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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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// Heriot-Watt University |
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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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namespace crocoddyl { |
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template <typename Scalar> |
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ActionModelLQRTpl<Scalar>::ActionModelLQRTpl(const MatrixXs& A, |
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const MatrixXs& B, |
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const MatrixXs& Q, |
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const MatrixXs& R, |
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const MatrixXs& N) |
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: Base(std::make_shared<StateVector>(A.cols()), B.cols(), 0), |
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drift_free_(true), |
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updated_lqr_(false) { |
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const std::size_t nx = state_->get_nx(); |
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MatrixXs G = MatrixXs::Zero(ng_, nx + nu_); |
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MatrixXs H = MatrixXs::Zero(nh_, nx + nu_); |
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VectorXs f = VectorXs::Zero(nx); |
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VectorXs q = VectorXs::Zero(nx); |
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VectorXs r = VectorXs::Zero(nu_); |
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VectorXs g = VectorXs::Zero(ng_); |
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VectorXs h = VectorXs::Zero(nh_); |
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set_LQR(A, B, Q, R, N, G, H, f, q, r, g, h); |
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} |
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template <typename Scalar> |
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ActionModelLQRTpl<Scalar>::ActionModelLQRTpl( |
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const MatrixXs& A, const MatrixXs& B, const MatrixXs& Q, const MatrixXs& R, |
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const MatrixXs& N, const VectorXs& f, const VectorXs& q, const VectorXs& r) |
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: Base(std::make_shared<StateVector>(A.cols()), B.cols(), 0), |
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drift_free_(false), |
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updated_lqr_(false) { |
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const std::size_t nx = state_->get_nx(); |
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MatrixXs G = MatrixXs::Zero(ng_, nx + nu_); |
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MatrixXs H = MatrixXs::Zero(ng_, nx + nu_); |
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VectorXs g = VectorXs::Zero(ng_); |
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VectorXs h = VectorXs::Zero(nh_); |
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set_LQR(A, B, Q, R, N, G, H, f, q, r, g, h); |
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} |
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template <typename Scalar> |
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ActionModelLQRTpl<Scalar>::ActionModelLQRTpl( |
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const MatrixXs& A, const MatrixXs& B, const MatrixXs& Q, const MatrixXs& R, |
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const MatrixXs& N, const MatrixXs& G, const MatrixXs& H, const VectorXs& f, |
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const VectorXs& q, const VectorXs& r, const VectorXs& g, const VectorXs& h) |
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: Base(std::make_shared<StateVector>(A.cols()), B.cols(), 0, G.rows(), |
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H.rows(), G.rows(), H.rows()), |
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drift_free_(false), |
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updated_lqr_(false) { |
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set_LQR(A, B, Q, R, N, G, H, f, q, r, g, h); |
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} |
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template <typename Scalar> |
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ActionModelLQRTpl<Scalar>::ActionModelLQRTpl(const std::size_t nx, |
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const std::size_t nu, |
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const bool drift_free) |
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: Base(std::make_shared<StateVector>(nx), nu, 0), |
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A_(MatrixXs::Identity(nx, nx)), |
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B_(MatrixXs::Identity(nx, nu)), |
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Q_(MatrixXs::Identity(nx, nx)), |
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R_(MatrixXs::Identity(nu, nu)), |
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N_(MatrixXs::Zero(nx, nu)), |
