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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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#ifndef CROCODDYL_CORE_ACTIONS_DIFF_LQR_HPP_ |
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#define CROCODDYL_CORE_ACTIONS_DIFF_LQR_HPP_ |
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#include "crocoddyl/core/diff-action-base.hpp" |
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#include "crocoddyl/core/fwd.hpp" |
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#include "crocoddyl/core/states/euclidean.hpp" |
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namespace crocoddyl { |
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/** |
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* @brief Linear-quadratic regulator (LQR) differential action model |
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* |
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* A linear-quadratic regulator (LQR) action has a transition model of the form |
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* \f[ \begin{equation} |
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* \mathbf{\dot{v}} = \mathbf{A_q q + A_v v + B u + f}. |
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* \end{equation} \f] |
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* Its cost function is quadratic of the form: |
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* \f[ \begin{equation} |
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* \ell(\mathbf{x},\mathbf{u}) = \begin{bmatrix}1 |
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* \\ \mathbf{x} \\ \mathbf{u}\end{bmatrix}^T \begin{bmatrix}0 & |
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* \mathbf{q}^T & \mathbf{r}^T \\ \mathbf{q} & \mathbf{Q} |
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* & |
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* \mathbf{N}^T \\ |
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* \mathbf{r} & \mathbf{N} & \mathbf{R}\end{bmatrix} |
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* \begin{bmatrix}1 \\ \mathbf{x} \\ |
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* \mathbf{u}\end{bmatrix} |
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* \end{equation} \f] |
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* and the linear equality and inequality constraints has the form: |
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* \f[ \begin{aligned} |
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* \mathbf{g(x,u)} = \mathbf{G}\begin{bmatrix} \mathbf{x} \\ \mathbf{u} |
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* \end{bmatrix} [x,u] + \mathbf{g} \leq \mathbf{0} |
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* &\mathbf{h(x,u)} = \mathbf{H}\begin{bmatrix} \mathbf{x} \\ \mathbf{u} |
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* \end{bmatrix} [x,u] + \mathbf{h} \end{aligned} \f] |
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*/ |
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template <typename _Scalar> |
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class DifferentialActionModelLQRTpl |
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: public DifferentialActionModelAbstractTpl<_Scalar> { |
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public: |
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EIGEN_MAKE_ALIGNED_OPERATOR_NEW |
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CROCODDYL_DERIVED_CAST(DifferentialActionModelBase, |
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DifferentialActionModelLQRTpl) |
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typedef _Scalar Scalar; |
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typedef MathBaseTpl<Scalar> MathBase; |
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typedef DifferentialActionModelAbstractTpl<Scalar> Base; |
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typedef DifferentialActionDataLQRTpl<Scalar> Data; |
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typedef StateVectorTpl<Scalar> StateVector; |
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typedef DifferentialActionDataAbstractTpl<Scalar> |
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DifferentialActionDataAbstract; |
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typedef typename MathBase::VectorXs VectorXs; |
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typedef typename MathBase::MatrixXs MatrixXs; |
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/** |
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* @brief Initialize the LQR action model |
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* |
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* @param[in] Aq Position matrix |
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* @param[in] Av Velocity matrix |
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* @param[in] B Input matrix |
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* @param[in] Q State weight matrix |
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* @param[in] R Input weight matrix |
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* @param[in] N State-input weight matrix |
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*/ |
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DifferentialActionModelLQRTpl(const MatrixXs& Aq, const MatrixXs& Av, |
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const MatrixXs& B, const MatrixXs& Q, |
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const MatrixXs& R, const MatrixXs& N); |
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/** |
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* @brief Initialize the LQR action model |
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* |
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* @param[in] Aq Position matrix |
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* @param[in] Av Velocity matrix |
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* @param[in] B Input matrix |
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* @param[in] Q State weight matrix |
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* @param[in] R Input weight matrix |
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* @param[in] N State-input weight matrix |
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* @param[in] f Dynamics drift |
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* @param[in] q State weight vector |
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* @param[in] r Input weight vector |
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*/ |
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DifferentialActionModelLQRTpl(const MatrixXs& Aq, const MatrixXs& Av, |
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const MatrixXs& B, const MatrixXs& Q, |
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const MatrixXs& R, const MatrixXs& N, |
