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/////////////////////////////////////////////////////////////////////////////// |
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// BSD 3-Clause License |
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// |
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// Copyright (C) 2019-2025, LAAS-CNRS, University of Edinburgh, |
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// New York University, Heriot-Watt University |
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// Max Planck Gesellschaft |
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// Copyright note valid unless otherwise stated in individual files. |
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// All rights reserved. |
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/////////////////////////////////////////////////////////////////////////////// |
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#include "crocoddyl/core/numdiff/diff-action.hpp" |
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namespace crocoddyl { |
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template <typename Scalar> |
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DifferentialActionModelNumDiffTpl<Scalar>::DifferentialActionModelNumDiffTpl( |
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std::shared_ptr<Base> model, const bool with_gauss_approx) |
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: Base(model->get_state(), model->get_nu(), model->get_nr(), |
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model->get_ng(), model->get_nh(), model->get_ng_T(), |
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model->get_nh_T()), |
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model_(model), |
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with_gauss_approx_(with_gauss_approx), |
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e_jac_(sqrt(Scalar(2.0) * std::numeric_limits<Scalar>::epsilon())) { |
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e_hess_ = sqrt(Scalar(2.0) * e_jac_); |
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if (with_gauss_approx_ && nr_ == 1) |
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throw_pretty("No Gauss approximation possible with nr = 1"); |
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} |
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template <typename Scalar> |
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void DifferentialActionModelNumDiffTpl<Scalar>::calc( |
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const std::shared_ptr<DifferentialActionDataAbstract>& data, |
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const Eigen::Ref<const VectorXs>& x, const Eigen::Ref<const VectorXs>& u) { |
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if (static_cast<std::size_t>(x.size()) != state_->get_nx()) { |
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throw_pretty( |
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"Invalid argument: " << "x has wrong dimension (it should be " + |
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std::to_string(state_->get_nx()) + ")"); |
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} |
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if (static_cast<std::size_t>(u.size()) != nu_) { |
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throw_pretty( |
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"Invalid argument: " << "u has wrong dimension (it should be " + |
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std::to_string(nu_) + ")"); |
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} |
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Data* d = static_cast<Data*>(data.get()); |
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model_->calc(d->data_0, x, u); |
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data->xout = d->data_0->xout; |
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data->cost = d->data_0->cost; |
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d->g = d->data_0->g; |
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d->h = d->data_0->h; |
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} |
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template <typename Scalar> |
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void DifferentialActionModelNumDiffTpl<Scalar>::calc( |
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const std::shared_ptr<DifferentialActionDataAbstract>& data, |
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const Eigen::Ref<const VectorXs>& x) { |
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if (static_cast<std::size_t>(x.size()) != state_->get_nx()) { |
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throw_pretty( |
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"Invalid argument: " << "x has wrong dimension (it should be " + |
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std::to_string(state_->get_nx()) + ")"); |
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} |
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Data* d = static_cast<Data*>(data.get()); |
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model_->calc(d->data_0, x); |
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data->xout = d->data_0->xout; |
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data->cost = d->data_0->cost; |
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d->g = d->data_0->g; |
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d->h = d->data_0->h; |
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} |
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template <typename Scalar> |
