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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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// University of Oxford, 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_ACTION_BASE_HPP_ |
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#define CROCODDYL_CORE_ACTION_BASE_HPP_ |
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#include "crocoddyl/core/fwd.hpp" |
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#include "crocoddyl/core/state-base.hpp" |
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namespace crocoddyl { |
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class ActionModelBase { |
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public: |
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virtual ~ActionModelBase() = default; |
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CROCODDYL_BASE_CAST(ActionModelBase, ActionModelAbstractTpl) |
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}; |
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/** |
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* @brief Abstract class for action model |
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* |
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* An action model combines dynamics, cost functions and constraints. Each node, |
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* in our optimal control problem, is described through an action model. Every |
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* time that we want describe a problem, we need to provide ways of computing |
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* the dynamics, cost functions, constraints and their derivatives. All these is |
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* described inside the action model. |
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* |
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* Concretely speaking, the action model describes a time-discrete action model |
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* with a first-order ODE along a cost function, i.e. |
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* - the state \f$\mathbf{z}\in\mathcal{Z}\f$ lies in a manifold described with |
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* a `nx`-tuple, |
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* - the state rate \f$\mathbf{\dot{x}}\in T_{\mathbf{q}}\mathcal{Q}\f$ is the |
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* tangent vector to the state manifold with `ndx` dimension, |
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* - the control input \f$\mathbf{u}\in\mathbb{R}^{nu}\f$ is an Euclidean |
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* vector |
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* - \f$\mathbf{r}(\cdot)\f$ and \f$a(\cdot)\f$ are the residual and activation |
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* functions (see `ResidualModelAbstractTpl` and `ActivationModelAbstractTpl`, |
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* respetively), |
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* - \f$\mathbf{g}(\cdot)\in\mathbb{R}^{ng}\f$ and |
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* \f$\mathbf{h}(\cdot)\in\mathbb{R}^{nh}\f$ are the inequality and equality |
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* vector functions, respectively. |
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* |
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* The computation of these equations are carried out out inside `calc()` |
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* function. In short, this function computes the system acceleration, cost and |
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* constraints values (also called constraints violations). This procedure is |
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* equivalent to running a forward pass of the action model. |
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* |
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* However, during numerical optimization, we also need to run backward passes |
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* of the action model. These calculations are performed by `calcDiff()`. In |
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* short, this method builds a linear-quadratic approximation of the action |
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* model, i.e.: \f[ \begin{aligned} |
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* &\delta\mathbf{x}_{k+1} = |
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* \mathbf{f_x}\delta\mathbf{x}_k+\mathbf{f_u}\delta\mathbf{u}_k, |
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* &\textrm{(dynamics)}\\ |
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* &\ell(\delta\mathbf{x}_k,\delta\mathbf{u}_k) = \begin{bmatrix}1 |
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* \\ \delta\mathbf{x}_k \\ \delta\mathbf{u}_k\end{bmatrix}^T \begin{bmatrix}0 & |
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* \mathbf{\ell_x}^T & \mathbf{\ell_u}^T \\ \mathbf{\ell_x} & \mathbf{\ell_{xx}} |
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* & |
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* \mathbf{\ell_{ux}}^T \\ |
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* \mathbf{\ell_u} & \mathbf{\ell_{ux}} & \mathbf{\ell_{uu}}\end{bmatrix} |
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* \begin{bmatrix}1 \\ \delta\mathbf{x}_k \\ |
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* \delta\mathbf{u}_k\end{bmatrix}, &\textrm{(cost)}\\ |
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* &\mathbf{g}(\delta\mathbf{x}_k,\delta\mathbf{u}_k)<\mathbf{0}, |
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* &\textrm{(inequality constraint)}\\ |
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* &\mathbf{h}(\delta\mathbf{x}_k,\delta\mathbf{u}_k)=\mathbf{0}, |
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* &\textrm{(equality constraint)} \end{aligned} \f] where |
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* - \f$\mathbf{f_x}\in\mathbb{R}^{ndx\times ndx}\f$ and |
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* \f$\mathbf{f_u}\in\mathbb{R}^{ndx\times nu}\f$ are the Jacobians of the |
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* dynamics, |
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* - \f$\mathbf{\ell_x}\in\mathbb{R}^{ndx}\f$ and |
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* \f$\mathbf{\ell_u}\in\mathbb{R}^{nu}\f$ are the Jacobians of the cost |
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* function, |
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* - \f$\mathbf{\ell_{xx}}\in\mathbb{R}^{ndx\times ndx}\f$, |
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* \f$\mathbf{\ell_{xu}}\in\mathbb{R}^{ndx\times nu}\f$ and |
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* \f$\mathbf{\ell_{uu}}\in\mathbb{R}^{nu\times nu}\f$ are the Hessians of the |
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* cost function, |
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* - \f$\mathbf{g_x}\in\mathbb{R}^{ng\times ndx}\f$ and |
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* \f$\mathbf{g_u}\in\mathbb{R}^{ng\times nu}\f$ are the Jacobians of the |
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* inequality constraints, and |
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* - \f$\mathbf{h_x}\in\mathbb{R}^{nh\times ndx}\f$ and |