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const VectorXs& f, const VectorXs& q, |
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const VectorXs& r); |
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/** |
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* @brief Initialize the LQR action model |
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* |
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* @param[in] Aq Position matrix |
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* @param[in] Av Velocity matrix |
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* @param[in] B Input matrix |
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* @param[in] Q State weight matrix |
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* @param[in] R Input weight matrix |
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* @param[in] N State-input weight matrix |
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* @param[in] G State-input inequality constraint matrix |
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* @param[in] H State-input equality constraint matrix |
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* @param[in] f Dynamics drift |
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* @param[in] q State weight vector |
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* @param[in] r Input weight vector |
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* @param[in] g State-input inequality constraint bias |
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* @param[in] h State-input equality constraint bias |
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*/ |
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DifferentialActionModelLQRTpl(const MatrixXs& Aq, const MatrixXs& Av, |
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const MatrixXs& B, const MatrixXs& Q, |
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const MatrixXs& R, const MatrixXs& N, |
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const MatrixXs& G, const MatrixXs& H, |
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const VectorXs& f, const VectorXs& q, |
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const VectorXs& r, const VectorXs& g, |
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const VectorXs& h); |
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/** |
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* @brief Initialize the LQR action model |
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* |
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* @param[in] nq Dimension of position vector |
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* @param[in] nu Dimension of control vector |
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* @param[in] drif_free Enable / disable the bias term of the linear dynamics |
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* (default true) |
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*/ |
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DifferentialActionModelLQRTpl(const std::size_t nq, const std::size_t nu, |
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const bool drift_free = true); |
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/** @brief Copy constructor */ |
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DifferentialActionModelLQRTpl(const DifferentialActionModelLQRTpl& copy); |
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virtual ~DifferentialActionModelLQRTpl() = default; |
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virtual void calc(const std::shared_ptr<DifferentialActionDataAbstract>& data, |
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const Eigen::Ref<const VectorXs>& x, |
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const Eigen::Ref<const VectorXs>& u) override; |
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virtual void calc(const std::shared_ptr<DifferentialActionDataAbstract>& data, |
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const Eigen::Ref<const VectorXs>& x) override; |
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virtual void 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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const Eigen::Ref<const VectorXs>& u) override; |
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virtual void calcDiff( |
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const std::shared_ptr<DifferentialActionDataAbstract>& data, |
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const Eigen::Ref<const VectorXs>& x) override; |
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virtual std::shared_ptr<DifferentialActionDataAbstract> createData() override; |
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/** |
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* @brief Cast the differential-LQR model to a different scalar type. |
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* |
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* It is useful for operations requiring different precision or scalar types. |
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* |
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* @tparam NewScalar The new scalar type to cast to. |
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* @return DifferentialActionModelLQRTpl<NewScalar> A differential-action |
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* model with the new scalar type. |
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*/ |
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template <typename NewScalar> |
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DifferentialActionModelLQRTpl<NewScalar> cast() const; |
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virtual bool checkData( |
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const std::shared_ptr<DifferentialActionDataAbstract>& data) override; |
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/** |
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* @brief Create a random LQR model |
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* |
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* @param[in] nq Position dimension |
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* @param[in] nu Control dimension |
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* @param[in] ng Inequality constraint dimension (default 0) |
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* @param[in] nh Equality constraint dimension (default 0) |
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*/ |
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static DifferentialActionModelLQRTpl Random(const std::size_t nq, |
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const std::size_t nu, |
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const std::size_t ng = 0, |
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const std::size_t nh = 0); |
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/** @brief Return the position matrix */ |
