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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_DIFF_ACTION_BASE_HPP_ |
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#define CROCODDYL_CORE_DIFF_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 DifferentialActionModelBase { |
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public: |
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virtual ~DifferentialActionModelBase() = default; |
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CROCODDYL_BASE_CAST(DifferentialActionModelBase, |
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DifferentialActionModelAbstractTpl) |
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}; |
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/** |
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* @brief Abstract class for differential action model |
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* |
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* A differential action model combines dynamics, cost and constraints models. |
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* We can use it in each node of our optimal control problem thanks to dedicated |
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* integration rules (e.g., `IntegratedActionModelEulerTpl` or |
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* `IntegratedActionModelRKTpl`). These integrated action models produce action |
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* models (`ActionModelAbstractTpl`). Thus, every time that we want to describe |
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* a problem, we need to provide ways of computing the dynamics, cost, |
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* constraints functions and their derivatives. All these are described inside |
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* the differential action model. |
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* |
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* Concretely speaking, the differential action model is the time-continuous |
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* version of an action model, i.e., \f[ \begin{aligned} |
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* &\dot{\mathbf{v}} = \mathbf{f}(\mathbf{q}, \mathbf{v}, \mathbf{u}), |
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* &\textrm{(dynamics)}\\ |
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* &\ell(\mathbf{q}, \mathbf{v},\mathbf{u}) = \int_0^{\delta t} |
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* a(\mathbf{r}(\mathbf{q}, \mathbf{v},\mathbf{u}))\,dt, |
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* &\textrm{(cost)}\\ |
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* &\mathbf{g}(\mathbf{q}, \mathbf{v},\mathbf{u})<\mathbf{0}, |
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* &\textrm{(inequality constraint)}\\ |
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* &\mathbf{h}(\mathbf{q}, \mathbf{v},\mathbf{u})=\mathbf{0}, &\textrm{(equality |
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* constraint)} \end{aligned} \f] where |
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* - the configuration \f$\mathbf{q}\in\mathcal{Q}\f$ lies in the configuration |
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* manifold described with a `nq`-tuple, |
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* - the velocity \f$\mathbf{v}\in T_{\mathbf{q}}\mathcal{Q}\f$ is the tangent |
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* vector to the configuration manifold with `nv` 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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* respectively), |
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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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* Both configuration and velocity describe the system space |
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* \f$\mathbf{x}=(\mathbf{q}, \mathbf{v})\in\mathcal{X}\f$ which lies in the |
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* state manifold. Note that the acceleration \f$\dot{\mathbf{v}}\in |
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* T_{\mathbf{q}}\mathcal{Q}\f$ lies also in the tangent space of the |
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* configuration manifold. The computation of these equations are carried out |
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* inside `calc()` function. In short, this function computes the system |
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* acceleration, cost and constraints values (also called constraints |
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* violations). This procedure is equivalent to running a forward pass of the |
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* 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 differential action model. These calculations are performed by |
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* `calcDiff()`. In short, this function builds a linear-quadratic approximation |
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* of the differential action model, i.e., \f[ \begin{aligned} |
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* &\delta\dot{\mathbf{v}} = |
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* \mathbf{f_{q}}\delta\mathbf{q}+\mathbf{f_{v}}\delta\mathbf{v}+\mathbf{f_{u}}\delta\mathbf{u}, |
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* &\textrm{(dynamics)}\\ |
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* &\ell(\delta\mathbf{q},\delta\mathbf{v},\delta\mathbf{u}) = \begin{bmatrix}1 |
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* \\ \delta\mathbf{q} \\ \delta\mathbf{v} |
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* \\ \delta\mathbf{u}\end{bmatrix}^T \begin{bmatrix}0 & \mathbf{\ell_q}^T & |
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* \mathbf{\ell_v}^T & \mathbf{\ell_u}^T \\ \mathbf{\ell_q} & \mathbf{\ell_{qq}} |
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* & |
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* \mathbf{\ell_{qv}} & \mathbf{\ell_{uq}}^T \\ |
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* \mathbf{\ell_v} & \mathbf{\ell_{vq}} & \mathbf{\ell_{vv}} & |
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* \mathbf{\ell_{uv}}^T \\ |
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* \mathbf{\ell_u} & \mathbf{\ell_{uq}} & \mathbf{\ell_{uv}} & |
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* \mathbf{\ell_{uu}}\end{bmatrix} \begin{bmatrix}1 \\ \delta\mathbf{q} |
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* \\ \delta\mathbf{v} \\ |