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* \f$\mathbf{h_u}\in\mathbb{R}^{nh\times nu}\f$ are the Jacobians of the |
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* equality constraints. |
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* |
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* Additionally, it is important to note that `calcDiff()` computes the |
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* derivatives using the latest stored values by `calc()`. Thus, we need to |
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* first run `calc()`. |
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* |
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* \sa `calc()`, `calcDiff()`, `createData()` |
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*/ |
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template <typename _Scalar> |
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class ActionModelAbstractTpl : public ActionModelBase { |
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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 typename ScalarSelector<Scalar>::type ScalarType; |
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typedef MathBaseTpl<Scalar> MathBase; |
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typedef ActionDataAbstractTpl<Scalar> ActionDataAbstract; |
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typedef StateAbstractTpl<Scalar> StateAbstract; |
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typedef typename MathBase::VectorXs VectorXs; |
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/** |
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* @brief Initialize the action model |
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* |
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* @param[in] state State description |
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* @param[in] nu Dimension of control vector |
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* @param[in] nr Dimension of cost-residual vector |
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* @param[in] ng Number of inequality constraints (default 0) |
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* @param[in] nh Number of equality constraints (default 0) |
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* @param[in] ng_T Number of inequality terminal constraints (default 0) |
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* @param[in] nh_T Number of equality terminal constraints (default 0) |
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*/ |
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ActionModelAbstractTpl(std::shared_ptr<StateAbstract> state, |
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const std::size_t nu, const std::size_t nr = 0, |
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const std::size_t ng = 0, const std::size_t nh = 0, |
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const std::size_t ng_T = 0, |
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const std::size_t nh_T = 0); |
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/** |
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* @brief Copy constructor |
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* @param other Action model to be copied |
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*/ |
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ActionModelAbstractTpl(const ActionModelAbstractTpl<Scalar>& other); |
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virtual ~ActionModelAbstractTpl() = default; |
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/** |
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* @brief Compute the next state and cost value |
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* |
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* @param[in] data Action 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 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) = 0; |
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/** |
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* @brief Compute the total cost value for nodes that depends only on the |
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* state |
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* |
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* It updates the total cost and the next state is not computed as it is not |
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* expected to change. This function is used in the terminal nodes of an |
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* optimal control problem. |
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* |
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* @param[in] data Action 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 std::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 derivatives of the dynamics and cost functions |
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* |
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* It computes the partial derivatives of the dynamical system and the cost |
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* function. It assumes that `calc()` has been run first. This function builds |
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* a linear-quadratic approximation of the action model (i.e. dynamical system |
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* and cost function). |
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* |
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* @param[in] data Action 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 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) = 0; |
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/** |
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* @brief Compute the derivatives of the cost functions with respect to the |
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* state only |
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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 Action 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 std::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 action data |
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* |
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* @return the action data |
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*/ |
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virtual std::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 std::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 Action 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 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)); |
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/** |
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* @copybrief quasicStatic() |
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* |
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* @copydetails quasicStatic() |
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* |
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* @param[in] data Action data |
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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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* @return Quasic static commands |
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*/ |
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VectorXs quasiStatic_x(const std::shared_ptr<ActionDataAbstract>& data, |
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const VectorXs& x, 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 Return the dimension of the control input |
