivative, // pos or velocity node
                                           double t_local) const
{
  switch (dfdt) {
    case kPos:
      return GetDerivativeOfPosWrtEndNode(node_derivative, t_local);
    case kVel:
      return GetDerivativeOfVelWrtEndNode(node_derivative, t_local);
    case kAcc:
      return GetDerivativeOfAccWrtEndNode(node_derivative, t_local);
    default:
      assert(false); // derivative not yet implemented
  }
}

double
CubicHermitePolynomial::GetDerivativeOfPosWrtStartNode(Dx node_value,
                                                       double t) const
{
  double t2 = std::pow(t,2);
  double t3 = std::pow(t,3);
  double T  = T_;
  double T2 = std::pow(T_,2);
  double T3 = std::pow(T_,3);

  switch (node_value) {
    case kPos: return (2*t3)/T3 - (3*t2)/T2 + 1;
    case kVel: return t - (2*t2)/T + t3/T2;
    default: assert(false); // only derivative wrt nodes values calculated
  }
}

double
CubicHermitePolynomial::GetDerivativeOfVelWrtStartNode (Dx node_value,
                                                  double t) const
{
  double t2 = std::pow(t,2);
  double T  = T_;
  double T2 = std::pow(T_,2);
  double T3 = std::pow(T_,3);

  switch (node_value) {
    case kPos: return (6*t2)/T3 - (6*t)/T2;
    case kVel: return (3*t2)/T2 - (4*t)/T + 1;
    default: assert(false); // only derivative wrt nodes values calculated
  }
}

double
CubicHermitePolynomial::GetDerivativeOfAccWrtStartNode (Dx node_value,
                                                  double t) const
{
  double T  = T_;
  double T2 = std::pow(T_,2);
  double T3 = std::pow(T_,3);

  switch (node_value) {
    case kPos: return (12*t)/T3 - 6/T2;
    case kVel: return (6*t)/T2 - 4/T;
    default: assert(false); // only derivative wrt nodes values calculated
  }
}

double
CubicHermitePolynomial::GetDerivativeOfPosWrtEndNode (Dx node_value,
                                                double t) const
{
  double t2 = std::pow(t,2);
  double t3 = std::pow(t,3);
  double T  = T_;
  double T2 = std::pow(T_,2);
  double T3 = std::pow(T_,3);

  switch (node_value) {
    case kPos: return (3*t2)/T2 - (2*t3)/T3;
    case kVel: return t3/T2 - t2/T;
    default: assert(false); // only derivative wrt nodes values calculated
  }
}

double
CubicHermitePolynomial::GetDerivativeOfVelWrtEndNode (Dx node_value,
                                                double t) const
{
  double t2 = std::pow(t,2);
  double T  = T_;
  double T2 = std::pow(T_,2);
  double T3 = std::pow(T_,3);

  switch (node_value) {
    case kPos: return (6*t)/T2 - (6*t2)/T3;
    case kVel: return (3*t2)/T2 - (2*t)/T;
    default: assert(false); // only derivative wrt nodes values calculated
  }
}

double
CubicHermitePolynomial::GetDerivativeOfAccWrtEndNode (Dx node_value,
                                                double t) const
{
  double T  = T_;
  double T2 = std::pow(T_,2);
  double T3 = std::pow(T_,3);

  switch (node_value) {
    case kPos: return 6/T2 - (12*t)/T3;
    case kVel: return (6*t)/T2 - 2/T;
    default: assert(false); // only derivative wrt nodes values calculated
  }
}

Eigen::VectorXd
CubicHermitePolynomial::GetDerivativeOfPosWrtDuration(double t) const
{
  VectorXd x0 = n0_.p();
  VectorXd x1 = n1_.p();
  VectorXd v0 = n0_.v();
  VectorXd v1 = n1_.v();

  double t2 = std::pow(t,2);
  double t3 = std::pow(t,3);
  double T  = T_;
  double T2 = std::pow(T_,2);
  double T3 = std::pow(T_,3);
  double T4 = std::pow(T_,4);

  VectorXd deriv = (t3*(v0 + v1))/T3
                 - (t2*(2*v0 + v1))/T2
                 - (3*t3*(2*x0 - 2*x1 + T*v0 + T*v1))/T4
                 + (2*t2*(3*x0 - 3*x1 + 2*T*v0 + T*v1))/T3;

  return deriv;
}

} // namespace towr