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* \delta\mathbf{u}\end{bmatrix}, &\textrm{(cost)}\\ |
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* &\mathbf{g_q}\delta\mathbf{q}+\mathbf{g_v}\delta\mathbf{v}+\mathbf{g_u}\delta\mathbf{u}\leq\mathbf{0}, |
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* &\textrm{(inequality constraints)}\\ |
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* &\mathbf{h_q}\delta\mathbf{q}+\mathbf{h_v}\delta\mathbf{v}+\mathbf{h_u}\delta\mathbf{u}=\mathbf{0}, |
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* &\textrm{(equality constraints)} \end{aligned} \f] where |
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* - \f$\mathbf{f_x}=(\mathbf{f_q};\,\, \mathbf{f_v})\in\mathbb{R}^{nv\times |
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* ndx}\f$ and \f$\mathbf{f_u}\in\mathbb{R}^{nv\times nu}\f$ are the Jacobians |
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* of the dynamics, |
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* - \f$\mathbf{\ell_x}=(\mathbf{\ell_q};\,\, |
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* \mathbf{\ell_v})\in\mathbb{R}^{ndx}\f$ 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$\mathbf{\ell_{xx}}=(\mathbf{\ell_{qq}}\,\, \mathbf{\ell_{qv}};\,\, |
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* \mathbf{\ell_{vq}}\, \mathbf{\ell_{vv}})\in\mathbb{R}^{ndx\times ndx}\f$, |
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* \f$\mathbf{\ell_{xu}}=(\mathbf{\ell_q};\,\, |
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* \mathbf{\ell_v})\in\mathbb{R}^{ndx\times nu}\f$ 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$\mathbf{g_x}=(\mathbf{g_q};\,\, \mathbf{g_v})\in\mathbb{R}^{ng\times |
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* ndx}\f$ and \f$\mathbf{g_u}\in\mathbb{R}^{ng\times nu}\f$ are the Jacobians |
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* of the inequality constraints, and |
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* - \f$\mathbf{h_x}=(\mathbf{h_q};\,\, \mathbf{h_v})\in\mathbb{R}^{nh\times |
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* ndx}\f$ and \f$\mathbf{h_u}\in\mathbb{R}^{nh\times nu}\f$ are the Jacobians |
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* of the 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 `ActionModelAbstractTpl`, `calc()`, `calcDiff()`, `createData()` |
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*/ |
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template <typename _Scalar> |
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class DifferentialActionModelAbstractTpl : public DifferentialActionModelBase { |
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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 DifferentialActionDataAbstractTpl<Scalar> |
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DifferentialActionDataAbstract; |
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typedef StateAbstractTpl<Scalar> StateAbstract; |
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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 differential 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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DifferentialActionModelAbstractTpl(std::shared_ptr<StateAbstract> state, |
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const std::size_t nu, |
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const std::size_t nr = 0, |
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const std::size_t ng = 0, |
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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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virtual ~DifferentialActionModelAbstractTpl() = default; |
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/** |
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* @brief Compute the system acceleration and cost value |
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* |
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* @param[in] data Differential 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<DifferentialActionDataAbstract>& 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 system acceleration is not updated as the |
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* control input is undefined. This function is used in the terminal nodes of |
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* an optimal control problem. |
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* |
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* @param[in] data Differential 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<DifferentialActionDataAbstract>& 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 quadratic approximation of the time-continuous action model (i.e. |
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* dynamical system and cost function). |
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* |
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* @param[in] data Differential 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( |
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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) = 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 Differential 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( |
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const std::shared_ptr<DifferentialActionDataAbstract>& data, |
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const Eigen::Ref<const VectorXs>& x); |
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/** |
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* @brief Create the differential action data |
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* |
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* @return the differential action data |
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*/ |
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virtual std::shared_ptr<DifferentialActionDataAbstract> 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( |
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const std::shared_ptr<DifferentialActionDataAbstract>& 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$\mathbf{f}(\mathbf{q},\mathbf{v}=\mathbf{0},\mathbf{u})=\mathbf{0}\f$ |
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* |
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* @param[in] data Differential 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( |
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const std::shared_ptr<DifferentialActionDataAbstract>& data, |
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Eigen::Ref<VectorXs> u, const Eigen::Ref<const VectorXs>& x, |
