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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, New York University, |
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// Max Planck Gesellschaft, 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_NUMDIFF_ACTION_HPP_ |
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#define CROCODDYL_CORE_NUMDIFF_ACTION_HPP_ |
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#include "crocoddyl/core/action-base.hpp" |
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#include "crocoddyl/core/fwd.hpp" |
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namespace crocoddyl { |
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/** |
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* @brief This class computes the numerical differentiation of an action model. |
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* |
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* It computes the Jacobian of the cost, its residual and dynamics via numerical |
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* differentiation. It considers that the action model owns a cost residual and |
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* the cost is the square of this residual, i.e., |
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* \f$\ell(\mathbf{x},\mathbf{u})=\frac{1}{2}\|\mathbf{r}(\mathbf{x},\mathbf{u})\|^2\f$, |
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* where \f$\mathbf{r}(\mathbf{x},\mathbf{u})\f$ is the residual vector. The |
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* Hessian is computed only through the Gauss-Newton approximation, i.e., |
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* \f{eqnarray*}{ |
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* \mathbf{\ell}_\mathbf{xx} &=& \mathbf{R_x}^T\mathbf{R_x} \\ |
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* \mathbf{\ell}_\mathbf{uu} &=& \mathbf{R_u}^T\mathbf{R_u} \\ |
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* \mathbf{\ell}_\mathbf{xu} &=& \mathbf{R_x}^T\mathbf{R_u} |
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* \f} |
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* where the Jacobians of the cost residuals are denoted by \f$\mathbf{R_x}\f$ |
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* and \f$\mathbf{R_u}\f$. Note that this approximation ignores the tensor |
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* products (e.g., \f$\mathbf{R_{xx}}\mathbf{r}\f$). |
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* |
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* Finally, in the case that the cost does not have a residual, we set the |
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* Hessian to zero, i.e., \f$\mathbf{L_{xx}} = \mathbf{L_{xu}} = \mathbf{L_{uu}} |
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* = \mathbf{0}\f$. |
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* |
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* \sa `ActionModelAbstractTpl()`, `calcDiff()` |
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*/ |
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template <typename _Scalar> |
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class ActionModelNumDiffTpl : public ActionModelAbstractTpl<_Scalar> { |
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public: |
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EIGEN_MAKE_ALIGNED_OPERATOR_NEW |
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CROCODDYL_DERIVED_CAST(ActionModelBase, ActionModelNumDiffTpl) |
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typedef _Scalar Scalar; |
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typedef ActionDataAbstractTpl<Scalar> ActionDataAbstract; |
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typedef ActionModelAbstractTpl<Scalar> Base; |
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typedef ActionDataNumDiffTpl<Scalar> Data; |
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typedef MathBaseTpl<Scalar> MathBase; |
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typedef typename MathBaseTpl<Scalar>::VectorXs VectorXs; |
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typedef typename MathBaseTpl<Scalar>::MatrixXs MatrixXs; |
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/** |
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* @brief Initialize the numdiff action model |
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* |
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* @param[in] model Action model that we want to apply the |
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* numerical differentiation |
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* @param[in] with_gauss_approx True if we want to use the Gauss |
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* approximation for computing the Hessians |
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*/ |
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explicit ActionModelNumDiffTpl(std::shared_ptr<Base> model, |
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bool with_gauss_approx = false); |
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virtual ~ActionModelNumDiffTpl() = default; |
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/** |
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* @brief @copydoc Base::calc() |
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*/ |
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virtual void calc(const std::shared_ptr<ActionDataAbstract>& 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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/** |
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* @brief @copydoc Base::calc(const std::shared_ptr<ActionDataAbstract>& |
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* data, const Eigen::Ref<const VectorXs>& x) |
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*/ |
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virtual void calc(const std::shared_ptr<ActionDataAbstract>& data, |
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const Eigen::Ref<const VectorXs>& x) override; |
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/** |
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* @brief @copydoc Base::calcDiff() |
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*/ |
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virtual void calcDiff(const std::shared_ptr<ActionDataAbstract>& 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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/** |
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* @brief @copydoc Base::calcDiff(const std::shared_ptr<ActionDataAbstract>& |
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* data, const Eigen::Ref<const VectorXs>& x) |
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*/ |
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virtual void calcDiff(const std::shared_ptr<ActionDataAbstract>& data, |
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const Eigen::Ref<const VectorXs>& x) override; |
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/** |
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* @brief @copydoc Base::createData() |
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*/ |
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virtual std::shared_ptr<ActionDataAbstract> createData() override; |
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/** |
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* @brief @copydoc Base::quasiStatic() |
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*/ |
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virtual void quasiStatic(const std::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)) override; |
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/** |
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* @brief Cast the action numdiff 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 ActionModelNumDiffTpl<NewScalar> An action model with the new |
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* scalar type. |
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*/ |
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template <typename NewScalar> |
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ActionModelNumDiffTpl<NewScalar> cast() const; |
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/** |
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* @brief Return the acton model that we use to numerical differentiate |
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*/ |
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const std::shared_ptr<Base>& get_model() const; |
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/** |
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* @brief Return the disturbance constant used in the numerical |
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* differentiation routine |
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*/ |
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const Scalar get_disturbance() const; |
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/** |
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* @brief Modify the disturbance constant used in the numerical |
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* differentiation routine |
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*/ |