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G_(MatrixXs::Zero(0, nx + nu)), |
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H_(MatrixXs::Zero(0, nx + nu)), |
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f_(drift_free ? VectorXs::Zero(nx) : VectorXs::Ones(nx)), |
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q_(VectorXs::Ones(nx)), |
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r_(VectorXs::Ones(nu)), |
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g_(VectorXs::Zero(0)), |
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h_(VectorXs::Zero(0)), |
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drift_free_(drift_free) {} |
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template <typename Scalar> |
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ActionModelLQRTpl<Scalar>::ActionModelLQRTpl(const ActionModelLQRTpl& copy) |
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: Base(std::make_shared<StateVector>(copy.get_A().cols()), |
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copy.get_B().cols(), 0, copy.get_G().rows(), copy.get_H().rows(), |
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copy.get_G().rows(), copy.get_H().rows()), |
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drift_free_(false), |
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updated_lqr_(false) { |
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set_LQR(copy.get_A(), copy.get_B(), copy.get_Q(), copy.get_R(), copy.get_N(), |
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copy.get_G(), copy.get_H(), copy.get_f(), copy.get_q(), copy.get_r(), |
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copy.get_g(), copy.get_h()); |
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} |
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template <typename Scalar> |
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void ActionModelLQRTpl<Scalar>::calc( |
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const std::shared_ptr<ActionDataAbstract>& 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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data->xnext.noalias() = A_ * x; |
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data->xnext.noalias() += B_ * u; |
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data->xnext += f_; |
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// cost = 0.5 * x^T * Q * x + 0.5 * u^T * R * u + x^T * N * u + q^T * x + r^T |
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// * u |
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d->Q_x_tmp.noalias() = Q_ * x; |
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data->cost = Scalar(0.5) * x.dot(d->Q_x_tmp); |
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d->R_u_tmp.noalias() = R_ * u; |
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data->cost += Scalar(0.5) * u.dot(d->R_u_tmp); |
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d->Q_x_tmp.noalias() = N_ * u; |
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data->cost += x.dot(d->Q_x_tmp); |
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data->cost += q_.dot(x); |
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data->cost += r_.dot(u); |
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// constraints |
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const std::size_t nx = state_->get_nx(); |
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data->g.noalias() = G_.leftCols(nx) * x; |
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data->g.noalias() += G_.rightCols(nu_) * u; |
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data->g += g_; |
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data->h.noalias() = H_.leftCols(nx) * x; |
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data->h.noalias() += H_.rightCols(nu_) * u; |
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data->h += h_; |
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} |
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template <typename Scalar> |
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void ActionModelLQRTpl<Scalar>::calc( |
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const std::shared_ptr<ActionDataAbstract>& 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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d->xnext = x; |
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// cost = 0.5 * x^T * Q * x + q^T * x |
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d->Q_x_tmp.noalias() = Q_ * x; |
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data->cost = Scalar(0.5) * x.dot(d->Q_x_tmp); |
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data->cost += q_.dot(x); |
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// constraints |
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const std::size_t nx = state_->get_nx(); |
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data->g.noalias() = G_.leftCols(nx) * x; |
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data->g += g_; |
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data->h.noalias() = H_.leftCols(nx) * x; |
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data->h += h_; |
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} |
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template <typename Scalar> |
