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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, INRIA, |
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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_STATE_BASE_HPP_ |
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#define CROCODDYL_CORE_STATE_BASE_HPP_ |
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#include "crocoddyl/core/fwd.hpp" |
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namespace crocoddyl { |
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enum Jcomponent { both = 0, first = 1, second = 2 }; |
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inline bool is_a_Jcomponent(Jcomponent firstsecond) { |
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return (firstsecond == first || firstsecond == second || firstsecond == both); |
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} |
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class StateBase { |
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public: |
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virtual ~StateBase() = default; |
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CROCODDYL_BASE_CAST(StateBase, StateAbstractTpl) |
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}; |
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/** |
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* @brief Abstract class for the state representation |
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* |
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* A state is represented by its operators: difference, integrates, transport |
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* and their derivatives. The difference operator returns the value of |
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* \f$\mathbf{x}_{1}\ominus\mathbf{x}_{0}\f$ operation. Instead the integrate |
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* operator returns the value of \f$\mathbf{x}\oplus\delta\mathbf{x}\f$. These |
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* operators are used to compared two points on the state manifold |
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* \f$\mathcal{M}\f$ or to advance the state given a tangential velocity |
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* (\f$T_\mathbf{x} \mathcal{M}\f$). Therefore the points \f$\mathbf{x}\f$, |
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* \f$\mathbf{x}_{0}\f$ and \f$\mathbf{x}_{1}\f$ belong to the manifold |
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* \f$\mathcal{M}\f$; and \f$\delta\mathbf{x}\f$ or |
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* \f$\mathbf{x}_{1}\ominus\mathbf{x}_{0}\f$ lie on its tangential space. |
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* |
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* \sa `diff()`, `integrate()`, `Jdiff()`, `Jintegrate()` and |
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* `JintegrateTransport()` |
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*/ |
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template <typename _Scalar> |
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class StateAbstractTpl : public StateBase { |
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public: |
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EIGEN_MAKE_ALIGNED_OPERATOR_NEW |
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typedef _Scalar Scalar; |
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typedef MathBaseTpl<Scalar> MathBase; |
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typedef typename MathBase::VectorXs VectorXs; |
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typedef typename MathBase::MatrixXs MatrixXs; |
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/** |
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* @brief Initialize the state dimensions |
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* |
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* @param[in] nx Dimension of state configuration tuple |
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* @param[in] ndx Dimension of state tangent vector |
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*/ |
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StateAbstractTpl(const std::size_t nx, const std::size_t ndx); |
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StateAbstractTpl(); |
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virtual ~StateAbstractTpl(); |
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/** |
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* @brief Generate a zero state |
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*/ |
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virtual VectorXs zero() const = 0; |
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/** |
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* @brief Generate a random state |
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*/ |
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virtual VectorXs rand() const = 0; |
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/** |
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* @brief Compute the state manifold differentiation. |
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* |
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* The state differentiation is defined as: |
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* \f{equation*}{ |
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* \delta\mathbf{x} = \mathbf{x}_{1} \ominus \mathbf{x}_{0}, |
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* \f} |
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* where \f$\mathbf{x}_{1}\f$, \f$\mathbf{x}_{0}\f$ are the current and |
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* previous state which lie in a manifold \f$\mathcal{M}\f$, and |
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* \f$\delta\mathbf{x} \in T_\mathbf{x} \mathcal{M}\f$ is the rate of change |
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* in the state in the tangent space of the manifold. |
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* |
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* @param[in] x0 Previous state point (size `nx`) |
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* @param[in] x1 Current state point (size `nx`) |
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* @param[out] dxout Difference between the current and previous state points |
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* (size `ndx`) |
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*/ |
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virtual void diff(const Eigen::Ref<const VectorXs>& x0, |
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const Eigen::Ref<const VectorXs>& x1, |
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Eigen::Ref<VectorXs> dxout) const = 0; |
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/** |
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* @brief Compute the state manifold integration. |
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* |
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* The state integration is defined as: |
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* \f{equation*}{ |
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* \mathbf{x}_{next} = \mathbf{x} \oplus \delta\mathbf{x}, |
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* \f} |
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* where \f$\mathbf{x}\f$, \f$\mathbf{x}_{next}\f$ are the current and next |
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* state which lie in a manifold \f$\mathcal{M}\f$, and \f$\delta\mathbf{x} |
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* \in T_\mathbf{x} \mathcal{M}\f$ is the rate of change in the state in the |
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* tangent space of the manifold. |
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* |
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* @param[in] x State point (size `nx`) |
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* @param[in] dx Velocity vector (size `ndx`) |
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* @param[out] xout Next state point (size `nx`) |
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*/ |
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virtual void integrate(const Eigen::Ref<const VectorXs>& x, |
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const Eigen::Ref<const VectorXs>& dx, |
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Eigen::Ref<VectorXs> xout) const = 0; |
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/** |
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* @brief Compute the Jacobian of the state manifold differentiation. |