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const std::size_t maxiter = 100, 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 Differential 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( |
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const std::shared_ptr<DifferentialActionDataAbstract>& 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 differential action model |
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*/ |
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template <class Scalar> |
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friend std::ostream& operator<<( |
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std::ostream& os, |
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const DifferentialActionModelAbstractTpl<Scalar>& model); |
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/** |
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* @brief Print relevant information of the differential 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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private: |
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std::size_t ng_internal_; //!< Internal object for storing the number of |
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//!< inequality constraints |
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std::size_t nh_internal_; //!< Internal object for storing the number of |
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//!< equality constraints |
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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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DifferentialActionModelAbstractTpl() |
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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 IntegratedActionModelAbstractTpl; |
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template <class Scalar> |
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friend class ConstraintModelManagerTpl; |
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}; |
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template <typename _Scalar> |
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struct DifferentialActionDataAbstractTpl { |
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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 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 DifferentialActionDataAbstractTpl(Model<Scalar>* const model) |
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: cost(Scalar(0.)), |
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xout(model->get_state()->get_nv()), |
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Fx(model->get_state()->get_nv(), model->get_state()->get_ndx()), |
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Fu(model->get_state()->get_nv(), 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(), |
| 415 |
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✗ |
model->get_state()->get_ndx()), |
| 416 |
|
✗ |
Gu(model->get_ng() > model->get_ng_T() ? model->get_ng() |
| 417 |
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✗ |
: model->get_ng_T(), |
| 418 |
|
✗ |
model->get_nu()), |
| 419 |
|
✗ |
h(model->get_nh() > model->get_nh_T() ? model->get_nh() |
| 420 |
|
✗ |
: model->get_nh_T()), |
| 421 |
|
✗ |
Hx(model->get_nh() > model->get_nh_T() ? model->get_nh() |
| 422 |
|
✗ |
: model->get_nh_T(), |
| 423 |
|
✗ |
model->get_state()->get_ndx()), |
| 424 |
|
✗ |
Hu(model->get_nh() > model->get_nh_T() ? model->get_nh() |
| 425 |
|
✗ |
: model->get_nh_T(), |
| 426 |
|
✗ |
model->get_nu()) { |
| 427 |
|
✗ |
xout.setZero(); |
| 428 |
|
✗ |
Fx.setZero(); |
| 429 |
|
✗ |
Fu.setZero(); |
| 430 |
|
✗ |
r.setZero(); |
| 431 |
|
✗ |
Lx.setZero(); |
| 432 |
|
✗ |
Lu.setZero(); |
| 433 |
|
✗ |
Lxx.setZero(); |
| 434 |
|
✗ |
Lxu.setZero(); |
| 435 |
|
✗ |
Luu.setZero(); |
| 436 |
|
✗ |
g.setZero(); |
| 437 |
|
✗ |
Gx.setZero(); |
| 438 |
|
✗ |
Gu.setZero(); |
| 439 |
|
✗ |
h.setZero(); |
| 440 |
|
✗ |
Hx.setZero(); |
| 441 |
|
✗ |
Hu.setZero(); |
| 442 |
|
|
} |
| 443 |
|
✗ |
virtual ~DifferentialActionDataAbstractTpl() = default; |
| 444 |
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|
| 445 |
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Scalar cost; //!< cost value |
| 446 |
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VectorXs xout; //!< evolution state |
| 447 |
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|
MatrixXs Fx; //!< Jacobian of the dynamics w.r.t. the state \f$\mathbf{x}\f$ |
| 448 |
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|
MatrixXs |
| 449 |
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Fu; //!< Jacobian of the dynamics w.r.t. the control \f$\mathbf{u}\f$ |
| 450 |
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VectorXs r; //!< Cost residual |
| 451 |
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|
VectorXs Lx; //!< Jacobian of the cost w.r.t. the state \f$\mathbf{x}\f$ |
| 452 |
|
|
VectorXs Lu; //!< Jacobian of the cost w.r.t. the control \f$\mathbf{u}\f$ |
| 453 |
|
|
MatrixXs Lxx; //!< Hessian of the cost w.r.t. the state \f$\mathbf{x}\f$ |
| 454 |
|
|
MatrixXs Lxu; //!< Hessian of the cost w.r.t. the state \f$\mathbf{x}\f$ and |
| 455 |
|
|
//!< control u |
| 456 |
|
|
MatrixXs Luu; //!< Hessian of the cost w.r.t. the control \f$\mathbf{u}\f$ |
| 457 |
|
|
VectorXs g; //!< Inequality constraint values |
| 458 |
|
|
MatrixXs Gx; //!< Jacobian of the inequality constraint w.r.t. the state |
| 459 |
|
|
//!< \f$\mathbf{x}\f$ |
| 460 |
|
|
MatrixXs Gu; //!< Jacobian of the inequality constraint w.r.t. the control |
| 461 |
|
|
//!< \f$\mathbf{u}\f$ |
| 462 |
|
|
VectorXs h; //!< Equality constraint values |
| 463 |
|
|
MatrixXs Hx; //!< Jacobian of the equality constraint w.r.t. the state |
| 464 |
|
|
//!< \f$\mathbf{x}\f$ |
| 465 |
|
|
MatrixXs Hu; //!< Jacobian of the equality constraint w.r.t the control |
| 466 |
|
|
//!< \f$\mathbf{u}\f$ |
| 467 |
|
|
}; |
| 468 |
|
|
|
| 469 |
|
|
} // namespace crocoddyl |
| 470 |
|
|
|
| 471 |
|
|
/* --- Details -------------------------------------------------------------- */ |
| 472 |
|
|
/* --- Details -------------------------------------------------------------- */ |
| 473 |
|
|
/* --- Details -------------------------------------------------------------- */ |
| 474 |
|
|
#include "crocoddyl/core/diff-action-base.hxx" |
| 475 |
|
|
|
| 476 |
|
|
CROCODDYL_DECLARE_EXTERN_TEMPLATE_CLASS( |
| 477 |
|
|
crocoddyl::DifferentialActionModelAbstractTpl) |
| 478 |
|
|
CROCODDYL_DECLARE_EXTERN_TEMPLATE_STRUCT( |
| 479 |
|
|
crocoddyl::DifferentialActionDataAbstractTpl) |
| 480 |
|
|
|
| 481 |
|
|
#endif // CROCODDYL_CORE_DIFF_ACTION_BASE_HPP_ |
| 482 |
|
|
|