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/////////////////////////////////////////////////////////////////////////////// |
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// BSD 3-Clause License |
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// |
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// Copyright (C) 2019-2022, LAAS-CNRS, IRI: CSIC-UPC, 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_INTEGRATOR_RK4_HPP_ |
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#define CROCODDYL_CORE_INTEGRATOR_RK4_HPP_ |
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#include "crocoddyl/core/fwd.hpp" |
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#include "crocoddyl/core/integ-action-base.hpp" |
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#include "crocoddyl/core/utils/deprecate.hpp" |
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namespace crocoddyl { |
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/** |
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* @brief Standard RK4 integrator |
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* |
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* It applies a standard RK4 integration scheme to a differential (i.e., |
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* continuous time) action model. |
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* |
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* This standard RK4 scheme introduces also the possibility to parametrize the |
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* control trajectory inside an integration step, for instance using |
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* polynomials. This requires introducing some notation to clarify the |
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* difference between the control inputs of the differential model and the |
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* control inputs to the integrated model. We have decided to use |
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* \f$\mathbf{w}\f$ to refer to the control inputs of the differential model and |
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* \f$\mathbf{u}\f$ for the control inputs of the integrated action model. |
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* |
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* \sa `IntegratedActionModelAbstractTpl`, `calc()`, `calcDiff()`, |
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* `createData()` |
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*/ |
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template <typename _Scalar> |
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class IntegratedActionModelRK4Tpl |
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: public IntegratedActionModelAbstractTpl<_Scalar> { |
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public: |
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EIGEN_MAKE_ALIGNED_OPERATOR_NEW |
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typedef _Scalar Scalar; |
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typedef MathBaseTpl<Scalar> MathBase; |
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typedef IntegratedActionModelAbstractTpl<Scalar> Base; |
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typedef IntegratedActionDataRK4Tpl<Scalar> Data; |
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typedef ActionDataAbstractTpl<Scalar> ActionDataAbstract; |
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typedef DifferentialActionModelAbstractTpl<Scalar> |
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DifferentialActionModelAbstract; |
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typedef ControlParametrizationModelAbstractTpl<Scalar> |
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ControlParametrizationModelAbstract; |
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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 RK4 integrator |
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* |
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* @param[in] model Differential action model |
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* @param[in] control Control parametrization |
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* @param[in] time_step Step time (default 1e-3) |
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* @param[in] with_cost_residual Compute cost residual (default true) |
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*/ |
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DEPRECATED("Use IntegratedActionModelRK", |
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IntegratedActionModelRK4Tpl( |
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boost::shared_ptr<DifferentialActionModelAbstract> model, |
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boost::shared_ptr<ControlParametrizationModelAbstract> control, |
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const Scalar time_step = Scalar(1e-3), |
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const bool with_cost_residual = true);) |
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/** |
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* @brief Initialize the RK4 integrator |
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* |
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* This initialization uses `ControlParametrizationPolyZeroTpl` for the |
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* control parametrization. |
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* |
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* @param[in] model Differential action model |
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* @param[in] time_step Step time (default 1e-3) |
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* @param[in] with_cost_residual Compute cost residual (default true) |
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*/ |
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DEPRECATED("Use IntegratedActionModelRK", |
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IntegratedActionModelRK4Tpl( |
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boost::shared_ptr<DifferentialActionModelAbstract> model, |
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const Scalar time_step = Scalar(1e-3), |
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const bool with_cost_residual = true);) |
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virtual ~IntegratedActionModelRK4Tpl(); |
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/** |
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* @brief Integrate the differential action model using RK4 scheme |
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* |
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* @param[in] data RK4 integrator data |
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* @param[in] x State point \f$\mathbf{x}\in\mathbb{R}^{ndx}\f$ |
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* @param[in] u Control input \f$\mathbf{u}\in\mathbb{R}^{nu}\f$ |
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*/ |
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virtual void calc(const boost::shared_ptr<ActionDataAbstract>& data, |
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const Eigen::Ref<const VectorXs>& x, |
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const Eigen::Ref<const VectorXs>& u); |
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/** |
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* @brief Integrate the total cost value for nodes that depends only on the |
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* state using RK4 scheme |
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* |
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* It computes the total cost and defines the next state as the current one. |
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* This function is used in the terminal nodes of an optimal control problem. |
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* |
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* @param[in] data RK4 integrator data |
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* @param[in] x State point \f$\mathbf{x}\in\mathbb{R}^{ndx}\f$ |
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*/ |
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virtual void calc(const boost::shared_ptr<ActionDataAbstract>& data, |
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const Eigen::Ref<const VectorXs>& x); |
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/** |
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* @brief Compute the partial derivatives of the RK4 integrator |
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* |
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* @param[in] data RK4 integrator data |
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* @param[in] x State point \f$\mathbf{x}\in\mathbb{R}^{ndx}\f$ |
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* @param[in] u Control input \f$\mathbf{u}\in\mathbb{R}^{nu}\f$ |