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void DifferentialActionModelNumDiffTpl<Scalar>::calcDiff( |
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const std::shared_ptr<DifferentialActionDataAbstract>& data, |
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const Eigen::Ref<const VectorXs>& x, const Eigen::Ref<const VectorXs>& u) { |
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// For details about the finite difference formulas see |
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// http://www.it.uom.gr/teaching/linearalgebra/NumericalRecipiesInC/c5-7.pdf |
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if (static_cast<std::size_t>(x.size()) != state_->get_nx()) { |
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throw_pretty( |
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"Invalid argument: " << "x has wrong dimension (it should be " + |
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std::to_string(state_->get_nx()) + ")"); |
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} |
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if (static_cast<std::size_t>(u.size()) != nu_) { |
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throw_pretty( |
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"Invalid argument: " << "u has wrong dimension (it should be " + |
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std::to_string(nu_) + ")"); |
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} |
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Data* d = static_cast<Data*>(data.get()); |
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const VectorXs& x0 = d->data_0->xout; |
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const Scalar c0 = d->data_0->cost; |
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const VectorXs& g0 = d->g; |
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const VectorXs& h0 = d->h; |
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const std::size_t ndx = state_->get_ndx(); |
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const std::size_t nu = model_->get_nu(); |
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const std::size_t ng = model_->get_ng(); |
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const std::size_t nh = model_->get_nh(); |
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d->Gx.conservativeResize(ng, ndx); |
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d->Gu.conservativeResize(ng, nu); |
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d->Hx.conservativeResize(nh, ndx); |
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d->Hu.conservativeResize(nh, nu); |
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d->du.setZero(); |
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assertStableStateFD(x); |
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// Computing the d action(x,u) / dx |
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model_->get_state()->diff(model_->get_state()->zero(), x, d->dx); |
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d->x_norm = d->dx.norm(); |
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d->dx.setZero(); |
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d->xh_jac = e_jac_ * std::max(Scalar(1.), d->x_norm); |
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for (std::size_t ix = 0; ix < ndx; ++ix) { |
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d->dx(ix) = d->xh_jac; |
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model_->get_state()->integrate(x, d->dx, d->xp); |
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model_->calc(d->data_x[ix], d->xp, u); |
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// dynamics |
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data->Fx.col(ix) = (d->data_x[ix]->xout - x0) / d->xh_jac; |
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// constraint |
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data->Gx.col(ix) = (d->data_x[ix]->g - g0) / d->xh_jac; |
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data->Hx.col(ix) = (d->data_x[ix]->h - h0) / d->xh_jac; |
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// cost |
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data->Lx(ix) = (d->data_x[ix]->cost - c0) / d->xh_jac; |
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d->Rx.col(ix) = (d->data_x[ix]->r - d->data_0->r) / d->xh_jac; |
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d->dx(ix) = Scalar(0.); |
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} |
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// Computing the d action(x,u) / du |
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d->uh_jac = e_jac_ * std::max(Scalar(1.), u.norm()); |
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for (std::size_t iu = 0; iu < nu; ++iu) { |
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d->du(iu) = d->uh_jac; |
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model_->calc(d->data_u[iu], x, u + d->du); |
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// dynamics |
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data->Fu.col(iu) = (d->data_u[iu]->xout - x0) / d->uh_jac; |
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// constraint |
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data->Gu.col(iu) = (d->data_u[iu]->g - g0) / d->uh_jac; |
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data->Hu.col(iu) = (d->data_u[iu]->h - h0) / d->uh_jac; |
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// cost |
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data->Lu(iu) = (d->data_u[iu]->cost - c0) / d->uh_jac; |