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const MatrixXs& get_Aq() const; |
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/** @brief Return the velocity matrix */ |
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const MatrixXs& get_Av() const; |
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/** @brief Return the input matrix */ |
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const MatrixXs& get_B() const; |
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/** @brief Return the dynamics drift */ |
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const VectorXs& get_f() const; |
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/** @brief Return the state weight matrix */ |
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const MatrixXs& get_Q() const; |
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/** @brief Return the input weight matrix */ |
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const MatrixXs& get_R() const; |
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/** @brief Return the state-input weight matrix */ |
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const MatrixXs& get_N() const; |
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/** @brief Return the state-input inequality constraint matrix */ |
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const MatrixXs& get_G() const; |
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/** @brief Return the state-input equality constraint matrix */ |
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const MatrixXs& get_H() const; |
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/** @brief Return the state weight vector */ |
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const VectorXs& get_q() const; |
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/** @brief Return the input weight vector */ |
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const VectorXs& get_r() const; |
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/** @brief Return the state-input inequality constraint bias */ |
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const VectorXs& get_g() const; |
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/** @brief Return the state-input equality constraint bias */ |
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const VectorXs& get_h() const; |
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/** |
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* @brief Modify the LQR action model |
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* |
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* @param[in] Aq Position matrix |
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* @param[in] Av Velocity matrix |
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* @param[in] B Input matrix |
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* @param[in] Q State weight matrix |
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* @param[in] R Input weight matrix |
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* @param[in] N State-input weight matrix |
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* @param[in] G State-input inequality constraint matrix |
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* @param[in] H State-input equality constraint matrix |
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* @param[in] f Dynamics drift |
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* @param[in] q State weight vector |
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* @param[in] r Input weight vector |
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* @param[in] g State-input inequality constraint bias |
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* @param[in] h State-input equality constraint bias |
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*/ |
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void set_LQR(const MatrixXs& Aq, const MatrixXs& Av, const MatrixXs& B, |
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const MatrixXs& Q, const MatrixXs& R, const MatrixXs& N, |
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const MatrixXs& G, const MatrixXs& H, const VectorXs& f, |
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const VectorXs& q, const VectorXs& r, const VectorXs& g, |
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const VectorXs& h); |
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DEPRECATED("Use get_Aq", const MatrixXs& get_Fq() const { return get_Aq(); }) |
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DEPRECATED("Use get_Av", const MatrixXs& get_Fv() const { return get_Av(); }) |
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DEPRECATED("Use get_B", const MatrixXs& get_Fu() const { return get_B(); }) |
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DEPRECATED("Use get_f", const VectorXs& get_f0() const { return get_f(); }) |
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DEPRECATED("Use get_q", const VectorXs& get_lx() const { return get_q(); }) |
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DEPRECATED("Use get_r", const VectorXs& get_lu() const { return get_r(); }) |
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DEPRECATED("Use get_Q", const MatrixXs& get_Lxx() const { return get_Q(); }) |
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DEPRECATED("Use get_N", const MatrixXs& get_Lxu() const { return get_N(); }) |
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DEPRECATED("Use get_R", const MatrixXs& get_Luu() const { return get_R(); }) |
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DEPRECATED( |
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"Use set_LQR", void set_Fq(const MatrixXs& Aq) { |
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set_LQR(Aq, Av_, B_, Q_, R_, N_, G_, H_, f_, q_, r_, g_, h_); |
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}) |
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DEPRECATED( |
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"Use set_LQR", void set_Fv(const MatrixXs& Av) { |
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set_LQR(Aq_, Av, B_, Q_, R_, N_, G_, H_, f_, q_, r_, g_, h_); |
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}) |
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DEPRECATED( |
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"Use set_LQR", void set_Fu(const MatrixXs& B) { |
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set_LQR(Aq_, Av_, B, Q_, R_, N_, G_, H_, f_, q_, r_, g_, h_); |
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}) |
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DEPRECATED( |
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"Use set_LQR", void set_f0(const VectorXs& f) { |
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set_LQR(Aq_, Av_, B_, Q_, R_, N_, G_, H_, f, q_, r_, g_, h_); |
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}) |
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DEPRECATED( |