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*/ |
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virtual void calcDiff(const boost::shared_ptr<ActionDataAbstract>& data, |
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const Eigen::Ref<const VectorXs>& x, |
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const Eigen::Ref<const VectorXs>& u); |
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/** |
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* @brief Compute the partial derivatives of the cost |
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* |
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* It updates the derivatives of the cost function with respect to the state |
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* only. This function is used in the terminal nodes of an optimal control |
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* problem. |
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* |
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* @param[in] data RK4 integrator data |
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* @param[in] x State point \f$\mathbf{x}\in\mathbb{R}^{ndx}\f$ |
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*/ |
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virtual void calcDiff(const boost::shared_ptr<ActionDataAbstract>& data, |
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const Eigen::Ref<const VectorXs>& x); |
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/** |
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* @brief Create the RK4 integrator data |
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* |
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* @return the RK4 integrator data |
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*/ |
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virtual boost::shared_ptr<ActionDataAbstract> createData(); |
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/** |
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* @brief Checks that a specific data belongs to this model |
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*/ |
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virtual bool checkData(const boost::shared_ptr<ActionDataAbstract>& data); |
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/** |
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* @brief Computes the quasic static commands |
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* |
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* The quasic static commands are the ones produced for a the reference |
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* posture as an equilibrium point, i.e. for |
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* \f$\mathbf{f^q_x}\delta\mathbf{q}+\mathbf{f_u}\delta\mathbf{u}=\mathbf{0}\f$ |
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* |
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* @param[in] data RK4 integrator data |
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* @param[out] u Quasic static commands |
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* @param[in] x State point (velocity has to be zero) |
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* @param[in] maxiter Maximum allowed number of iterations |
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* @param[in] tol Tolerance |
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*/ |
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virtual void quasiStatic(const boost::shared_ptr<ActionDataAbstract>& data, |
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Eigen::Ref<VectorXs> u, |
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const Eigen::Ref<const VectorXs>& x, |
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const std::size_t maxiter = 100, |
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const Scalar tol = Scalar(1e-9)); |
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/** |
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* @brief Print relevant information of the RK4 integrator 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; |
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protected: |
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using Base::control_; //!< Control parametrization |
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using Base::differential_; //!< Differential action model |
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using Base::ng_; //!< Number of inequality constraints |
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using Base::nh_; //!< Number of equality constraints |
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using Base::nu_; //!< Dimension of the control |
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using Base::state_; //!< Model of the state |
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using Base::time_step2_; //!< Square of the time step used for integration |
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using Base::time_step_; //!< Time step used for integration |
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using Base::with_cost_residual_; //!< Flag indicating whether a cost residual |
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//!< is used |
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private: |
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std::array<Scalar, 4> rk4_c_; |
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}; |
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template <typename _Scalar> |
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struct IntegratedActionDataRK4Tpl |
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: public IntegratedActionDataAbstractTpl<_Scalar> { |
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EIGEN_MAKE_ALIGNED_OPERATOR_NEW |
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typedef _Scalar Scalar; |
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typedef MathBaseTpl<Scalar> MathBase; |
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typedef IntegratedActionDataAbstractTpl<Scalar> Base; |
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typedef DifferentialActionDataAbstractTpl<Scalar> |
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DifferentialActionDataAbstract; |
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typedef ControlParametrizationDataAbstractTpl<Scalar> |
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ControlParametrizationDataAbstract; |
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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 IntegratedActionDataRK4Tpl(Model<Scalar>* const model) |
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: Base(model), |
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integral(4, Scalar(0.)), |
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dx(model->get_state()->get_ndx()), |
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ki(4, VectorXs::Zero(model->get_state()->get_ndx())), |
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y(4, VectorXs::Zero(model->get_state()->get_nx())), |
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ws(4, VectorXs::Zero(model->get_control()->get_nw())), |
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dx_rk4(4, VectorXs::Zero(model->get_state()->get_ndx())), |
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dki_dx(4, MatrixXs::Zero(model->get_state()->get_ndx(), |
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model->get_state()->get_ndx())), |
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dki_du(4, |
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MatrixXs::Zero(model->get_state()->get_ndx(), model->get_nu())), |
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dyi_dx(4, MatrixXs::Zero(model->get_state()->get_ndx(), |
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model->get_state()->get_ndx())), |
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dyi_du(4, |
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MatrixXs::Zero(model->get_state()->get_ndx(), model->get_nu())), |
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dli_dx(4, VectorXs::Zero(model->get_state()->get_ndx())), |
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dli_du(4, VectorXs::Zero(model->get_nu())), |
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ddli_ddx(4, MatrixXs::Zero(model->get_state()->get_ndx(), |
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model->get_state()->get_ndx())), |
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ddli_ddw(4, MatrixXs::Zero(model->get_control()->get_nw(), |
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model->get_control()->get_nw())), |
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ddli_ddu(4, MatrixXs::Zero(model->get_nu(), model->get_nu())), |
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ddli_dxdw(4, MatrixXs::Zero(model->get_state()->get_ndx(), |
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model->get_control()->get_nw())), |
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ddli_dxdu( |