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void ActionModelLQRTpl<Scalar>::calcDiff( |
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const std::shared_ptr<ActionDataAbstract>& 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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const std::size_t nx = state_->get_nx(); |
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if (!updated_lqr_) { |
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data->Fx = A_; |
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data->Fu = B_; |
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data->Lxx = Q_; |
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data->Luu = R_; |
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data->Lxu = N_; |
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data->Gx = G_.leftCols(nx); |
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data->Gu = G_.rightCols(nu_); |
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data->Hx = H_.leftCols(nx); |
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data->Hu = H_.rightCols(nu_); |
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updated_lqr_ = true; |
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} |
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data->Lx = q_; |
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data->Lx.noalias() += Q_ * x; |
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data->Lx.noalias() += N_ * u; |
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data->Lu = r_; |
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data->Lu.noalias() += N_.transpose() * x; |
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data->Lu.noalias() += R_ * u; |
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} |
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template <typename Scalar> |
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void ActionModelLQRTpl<Scalar>::calcDiff( |
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const std::shared_ptr<ActionDataAbstract>& 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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const std::size_t nx = state_->get_nx(); |
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if (!updated_lqr_) { |
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data->Lxx = Q_; |
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data->Gx = G_.leftCols(nx); |
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data->Hx = H_.leftCols(nx); |
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updated_lqr_ = true; |
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} |
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data->Lx = q_; |
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data->Lx.noalias() += Q_ * x; |
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} |
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template <typename Scalar> |
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std::shared_ptr<ActionDataAbstractTpl<Scalar>> |
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ActionModelLQRTpl<Scalar>::createData() { |
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return std::allocate_shared<Data>(Eigen::aligned_allocator<Data>(), this); |
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} |
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template <typename Scalar> |
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template <typename NewScalar> |
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ActionModelLQRTpl<NewScalar> ActionModelLQRTpl<Scalar>::cast() const { |
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typedef ActionModelLQRTpl<NewScalar> ReturnType; |
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ReturnType ret(A_.template cast<NewScalar>(), B_.template cast<NewScalar>(), |
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Q_.template cast<NewScalar>(), R_.template cast<NewScalar>(), |
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N_.template cast<NewScalar>(), G_.template cast<NewScalar>(), |
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H_.template cast<NewScalar>(), f_.template cast<NewScalar>(), |
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q_.template cast<NewScalar>(), r_.template cast<NewScalar>(), |
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g_.template cast<NewScalar>(), h_.template cast<NewScalar>()); |
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return ret; |
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} |
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template <typename Scalar> |
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bool ActionModelLQRTpl<Scalar>::checkData( |
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const std::shared_ptr<ActionDataAbstract>& data) { |
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std::shared_ptr<Data> d = std::dynamic_pointer_cast<Data>(data); |
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if (d != NULL) { |
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return true; |
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} else { |
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return false; |
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} |
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} |