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d->Ru.col(iu) = (d->data_u[iu]->r - d->data_0->r) / d->uh_jac; |
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d->du(iu) = Scalar(0.); |
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} |
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#ifdef NDEBUG |
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// Computing the d^2 cost(x,u) / dx^2 |
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d->xh_hess = e_hess_ * std::max(Scalar(1.), d->x_norm); |
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d->xh_hess_pow2 = d->xh_hess * d->xh_hess; |
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for (std::size_t ix = 0; ix < ndx; ++ix) { |
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d->dx(ix) = d->xh_hess; |
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model_->get_state()->integrate(x, d->dx, d->xp); |
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model_->calc(d->data_x[ix], d->xp, u); |
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const Scalar cp = d->data_x[ix]->cost; |
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model_->get_state()->integrate(x, -d->dx, d->xp); |
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model_->calc(d->data_x[ix], d->xp, u); |
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const Scalar cm = d->data_x[ix]->cost; |
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data->Lxx(ix, ix) = (cp - 2 * c0 + cm) / d->xh_hess_pow2; |
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for (std::size_t jx = ix + 1; jx < ndx; ++jx) { |
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d->dx(jx) = d->xh_hess; |
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model_->get_state()->integrate(x, d->dx, d->xp); |
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model_->calc(d->data_x[ix], d->xp, u); |
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const Scalar cpp = |
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d->data_x[ix] |
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->cost; // cost due to positive disturbance in both directions |
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d->dx(ix) = Scalar(0.); |
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model_->get_state()->integrate(x, d->dx, d->xp); |
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model_->calc(d->data_x[ix], d->xp, u); |
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const Scalar czp = |
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d->data_x[ix]->cost; // cost due to zero disturance in 'i' and |
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// positive disturbance in 'j' direction |
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data->Lxx(ix, jx) = (cpp - czp - cp + c0) / d->xh_hess_pow2; |
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data->Lxx(jx, ix) = data->Lxx(ix, jx); |
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d->dx(ix) = d->xh_hess; |
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d->dx(jx) = Scalar(0.); |
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} |
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d->dx(ix) = Scalar(0.); |
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} |
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// Computing the d^2 cost(x,u) / du^2 |
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d->uh_hess = e_hess_ * std::max(Scalar(1.), u.norm()); |
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d->uh_hess_pow2 = d->uh_hess * d->uh_hess; |
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for (std::size_t iu = 0; iu < nu; ++iu) { |
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d->du(iu) = d->uh_hess; |
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model_->calc(d->data_u[iu], x, u + d->du); |
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const Scalar cp = d->data_u[iu]->cost; |
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model_->calc(d->data_u[iu], x, u - d->du); |
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const Scalar cm = d->data_u[iu]->cost; |
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data->Luu(iu, iu) = (cp - 2 * c0 + cm) / d->uh_hess_pow2; |
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for (std::size_t ju = iu + 1; ju < nu; ++ju) { |
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d->du(ju) = d->uh_hess; |
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model_->calc(d->data_u[iu], x, u + d->du); |
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const Scalar cpp = |
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d->data_u[iu] |
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->cost; // cost due to positive disturbance in both directions |
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d->du(iu) = Scalar(0.); |
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model_->calc(d->data_u[iu], x, u + d->du); |
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const Scalar czp = |
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d->data_u[iu]->cost; // cost due to zero disturance in 'i' and |
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// positive disturbance in 'j' direction |
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data->Luu(iu, ju) = (cpp - czp - cp + c0) / d->uh_hess_pow2; |
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data->Luu(ju, iu) = data->Luu(iu, ju); |
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d->du(iu) = d->uh_hess; |
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d->du(ju) = Scalar(0.); |
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} |
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d->du(iu) = Scalar(0.); |