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4, MatrixXs::Zero(model->get_state()->get_ndx(), model->get_nu())), |
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ddli_dwdu( |
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4, MatrixXs::Zero(model->get_control()->get_nw(), model->get_nu())), |
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Luu_partialx(4, MatrixXs::Zero(model->get_nu(), model->get_nu())), |
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Lxu_i(4, |
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MatrixXs::Zero(model->get_state()->get_ndx(), model->get_nu())), |
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Lxx_partialx(4, MatrixXs::Zero(model->get_state()->get_ndx(), |
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model->get_state()->get_ndx())), |
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Lxx_partialu( |
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4, MatrixXs::Zero(model->get_state()->get_ndx(), model->get_nu())) { |
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dx.setZero(); |
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for (std::size_t i = 0; i < 4; ++i) { |
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differential.push_back(boost::shared_ptr<DifferentialActionDataAbstract>( |
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model->get_differential()->createData())); |
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control.push_back(boost::shared_ptr<ControlParametrizationDataAbstract>( |
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model->get_control()->createData())); |
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} |
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const std::size_t nv = model->get_state()->get_nv(); |
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dyi_dx[0].diagonal().setOnes(); |
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dki_dx[0].topRightCorner(nv, nv).diagonal().setOnes(); |
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} |
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virtual ~IntegratedActionDataRK4Tpl() {} |
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std::vector<boost::shared_ptr<DifferentialActionDataAbstract> > |
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differential; //!< List of differential model data |
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std::vector<boost::shared_ptr<ControlParametrizationDataAbstract> > |
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control; //!< List of control parametrization data |
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std::vector<Scalar> integral; |
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VectorXs dx; //!< State rate |
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std::vector<VectorXs> ki; //!< List of RK4 terms related to system dynamics |
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std::vector<VectorXs> |
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y; //!< List of states where f is evaluated in the RK4 integration |
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std::vector<VectorXs> |
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ws; //!< Control inputs evaluated in the RK4 integration |
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std::vector<VectorXs> dx_rk4; |
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std::vector<MatrixXs> |
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dki_dx; //!< List of partial derivatives of RK4 nodes with respect to the |
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//!< state of the RK4 integration. dki/dx |
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std::vector<MatrixXs> |
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dki_du; //!< List of partial derivatives of RK4 nodes with respect to the |
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//!< control parameters of the RK4 integration. dki/du |
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std::vector<MatrixXs> |
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dyi_dx; //!< List of partial derivatives of RK4 dynamics with respect to |
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//!< the state of the RK4 integrator. dyi/dx |
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std::vector<MatrixXs> |
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dyi_du; //!< List of partial derivatives of RK4 dynamics with respect to |
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//!< the control parameters of the RK4 integrator. dyi/du |
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std::vector<VectorXs> |
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dli_dx; //!< List of partial derivatives of the cost with respect to the |
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//!< state of the RK4 integration. dli_dx |
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std::vector<VectorXs> |
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dli_du; //!< List of partial derivatives of the cost with respect to the |
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//!< control input of the RK4 integration. dli_du |
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std::vector<MatrixXs> |
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ddli_ddx; //!< List of second partial derivatives of the cost with |
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//!< respect to the state of the RK4 integration. ddli_ddx |
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std::vector<MatrixXs> |
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ddli_ddw; //!< List of second partial derivatives of the cost with |
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//!< respect to the control parameters of the RK4 integration. |
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//!< ddli_ddw |
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std::vector<MatrixXs> ddli_ddu; //!< List of second partial derivatives of |
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//!< the cost with respect to the control |
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//!< input of the RK4 integration. ddli_ddu |
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std::vector<MatrixXs> |
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ddli_dxdw; //!< List of second partial derivatives of the cost with |
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//!< respect to the state and control input of the RK4 |
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//!< integration. ddli_dxdw |
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std::vector<MatrixXs> |
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ddli_dxdu; //!< List of second partial derivatives of the cost with |
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//!< respect to the state and control parameters of the RK4 |
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//!< integration. ddli_dxdu |
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std::vector<MatrixXs> |
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ddli_dwdu; //!< List of second partial derivatives of the cost with |
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//!< respect to the control parameters and inputs control of |
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//!< the RK4 integration. ddli_dwdu |
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std::vector<MatrixXs> Luu_partialx; |
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std::vector<MatrixXs> Lxu_i; |
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std::vector<MatrixXs> Lxx_partialx; |
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std::vector<MatrixXs> Lxx_partialu; |
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using Base::cost; |
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using Base::Fu; |
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using Base::Fx; |
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using Base::Lu; |
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using Base::Luu; |
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using Base::Lx; |
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using Base::Lxu; |
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using Base::Lxx; |
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using Base::r; |
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using Base::xnext; |
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}; |
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} // namespace crocoddyl |
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/* --- Details -------------------------------------------------------------- */ |
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/* --- Details -------------------------------------------------------------- */ |
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/* --- Details -------------------------------------------------------------- */ |
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#include "crocoddyl/core/integrator/rk4.hxx" |
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#endif // CROCODDYL_CORE_INTEGRATOR_RK4_HPP_ |
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