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template <typename Scalar> |
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✗ |
ActionModelLQRTpl<Scalar> ActionModelLQRTpl<Scalar>::Random( |
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const std::size_t nx, const std::size_t nu, const std::size_t ng, |
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const std::size_t nh) { |
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MatrixXs A = MatrixXs::Random(nx, nx); |
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MatrixXs B = MatrixXs::Random(nx, nu); |
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MatrixXs L_tmp = MatrixXs::Random(nx + nu, nx + nu); |
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MatrixXs L = L_tmp.transpose() * L_tmp; |
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const Eigen::Block<MatrixXs> Q = L.topLeftCorner(nx, nx); |
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const Eigen::Block<MatrixXs> R = L.bottomRightCorner(nu, nu); |
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const Eigen::Block<MatrixXs> N = L.topRightCorner(nx, nu); |
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MatrixXs G = MatrixXs::Random(ng, nx + nu); |
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MatrixXs H = MatrixXs::Random(nh, nx + nu); |
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VectorXs f = VectorXs::Random(nx); |
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VectorXs q = VectorXs::Random(nx); |
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VectorXs r = VectorXs::Random(nu); |
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VectorXs g = VectorXs::Random(ng); |
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VectorXs h = VectorXs::Random(nh); |
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return ActionModelLQRTpl<Scalar>(A, B, Q, R, N, G, H, f, q, r, g, h); |
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} |
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template <typename Scalar> |
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✗ |
void ActionModelLQRTpl<Scalar>::print(std::ostream& os) const { |
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✗ |
os << "ActionModelLQR {nx=" << state_->get_nx() << ", nu=" << nu_ |
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✗ |
<< ", ng=" << ng_ << ", nh=" << nh_ << ", drift_free=" << drift_free_ |
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✗ |
<< "}"; |
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} |
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template <typename Scalar> |
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✗ |
const typename MathBaseTpl<Scalar>::MatrixXs& ActionModelLQRTpl<Scalar>::get_A() |
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const { |
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return A_; |
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} |
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template <typename Scalar> |
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const typename MathBaseTpl<Scalar>::MatrixXs& ActionModelLQRTpl<Scalar>::get_B() |
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const { |
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return B_; |
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} |
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template <typename Scalar> |
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const typename MathBaseTpl<Scalar>::VectorXs& ActionModelLQRTpl<Scalar>::get_f() |
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const { |
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return f_; |
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} |
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template <typename Scalar> |
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✗ |
const typename MathBaseTpl<Scalar>::MatrixXs& ActionModelLQRTpl<Scalar>::get_Q() |
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const { |
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return Q_; |
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} |
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template <typename Scalar> |
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✗ |
const typename MathBaseTpl<Scalar>::MatrixXs& ActionModelLQRTpl<Scalar>::get_R() |
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const { |
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✗ |
return R_; |
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} |
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template <typename Scalar> |
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const typename MathBaseTpl<Scalar>::MatrixXs& ActionModelLQRTpl<Scalar>::get_N() |
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const { |
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return N_; |
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} |
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| 308 |
|
|
template <typename Scalar> |
| 309 |
|
✗ |
const typename MathBaseTpl<Scalar>::MatrixXs& ActionModelLQRTpl<Scalar>::get_G() |
| 310 |
|
|
const { |
| 311 |
|
✗ |
return G_; |
| 312 |
|
|
} |
| 313 |
|
|
|
| 314 |
|
|
template <typename Scalar> |
| 315 |
|
✗ |
const typename MathBaseTpl<Scalar>::MatrixXs& ActionModelLQRTpl<Scalar>::get_H() |
| 316 |
|
|
const { |
| 317 |