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void set_disturbance(const Scalar disturbance); |
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/** |
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* @brief Identify if the Gauss approximation is going to be used or not. |
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*/ |
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bool get_with_gauss_approx(); |
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/** |
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* @brief Print relevant information of the diff-action numdiff 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::has_control_limits_; //!< Indicates whether any of the control |
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//!< limits |
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using Base::nr_; //!< Dimension of the cost residual |
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using Base::nu_; //!< Control dimension |
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using Base::state_; //!< Model of the state |
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using Base::u_lb_; //!< Lower control limits |
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using Base::u_ub_; //!< Upper control limits |
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private: |
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/** |
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* @brief Make sure that when we finite difference the Action Model, the user |
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* does not face unknown behaviour because of the finite differencing of a |
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* quaternion around pi. This behaviour might occur if CostModelState and |
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* FloatingInContact differential model are used together. |
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* |
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* For full discussions see issue |
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* https://gepgitlab.laas.fr/loco-3d/crocoddyl/issues/139 |
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* |
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* @param x is the state at which the check is performed. |
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*/ |
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void assertStableStateFD(const Eigen::Ref<const VectorXs>& x); |
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std::shared_ptr<Base> model_; //!< Action model hat we want to apply the |
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//!< numerical differentiation |
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Scalar e_jac_; //!< Constant used for computing disturbances in Jacobian |
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//!< calculation |
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Scalar e_hess_; //!< Constant used for computing disturbances in Hessian |
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//!< calculation |
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bool with_gauss_approx_; //!< True if we want to use the Gauss approximation |
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//!< for computing the Hessians |
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}; |
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template <typename _Scalar> |
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struct ActionDataNumDiffTpl : public ActionDataAbstractTpl<_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 ActionDataAbstractTpl<Scalar> Base; |
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typedef typename MathBaseTpl<Scalar>::VectorXs VectorXs; |
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typedef typename MathBaseTpl<Scalar>::MatrixXs MatrixXs; |
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/** |
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* @brief Initialize the numdiff action data |
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* |
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* @tparam Model is the type of the `ActionModelAbstractTpl`. |
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* @param model is the object to compute the numerical differentiation from. |
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*/ |
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template <template <typename Scalar> class Model> |
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explicit ActionDataNumDiffTpl(Model<Scalar>* const model) |
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: Base(model), |
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Rx(model->get_model()->get_nr(), |
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model->get_model()->get_state()->get_ndx()), |
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Ru(model->get_model()->get_nr(), model->get_model()->get_nu()), |
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dx(model->get_model()->get_state()->get_ndx()), |
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du(model->get_model()->get_nu()), |
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xp(model->get_model()->get_state()->get_nx()) { |
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Rx.setZero(); |
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Ru.setZero(); |
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dx.setZero(); |
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du.setZero(); |
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xp.setZero(); |
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const std::size_t ndx = model->get_model()->get_state()->get_ndx(); |
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const std::size_t nu = model->get_model()->get_nu(); |
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data_0 = model->get_model()->createData(); |
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for (std::size_t i = 0; i < ndx; ++i) { |
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data_x.push_back(model->get_model()->createData()); |
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} |
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for (std::size_t i = 0; i < nu; ++i) { |
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data_u.push_back(model->get_model()->createData()); |
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} |
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} |
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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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Scalar x_norm; //!< Norm of the state vector |
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Scalar |
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xh_jac; //!< Disturbance value used for computing \f$ \ell_\mathbf{x} \f$ |
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Scalar |
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uh_jac; //!< Disturbance value used for computing \f$ \ell_\mathbf{u} \f$ |
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Scalar xh_hess; //!< Disturbance value used for computing \f$ |
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//!< \ell_\mathbf{xx} \f$ |
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Scalar uh_hess; //!< Disturbance value used for computing \f$ |
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//!< \ell_\mathbf{uu} \f$ |
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Scalar xh_hess_pow2; |
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Scalar uh_hess_pow2; |
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Scalar xuh_hess_pow2; |
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MatrixXs Rx; //!< Cost residual jacobian: \f$ \frac{d r(x,u)}{dx} \f$ |
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MatrixXs Ru; //!< Cost residual jacobian: \f$ \frac{d r(x,u)}{du} \f$ |
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VectorXs dx; //!< State disturbance |
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VectorXs du; //!< Control disturbance |
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VectorXs xp; //!< The integrated state from the disturbance on one DoF "\f$ |
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//!< \int x dx_i \f$" |
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std::shared_ptr<Base> data_0; //!< The data that contains the final results |
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std::vector<std::shared_ptr<Base> > |
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data_x; //!< The temporary data associated with the state variation |
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std::vector<std::shared_ptr<Base> > |
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data_u; //!< The temporary data associated with the control variation |
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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/numdiff/action.hxx" |
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CROCODDYL_DECLARE_EXTERN_TEMPLATE_CLASS(crocoddyl::ActionModelNumDiffTpl) |
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CROCODDYL_DECLARE_EXTERN_TEMPLATE_STRUCT(crocoddyl::ActionDataNumDiffTpl) |
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#endif // CROCODDYL_CORE_NUMDIFF_ACTION_HPP_ |
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