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*/ |
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std::size_t get_nu() const; |
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/** |
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* @brief Return the dimension of the cost-residual vector |
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*/ |
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std::size_t get_nr() const; |
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/** |
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* @brief Return the number of inequality constraints |
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*/ |
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virtual std::size_t get_ng() const; |
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/** |
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* @brief Return the number of equality constraints |
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*/ |
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virtual std::size_t get_nh() const; |
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/** |
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* @brief Return the number of inequality terminal constraints |
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*/ |
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virtual std::size_t get_ng_T() const; |
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/** |
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* @brief Return the number of equality terminal constraints |
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*/ |
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virtual std::size_t get_nh_T() const; |
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/** |
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* @brief Return the state |
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*/ |
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const std::shared_ptr<StateAbstract>& get_state() const; |
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/** |
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* @brief Return the lower bound of the inequality constraints |
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*/ |
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virtual const VectorXs& get_g_lb() const; |
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/** |
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* @brief Return the upper bound of the inequality constraints |
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*/ |
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virtual const VectorXs& get_g_ub() const; |
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/** |
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* @brief Return the control lower bound |
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*/ |
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const VectorXs& get_u_lb() const; |
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/** |
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* @brief Return the control upper bound |
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*/ |
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const VectorXs& get_u_ub() const; |
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/** |
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* @brief Indicates if there are defined control limits |
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*/ |
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bool get_has_control_limits() const; |
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/** |
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* @brief Modify the lower bound of the inequality constraints |
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*/ |
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void set_g_lb(const VectorXs& g_lb); |
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/** |
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* @brief Modify the upper bound of the inequality constraints |
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*/ |
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void set_g_ub(const VectorXs& g_ub); |
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/** |
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* @brief Modify the control lower bounds |
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*/ |
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void set_u_lb(const VectorXs& u_lb); |
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/** |
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* @brief Modify the control upper bounds |
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*/ |
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void set_u_ub(const VectorXs& u_ub); |
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/** |
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* @brief Print information on the action model |
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*/ |
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template <class Scalar> |
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friend std::ostream& operator<<(std::ostream& os, |
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const ActionModelAbstractTpl<Scalar>& model); |
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/** |
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* @brief Print relevant information of the action 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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std::size_t nu_; //!< Control dimension |
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std::size_t nr_; //!< Dimension of the cost residual |
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std::size_t ng_; //!< Number of inequality constraints |
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std::size_t nh_; //!< Number of equality constraints |
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std::size_t ng_T_; //!< Number of inequality terminal constraints |
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std::size_t nh_T_; //!< Number of equality terminal constraints |
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std::shared_ptr<StateAbstract> state_; //!< Model of the state |
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VectorXs unone_; //!< Neutral state |
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VectorXs g_lb_; //!< Lower bound of the inequality constraints |
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VectorXs g_ub_; //!< Lower bound of the inequality constraints |
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VectorXs u_lb_; //!< Lower control limits |
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VectorXs u_ub_; //!< Upper control limits |
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bool has_control_limits_; //!< Indicates whether any of the control limits is |
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//!< finite |
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ActionModelAbstractTpl() |
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: nu_(0), nr_(0), ng_(0), nh_(0), ng_T_(0), nh_T_(0), state_(nullptr) {} |
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/** |
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* @brief Update the status of the control limits (i.e. if there are defined |
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* limits) |
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*/ |
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void update_has_control_limits(); |