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} |
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// Computing the d^2 cost(x,u) / dxu |
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d->xuh_hess_pow2 = Scalar(4.) * d->xh_hess * d->uh_hess; |
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for (std::size_t ix = 0; ix < ndx; ++ix) { |
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for (std::size_t ju = 0; ju < nu; ++ju) { |
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d->dx(ix) = d->xh_hess; |
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model_->get_state()->integrate(x, d->dx, d->xp); |
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d->du(ju) = d->uh_hess; |
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model_->calc(d->data_x[ix], d->xp, u + d->du); |
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const Scalar cpp = d->data_x[ix]->cost; |
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model_->calc(d->data_x[ix], d->xp, u - d->du); |
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const Scalar cpm = d->data_x[ix]->cost; |
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model_->get_state()->integrate(x, -d->dx, d->xp); |
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model_->calc(d->data_x[ix], d->xp, u + d->du); |
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const Scalar cmp = d->data_x[ix]->cost; |
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model_->calc(d->data_x[ix], d->xp, u - d->du); |
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const Scalar cmm = d->data_x[ix]->cost; |
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data->Lxu(ix, ju) = (cpp - cpm - cmp + cmm) / d->xuh_hess_pow2; |
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d->dx(ix) = Scalar(0.); |
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d->du(ju) = Scalar(0.); |
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} |
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} |
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#endif |
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✗ |
if (with_gauss_approx_) { |
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data->Lxx = d->Rx.transpose() * d->Rx; |
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data->Lxu = d->Rx.transpose() * d->Ru; |
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data->Luu = d->Ru.transpose() * d->Ru; |
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} |
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} |
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template <typename Scalar> |
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✗ |
void DifferentialActionModelNumDiffTpl<Scalar>::calcDiff( |
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const std::shared_ptr<DifferentialActionDataAbstract>& data, |
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const Eigen::Ref<const VectorXs>& x) { |
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// For details about the finite difference formulas see |
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// http://www.it.uom.gr/teaching/linearalgebra/NumericalRecipiesInC/c5-7.pdf |
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✗ |
if (static_cast<std::size_t>(x.size()) != state_->get_nx()) { |
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throw_pretty( |
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"Invalid argument: " << "x has wrong dimension (it should be " + |
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std::to_string(state_->get_nx()) + ")"); |
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} |
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Data* d = static_cast<Data*>(data.get()); |
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const Scalar c0 = d->data_0->cost; |
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const VectorXs& g0 = d->g; |
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const VectorXs& h0 = d->h; |
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const std::size_t ndx = state_->get_ndx(); |
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d->Gx.conservativeResize(model_->get_ng_T(), ndx); |
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d->Hx.conservativeResize(model_->get_nh_T(), ndx); |
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✗ |
assertStableStateFD(x); |
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// Computing the d action(x,u) / dx |
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✗ |
model_->get_state()->diff(model_->get_state()->zero(), x, d->dx); |
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d->x_norm = d->dx.norm(); |
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d->dx.setZero(); |
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d->xh_jac = e_jac_ * std::max(Scalar(1.), d->x_norm); |
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✗ |
for (std::size_t ix = 0; ix < ndx; ++ix) { |
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d->dx(ix) = d->xh_jac; |
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model_->get_state()->integrate(x, d->dx, d->xp); |
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✗ |
model_->calc(d->data_x[ix], d->xp); |
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// cost |
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data->Lx(ix) = (d->data_x[ix]->cost - c0) / d->xh_jac; |
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d->Rx.col(ix) = (d->data_x[ix]->r - d->data_0->r) / d->xh_jac; |
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// constraint |
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✗ |