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"Use set_LQR", void set_lx(const VectorXs& q) { |
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set_LQR(Aq_, Av_, B_, Q_, R_, N_, G_, H_, f_, q, r_, g_, h_); |
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}) |
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DEPRECATED( |
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"Use set_LQR", void set_lu(const VectorXs& r) { |
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set_LQR(Aq_, Av_, B_, Q_, R_, N_, G_, H_, f_, q_, r, g_, h_); |
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}) |
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DEPRECATED( |
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"Use set_LQR", void set_Lxx(const MatrixXs& Q) { |
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set_LQR(Aq_, Av_, B_, Q, R_, N_, G_, H_, f_, q_, r_, g_, h_); |
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}) |
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DEPRECATED( |
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"Use set_LQR", void set_Lxu(const MatrixXs& N) { |
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set_LQR(Aq_, Av_, B_, Q_, R_, N, G_, H_, f_, q_, r_, g_, h_); |
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}) |
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DEPRECATED( |
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"Use set_LQR", void set_Luu(const MatrixXs& R) { |
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set_LQR(Aq_, Av_, B_, Q_, R, N_, G_, H_, f_, q_, r_, g_, h_); |
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}) |
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/** |
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* @brief Print relevant information of the LQR model |
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* |
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* @param[out] os Output stream object |
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*/ |
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virtual void print(std::ostream& os) const override; |
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protected: |
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using Base::ng_; //!< Equality constraint dimension |
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using Base::nh_; //!< Inequality constraint dimension |
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using Base::nu_; //!< Control dimension |
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using Base::state_; //!< Model of the state |
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private: |
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MatrixXs Aq_; |
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MatrixXs Av_; |
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MatrixXs B_; |
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MatrixXs Q_; |
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MatrixXs R_; |
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MatrixXs N_; |
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MatrixXs G_; |
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MatrixXs H_; |
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VectorXs f_; |
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VectorXs q_; |
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VectorXs r_; |
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VectorXs g_; |
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VectorXs h_; |
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MatrixXs L_; |
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bool drift_free_; |
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bool updated_lqr_; |
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}; |
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template <typename _Scalar> |
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struct DifferentialActionDataLQRTpl |
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: public DifferentialActionDataAbstractTpl<_Scalar> { |
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typedef _Scalar Scalar; |
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typedef MathBaseTpl<Scalar> MathBase; |
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typedef DifferentialActionDataAbstractTpl<Scalar> Base; |
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typedef typename MathBase::VectorXs VectorXs; |
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typedef typename MathBase::MatrixXs MatrixXs; |
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template <template <typename Scalar> class Model> |
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explicit DifferentialActionDataLQRTpl(Model<Scalar>* const model) |
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: Base(model) { |
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// Setting the linear model and quadratic cost as they are constant |
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const std::size_t nq = model->get_state()->get_nq(); |
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const std::size_t nu = model->get_nu(); |
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Fx.leftCols(nq) = model->get_Aq(); |
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✗ |
Fx.rightCols(nq) = model->get_Av(); |
| 335 |
|
✗ |
Fu = model->get_B(); |
| 336 |
|
✗ |
Lxx = model->get_Q(); |
| 337 |
|
✗ |
Luu = model->get_R(); |
| 338 |
|
✗ |
Lxu = model->get_N(); |
| 339 |
|
✗ |
Gx = model->get_G().leftCols(2 * nq); |
| 340 |
|
✗ |
Gu = model->get_G().rightCols(nu); |
| 341 |
|
✗ |
Hx = model->get_H().leftCols(2 * nq); |
| 342 |
|
✗ |
Hu = model->get_H().rightCols(nu); |
| 343 |
|
|
} |
| 344 |
|
✗ |
virtual ~DifferentialActionDataLQRTpl() = default; |
| 345 |
|
|
|
| 346 |
|
|
using Base::cost; |
| 347 |
|
|
using Base::Fu; |
| 348 |
|
|
using Base::Fx; |
| 349 |
|
|
using Base::Gu; |
| 350 |
|
|
using Base::Gx; |
| 351 |
|
|
using Base::Hu; |
| 352 |
|
|
using Base::Hx; |
| 353 |
|
|
using Base::Lu; |
| 354 |
|
|
using Base::Luu; |
| 355 |
|
|
using Base::Lx; |
| 356 |
|
|
using Base::Lxu; |
| 357 |
|
|
using Base::Lxx; |
| 358 |
|
|
using Base::r; |
| 359 |
|
|
using Base::xout; |
| 360 |
|
|
}; |
| 361 |
|
|
|
| 362 |
|
|
} // namespace crocoddyl |
| 363 |
|
|
|
| 364 |
|
|
/* --- Details -------------------------------------------------------------- */ |
| 365 |
|
|
/* --- Details -------------------------------------------------------------- */ |
| 366 |
|
|
/* --- Details -------------------------------------------------------------- */ |
| 367 |
|
|
#include "crocoddyl/core/actions/diff-lqr.hxx" |
| 368 |
|
|
|
| 369 |
|
|
CROCODDYL_DECLARE_EXTERN_TEMPLATE_CLASS( |
| 370 |
|
|
crocoddyl::DifferentialActionModelLQRTpl) |
| 371 |
|
|
CROCODDYL_DECLARE_EXTERN_TEMPLATE_STRUCT( |
| 372 |
|
|
crocoddyl::DifferentialActionDataLQRTpl) |
| 373 |
|
|
|
| 374 |
|
|
#endif // CROCODDYL_CORE_ACTIONS_DIFF_LQR_HPP_ |
| 375 |
|
|
|