|
✗ |
return H_; |
| 318 |
|
|
} |
| 319 |
|
|
|
| 320 |
|
|
template <typename Scalar> |
| 321 |
|
✗ |
const typename MathBaseTpl<Scalar>::VectorXs& ActionModelLQRTpl<Scalar>::get_q() |
| 322 |
|
|
const { |
| 323 |
|
✗ |
return q_; |
| 324 |
|
|
} |
| 325 |
|
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|
| 326 |
|
|
template <typename Scalar> |
| 327 |
|
✗ |
const typename MathBaseTpl<Scalar>::VectorXs& ActionModelLQRTpl<Scalar>::get_r() |
| 328 |
|
|
const { |
| 329 |
|
✗ |
return r_; |
| 330 |
|
|
} |
| 331 |
|
|
|
| 332 |
|
|
template <typename Scalar> |
| 333 |
|
✗ |
const typename MathBaseTpl<Scalar>::VectorXs& ActionModelLQRTpl<Scalar>::get_g() |
| 334 |
|
|
const { |
| 335 |
|
✗ |
return g_; |
| 336 |
|
|
} |
| 337 |
|
|
|
| 338 |
|
|
template <typename Scalar> |
| 339 |
|
✗ |
const typename MathBaseTpl<Scalar>::VectorXs& ActionModelLQRTpl<Scalar>::get_h() |
| 340 |
|
|
const { |
| 341 |
|
✗ |
return h_; |
| 342 |
|
|
} |
| 343 |
|
|
|
| 344 |
|
|
template <typename Scalar> |
| 345 |
|
✗ |
void ActionModelLQRTpl<Scalar>::set_LQR(const MatrixXs& A, const MatrixXs& B, |
| 346 |
|
|
const MatrixXs& Q, const MatrixXs& R, |
| 347 |
|
|
const MatrixXs& N, const MatrixXs& G, |
| 348 |
|
|
const MatrixXs& H, const VectorXs& f, |
| 349 |
|
|
const VectorXs& q, const VectorXs& r, |
| 350 |
|
|
const VectorXs& g, const VectorXs& h) { |
| 351 |
|
✗ |
const std::size_t nx = state_->get_nx(); |
| 352 |
|
✗ |
if (static_cast<std::size_t>(A.rows()) != nx) { |
| 353 |
|
✗ |
throw_pretty( |
| 354 |
|
|
"Invalid argument: " << "A should be a squared matrix with size " + |
| 355 |
|
|
std::to_string(nx)); |
| 356 |
|
|
} |
| 357 |
|
✗ |
if (static_cast<std::size_t>(B.rows()) != nx) { |
| 358 |
|
✗ |
throw_pretty( |
| 359 |
|
|
"Invalid argument: " << "B has wrong dimension (it should have " + |
| 360 |
|
|
std::to_string(nx) + " rows)"); |
| 361 |
|
|
} |
| 362 |
|
✗ |
if (static_cast<std::size_t>(Q.rows()) != nx || |
| 363 |
|
✗ |
static_cast<std::size_t>(Q.cols()) != nx) { |
| 364 |
|
✗ |
throw_pretty("Invalid argument: " |
| 365 |
|
|
<< "Q has wrong dimension (it should be " + |
| 366 |
|
|
std::to_string(nx) + " x " + std::to_string(nx) + ")"); |
| 367 |
|
|
} |
| 368 |
|
✗ |
if (static_cast<std::size_t>(R.rows()) != nu_ || |
| 369 |
|
✗ |
static_cast<std::size_t>(R.cols()) != nu_) { |
| 370 |
|
✗ |
throw_pretty( |
| 371 |
|
|
"Invalid argument: " << "R has wrong dimension (it should be " + |
| 372 |
|
|
std::to_string(nu_) + " x " + |
| 373 |
|
|
std::to_string(nu_) + ")"); |
| 374 |
|
|
} |
| 375 |
|
✗ |
if (static_cast<std::size_t>(N.rows()) != nx || |
| 376 |
|
✗ |
static_cast<std::size_t>(N.cols()) != nu_) { |
| 377 |
|
✗ |
throw_pretty("Invalid argument: " |
| 378 |
|
|
<< "N has wrong dimension (it should be " + |
| 379 |
|
|
std::to_string(nx) + " x " + std::to_string(nu_) + ")"); |
| 380 |
|
|
} |
| 381 |
|
✗ |
if (static_cast<std::size_t>(G.rows()) != ng_ || |
| 382 |
|
✗ |
static_cast<std::size_t>(G.cols()) != nx + nu_) { |
| 383 |
|
✗ |
throw_pretty( |
| 384 |
|
|
"Invalid argument: " << "G has wrong dimension (it should be " + |
| 385 |
|
|
std::to_string(ng_) + " x " + |
| 386 |
|
|
std::to_string(nx + nu_) + ")"); |
| 387 |
|
|
} |
| 388 |
|
✗ |
if (static_cast<std::size_t>(H.rows()) != nh_ || |
| 389 |
|
✗ |
static_cast<std::size_t>(H.cols()) != nx + nu_) { |
| 390 |
|
✗ |
throw_pretty( |
| 391 |
|
|
"Invalid argument: " << "H has wrong dimension (it should be " + |
| 392 |
|
|
std::to_string(nh_) + " x " + |
| 393 |
|
|
std::to_string(nx + nu_) + ")"); |
| 394 |
|
|
} |
| 395 |
|
✗ |
if (static_cast<std::size_t>(f.size()) != nx) { |
| 396 |
|
✗ |
throw_pretty( |
| 397 |
|
|
"Invalid argument: " << "f has wrong dimension (it should be " + |
| 398 |
|
|
std::to_string(nx) + ")"); |
| 399 |
|
|
} |
| 400 |
|
✗ |
if (static_cast<std::size_t>(q.size()) != nx) { |
| 401 |
|
✗ |
throw_pretty( |
| 402 |
|
|
"Invalid argument: " << "q has wrong dimension (it should be " + |
| 403 |
|
|
std::to_string(nx) + ")"); |
| 404 |
|
|
} |
| 405 |
|
✗ |
if (static_cast<std::size_t>(r.size()) != nu_) { |
| 406 |
|
✗ |
throw_pretty( |
| 407 |
|
|
"Invalid argument: " << "r has wrong dimension (it should be " + |
| 408 |
|
|
std::to_string(nu_) + ")"); |
| 409 |
|
|
} |
| 410 |
|
✗ |
if (static_cast<std::size_t>(g.size()) != ng_) { |
| 411 |
|
✗ |
throw_pretty( |
| 412 |
|
|
"Invalid argument: " << "g has wrong dimension (it should be " + |
| 413 |
|
|
std::to_string(ng_) + ")"); |
| 414 |
|
|
} |
| 415 |
|
✗ |
if (static_cast<std::size_t>(h.size()) != nh_) { |
| 416 |
|
✗ |
throw_pretty( |
| 417 |
|
|
"Invalid argument: " << "h has wrong dimension (it should be " + |
| 418 |
|
|
std::to_string(nh_) + ")"); |
| 419 |
|
|
} |
| 420 |
|
✗ |
L_ = MatrixXs::Zero(nx + nu_, nx + nu_); |
| 421 |
|
✗ |
L_ << Q, N, N.transpose(), R; |
| 422 |
|
✗ |
if (!checkPSD(L_)) { |
| 423 |
|
✗ |
throw_pretty("Invalid argument " |
| 424 |
|
|
<< "[Q, N; N.T, R] is not positive semi-definite"); |
| 425 |
|
|
} |
| 426 |
|
✗ |
A_ = A; |
| 427 |
|
✗ |
B_ = B; |
| 428 |
|
✗ |
f_ = f; |
| 429 |
|
✗ |
Q_ = Q; |
| 430 |
|
✗ |
R_ = R; |
| 431 |
|
✗ |
N_ = N; |
| 432 |
|
✗ |
G_ = G; |
| 433 |
|
✗ |
H_ = H; |
| 434 |
|
✗ |
q_ = q; |
| 435 |
|
✗ |
r_ = r; |
| 436 |
|
✗ |
g_ = g; |
| 437 |
|
✗ |
h_ = h; |
| 438 |
|
✗ |
updated_lqr_ = false; |
| 439 |
|
|
} |
| 440 |
|
|
|
| 441 |
|
|
} // namespace crocoddyl |
| 442 |
|
|
|