data->Gx.col(ix) = (d->data_x[ix]->g - g0) / d->xh_jac; |
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data->Hx.col(ix) = (d->data_x[ix]->h - h0) / d->xh_jac; |
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✗ |
d->dx(ix) = Scalar(0.); |
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} |
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#ifdef NDEBUG |
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// Computing the d^2 cost(x,u) / dx^2 |
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d->xh_hess = e_hess_ * std::max(Scalar(1.), d->x_norm); |
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d->xh_hess_pow2 = d->xh_hess * d->xh_hess; |
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for (std::size_t ix = 0; ix < ndx; ++ix) { |
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// We can apply the same formulas for finite difference as above |
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d->dx(ix) = d->xh_hess; |
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model_->get_state()->integrate(x, d->dx, d->xp); |
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model_->calc(d->data_x[ix], d->xp); |
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const Scalar cp = d->data_x[ix]->cost; |
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model_->get_state()->integrate(x, -d->dx, d->xp); |
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model_->calc(d->data_x[ix], d->xp); |
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const Scalar cm = d->data_x[ix]->cost; |
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data->Lxx(ix, ix) = (cp - 2 * c0 + cm) / d->xh_hess_pow2; |
| 285 |
|
|
for (std::size_t jx = ix + 1; jx < ndx; ++jx) { |
| 286 |
|
|
d->dx(jx) = d->xh_hess; |
| 287 |
|
|
model_->get_state()->integrate(x, d->dx, d->xp); |
| 288 |
|
|
model_->calc(d->data_x[ix], d->xp); |
| 289 |
|
|
const Scalar cpp = |
| 290 |
|
|
d->data_x[ix] |
| 291 |
|
|
->cost; // cost due to positive disturbance in both directions |
| 292 |
|
|
d->dx(ix) = Scalar(0.); |
| 293 |
|
|
model_->get_state()->integrate(x, d->dx, d->xp); |
| 294 |
|
|
model_->calc(d->data_x[ix], d->xp); |
| 295 |
|
|
const Scalar czp = |
| 296 |
|
|
d->data_x[ix]->cost; // cost due to zero disturance in 'i' and |
| 297 |
|
|
// positive disturbance in 'j' direction |
| 298 |
|
|
data->Lxx(ix, jx) = (cpp - czp - cp + c0) / d->xh_hess_pow2; |
| 299 |
|
|
data->Lxx(jx, ix) = data->Lxx(ix, jx); |
| 300 |
|
|
d->dx(ix) = d->xh_hess; |
| 301 |
|
|
d->dx(jx) = Scalar(0.); |
| 302 |
|
|
} |
| 303 |
|
|
d->dx(ix) = Scalar(0.); |
| 304 |
|
|
} |
| 305 |
|
|
#endif |
| 306 |
|
|
|
| 307 |
|
✗ |
if (with_gauss_approx_) { |
| 308 |
|
✗ |
data->Lxx = d->Rx.transpose() * d->Rx; |
| 309 |
|
|
} |
| 310 |
|
|
} |
| 311 |
|
|
|
| 312 |
|
|
template <typename Scalar> |
| 313 |
|
|
std::shared_ptr<DifferentialActionDataAbstractTpl<Scalar> > |
| 314 |
|
✗ |
DifferentialActionModelNumDiffTpl<Scalar>::createData() { |
| 315 |
|
✗ |
return std::allocate_shared<Data>(Eigen::aligned_allocator<Data>(), this); |
| 316 |
|
|
} |
| 317 |
|
|
|
| 318 |
|
|
template <typename Scalar> |
| 319 |
|
✗ |
void DifferentialActionModelNumDiffTpl<Scalar>::quasiStatic( |
| 320 |
|
|
const std::shared_ptr<DifferentialActionDataAbstract>& data, |
| 321 |
|
|
Eigen::Ref<VectorXs> u, const Eigen::Ref<const VectorXs>& x, |
| 322 |
|
|
const std::size_t maxiter, const Scalar tol) { |
| 323 |
|
✗ |
Data* d = static_cast<Data*>(data.get()); |
| 324 |
|
✗ |
model_->quasiStatic(d->data_0, u, x, maxiter, tol); |
| 325 |
|
|
} |
| 326 |
|
|
|
| 327 |
|
|
template <typename Scalar> |
| 328 |
|
|
template <typename NewScalar> |
| 329 |
|
|
DifferentialActionModelNumDiffTpl<NewScalar> |
| 330 |
|
✗ |
DifferentialActionModelNumDiffTpl<Scalar>::cast() const { |
| 331 |
|
|
typedef DifferentialActionModelNumDiffTpl<NewScalar> ReturnType; |
| 332 |
|
✗ |
ReturnType res(model_->template cast<NewScalar>()); |
| 333 |
|
✗ |
return res; |
| 334 |
|
|
} |
| 335 |
|
|
|
| 336 |
|
|
template <typename Scalar> |
| 337 |
|
|
const std::shared_ptr<DifferentialActionModelAbstractTpl<Scalar> >& |
| 338 |
|
✗ |
DifferentialActionModelNumDiffTpl<Scalar>::get_model() const { |
| 339 |
|
✗ |
return model_; |
| 340 |
|
|
} |
| 341 |
|
|
|
| 342 |
|
|
template <typename Scalar> |
| 343 |
|
✗ |
const Scalar DifferentialActionModelNumDiffTpl<Scalar>::get_disturbance() |
| 344 |
|
|
const { |
| 345 |
|
✗ |
return e_jac_; |
| 346 |
|
|
} |
| 347 |
|
|
|
| 348 |
|
|
template <typename Scalar> |
| 349 |
|
✗ |
void DifferentialActionModelNumDiffTpl<Scalar>::set_disturbance( |
| 350 |
|
|
const Scalar disturbance) { |
| 351 |
|
✗ |
if (disturbance < Scalar(0.)) { |
| 352 |
|
✗ |
throw_pretty("Invalid argument: " << "Disturbance constant is positive"); |
| 353 |
|
|
} |
| 354 |
|
✗ |
e_jac_ = disturbance; |
| 355 |
|
✗ |
e_hess_ = sqrt(Scalar(2.0) * e_jac_); |
| 356 |
|
|
} |
| 357 |
|
|
|
| 358 |
|
|
template <typename Scalar> |
| 359 |
|
✗ |
bool DifferentialActionModelNumDiffTpl<Scalar>::get_with_gauss_approx() { |
| 360 |
|
✗ |
return with_gauss_approx_; |
| 361 |
|
|
} |
| 362 |
|
|
|
| 363 |
|
|
template <typename Scalar> |
| 364 |
|
✗ |
void DifferentialActionModelNumDiffTpl<Scalar>::print(std::ostream& os) const { |
| 365 |
|
✗ |
os << "DifferentialActionModelNumDiffTpl {action=" << *model_ << "}"; |
| 366 |
|
|
} |
| 367 |
|
|
|
| 368 |
|
|
template <typename Scalar> |
| 369 |
|
✗ |
void DifferentialActionModelNumDiffTpl<Scalar>::assertStableStateFD( |
| 370 |
|
|
const Eigen::Ref<const VectorXs>& /** x */) { |
| 371 |
|
|
// TODO(cmastalli): First we need to do it AMNumDiff and then to replicate it. |
| 372 |
|
|
} |
| 373 |
|
|
|
| 374 |
|
|
} // namespace crocoddyl |
| 375 |
|
|
|