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template <class Scalar> |
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friend class ConstraintModelManagerTpl; |
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}; |
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| 355 |
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template <typename _Scalar> |
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struct ActionDataAbstractTpl { |
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EIGEN_MAKE_ALIGNED_OPERATOR_NEW |
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| 359 |
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typedef _Scalar Scalar; |
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typedef MathBaseTpl<Scalar> MathBase; |
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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 ActionDataAbstractTpl(Model<Scalar>* const model) |
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: cost(Scalar(0.)), |
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xnext(model->get_state()->get_nx()), |
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Fx(model->get_state()->get_ndx(), model->get_state()->get_ndx()), |
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Fu(model->get_state()->get_ndx(), model->get_nu()), |
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r(model->get_nr()), |
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Lx(model->get_state()->get_ndx()), |
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Lu(model->get_nu()), |
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Lxx(model->get_state()->get_ndx(), model->get_state()->get_ndx()), |
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Lxu(model->get_state()->get_ndx(), model->get_nu()), |
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Luu(model->get_nu(), model->get_nu()), |
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g(model->get_ng() > model->get_ng_T() ? model->get_ng() |
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: model->get_ng_T()), |
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Gx(model->get_ng() > model->get_ng_T() ? model->get_ng() |
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: model->get_ng_T(), |
| 380 |
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model->get_state()->get_ndx()), |
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Gu(model->get_ng() > model->get_ng_T() ? model->get_ng() |
| 382 |
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: model->get_ng_T(), |
| 383 |
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model->get_nu()), |
| 384 |
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h(model->get_nh() > model->get_nh_T() ? model->get_nh() |
| 385 |
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: model->get_nh_T()), |
| 386 |
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Hx(model->get_nh() > model->get_nh_T() ? model->get_nh() |
| 387 |
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: model->get_nh_T(), |
| 388 |
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model->get_state()->get_ndx()), |
| 389 |
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Hu(model->get_nh() > model->get_nh_T() ? model->get_nh() |
| 390 |
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: model->get_nh_T(), |
| 391 |
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model->get_nu()) { |
| 392 |
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xnext.setZero(); |
| 393 |
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Fx.setZero(); |
| 394 |
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Fu.setZero(); |
| 395 |
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r.setZero(); |
| 396 |
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Lx.setZero(); |
| 397 |
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✗ |
Lu.setZero(); |
| 398 |
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✗ |
Lxx.setZero(); |
| 399 |
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✗ |
Lxu.setZero(); |
| 400 |
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✗ |
Luu.setZero(); |
| 401 |
|
✗ |
g.setZero(); |
| 402 |
|
✗ |
Gx.setZero(); |
| 403 |
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✗ |
Gu.setZero(); |
| 404 |
|
✗ |
h.setZero(); |
| 405 |
|
✗ |
Hx.setZero(); |
| 406 |
|
✗ |
Hu.setZero(); |
| 407 |
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|
} |
| 408 |
|
✗ |
virtual ~ActionDataAbstractTpl() = default; |
| 409 |
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| 410 |
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Scalar cost; //!< cost value |
| 411 |
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VectorXs xnext; //!< evolution state |
| 412 |
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MatrixXs Fx; //!< Jacobian of the dynamics w.r.t. the state \f$\mathbf{x}\f$ |
| 413 |
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MatrixXs |
| 414 |
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Fu; //!< Jacobian of the dynamics w.r.t. the control \f$\mathbf{u}\f$ |
| 415 |
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VectorXs r; //!< Cost residual |
| 416 |
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|
VectorXs Lx; //!< Jacobian of the cost w.r.t. the state \f$\mathbf{x}\f$ |
| 417 |
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|
VectorXs Lu; //!< Jacobian of the cost w.r.t. the control \f$\mathbf{u}\f$ |
| 418 |
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MatrixXs Lxx; //!< Hessian of the cost w.r.t. the state \f$\mathbf{x}\f$ |
| 419 |
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|
MatrixXs Lxu; //!< Hessian of the cost w.r.t. the state \f$\mathbf{x}\f$ and |
| 420 |
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|
//!< control \f$\mathbf{u}\f$ |
| 421 |
|
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MatrixXs Luu; //!< Hessian of the cost w.r.t. the control \f$\mathbf{u}\f$ |
| 422 |
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VectorXs g; //!< Inequality constraint values |
| 423 |
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MatrixXs Gx; //!< Jacobian of the inequality constraint w.r.t. the state |
| 424 |
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|
//!< \f$\mathbf{x}\f$ |
| 425 |
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|
MatrixXs Gu; //!< Jacobian of the inequality constraint w.r.t. the control |
| 426 |
|
|
//!< \f$\mathbf{u}\f$ |
| 427 |
|
|
VectorXs h; //!< Equality constraint values |
| 428 |
|
|
MatrixXs Hx; //!< Jacobian of the equality constraint w.r.t. the state |
| 429 |
|
|
//!< \f$\mathbf{x}\f$ |
| 430 |
|
|
MatrixXs Hu; //!< Jacobian of the equality constraint w.r.t. the control |
| 431 |
|
|
//!< \f$\mathbf{u}\f$ |
| 432 |
|
|
}; |
| 433 |
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|
| 434 |
|
|
} // namespace crocoddyl |
| 435 |
|
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|
| 436 |
|
|
/* --- Details -------------------------------------------------------------- */ |
| 437 |
|
|
/* --- Details -------------------------------------------------------------- */ |
| 438 |
|
|
/* --- Details -------------------------------------------------------------- */ |
| 439 |
|
|
#include "crocoddyl/core/action-base.hxx" |
| 440 |
|
|
|
| 441 |
|
|
CROCODDYL_DECLARE_EXTERN_TEMPLATE_CLASS(crocoddyl::ActionModelAbstractTpl) |
| 442 |
|
|
CROCODDYL_DECLARE_EXTERN_TEMPLATE_STRUCT(crocoddyl::ActionDataAbstractTpl) |
| 443 |
|
|
|
| 444 |
|
|
#endif // CROCODDYL_CORE_ACTION_BASE_HPP_ |
| 445 |
|
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|