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* |
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* The state differentiation is defined as: |
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* \f{equation*}{ |
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* \delta\mathbf{x} = \mathbf{x}_{1} \ominus \mathbf{x}_{0}, |
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* \f} |
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* where \f$\mathbf{x}_{1}\f$, \f$\mathbf{x}_{0}\f$ are the current and |
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* previous state which lie in a manifold \f$\mathcal{M}\f$, and |
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* \f$\delta\mathbf{x} \in T_\mathbf{x} \mathcal{M}\f$ is the rate of change |
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* in the state in the tangent space of the manifold. |
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* |
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* The Jacobians lie in the tangent space of manifold, i.e. |
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* \f$\mathbb{R}^{\textrm{ndx}\times\textrm{ndx}}\f$. Note that the state is |
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* represented as a tuple of `nx` values and its dimension is `ndx`. Calling |
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* \f$\boldsymbol{\Delta}(\mathbf{x}_{0}, \mathbf{x}_{1}) \f$, the difference |
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* function, these Jacobians satisfy the following relationships: |
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* - |
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* \f$\boldsymbol{\Delta}(\mathbf{x}_{0},\mathbf{x}_{0}\oplus\delta\mathbf{y}) |
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* - \boldsymbol{\Delta}(\mathbf{x}_{0},\mathbf{x}_{1}) = |
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* \mathbf{J}_{\mathbf{x}_{1}}\delta\mathbf{y} + |
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* \mathbf{o}(\mathbf{x}_{0})\f$. |
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* - |
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* \f$\boldsymbol{\Delta}(\mathbf{x}_{0}\oplus\delta\mathbf{y},\mathbf{x}_{1}) |
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* - \boldsymbol{\Delta}(\mathbf{x}_{0},\mathbf{x}_{1}) = |
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* \mathbf{J}_{\mathbf{x}_{0}}\delta\mathbf{y} + |
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* \mathbf{o}(\mathbf{x}_{0})\f$, |
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* |
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* where \f$\mathbf{J}_{\mathbf{x}_{1}}\f$ and |
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* \f$\mathbf{J}_{\mathbf{x}_{0}}\f$ are the Jacobian with respect to the |
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* current and previous state, respectively. |
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* |
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* @param[in] x0 Previous state point (size `nx`) |
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* @param[in] x1 Current state point (size `nx`) |
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* @param[out] Jfirst Jacobian of the difference operation relative to |
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* the previous state point (size `ndx`\f$\times\f$`ndx`) |
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* @param[out] Jsecond Jacobian of the difference operation relative to |
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* the current state point (size `ndx`\f$\times\f$`ndx`) |
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* @param[in] firstsecond Argument (either x0 and / or x1) with respect to |
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* which the differentiation is performed. |
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*/ |
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virtual void Jdiff(const Eigen::Ref<const VectorXs>& x0, |
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const Eigen::Ref<const VectorXs>& x1, |
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Eigen::Ref<MatrixXs> Jfirst, Eigen::Ref<MatrixXs> Jsecond, |
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const Jcomponent firstsecond = both) const = 0; |
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/** |
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* @brief Compute the Jacobian of the state manifold integration. |
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* |
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* The state integration is defined as: |
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* \f{equation*}{ |
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* \mathbf{x}_{next} = \mathbf{x} \oplus \delta\mathbf{x}, |
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* \f} |
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* where \f$\mathbf{x}\f$, \f$\mathbf{x}_{next}\f$ are the current and next |
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* state which lie in a manifold \f$\mathcal{M}\f$, and \f$\delta\mathbf{x} |
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* \in T_\mathbf{x} \mathcal{M}\f$ is the rate of change in the state in the |
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* tangent space of the manifold. |
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* |
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* The Jacobians lie in the tangent space of manifold, i.e. |
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* \f$\mathbb{R}^{\textrm{ndx}\times\textrm{ndx}}\f$. Note that the state is |
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* represented as a tuple of `nx` values and its dimension is `ndx`. Calling |
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* \f$ \mathbf{f}(\mathbf{x}, \delta\mathbf{x}) \f$, the integrate function, |
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* these Jacobians satisfy the following relationships: |
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* - |
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* \f$\mathbf{f}(\mathbf{x}\oplus\delta\mathbf{y},\delta\mathbf{x})\ominus\mathbf{f}(\mathbf{x},\delta\mathbf{x}) |
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* = \mathbf{J}_\mathbf{x}\delta\mathbf{y} + \mathbf{o}(\delta\mathbf{x})\f$. |
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* - |
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* \f$\mathbf{f}(\mathbf{x},\delta\mathbf{x}+\delta\mathbf{y})\ominus\mathbf{f}(\mathbf{x},\delta\mathbf{x}) |
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* = \mathbf{J}_{\delta\mathbf{x}}\delta\mathbf{y} + |
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* \mathbf{o}(\delta\mathbf{x})\f$, |
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* |
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* where \f$\mathbf{J}_{\delta\mathbf{x}}\f$ and \f$\mathbf{J}_{\mathbf{x}}\f$ |
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* are the Jacobian with respect to the state and velocity, respectively. |
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* |
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* @param[in] x State point (size `nx`) |
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* @param[in] dx Velocity vector (size `ndx`) |
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* @param[out] Jfirst Jacobian of the integration operation relative to |
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* the state point (size `ndx`\f$\times\f$`ndx`) |
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* @param[out] Jsecond Jacobian of the integration operation relative to |
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* the velocity vector (size `ndx`\f$\times\f$`ndx`) |
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* @param[in] firstsecond Argument (either x and / or dx) with respect to |
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* which the differentiation is performed |
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* @param[in] op Assignment operator which sets, adds, or removes |
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* the given Jacobian matrix |
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*/ |
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virtual void Jintegrate(const Eigen::Ref<const VectorXs>& x, |
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const Eigen::Ref<const VectorXs>& dx, |
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Eigen::Ref<MatrixXs> Jfirst, |
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Eigen::Ref<MatrixXs> Jsecond, |
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const Jcomponent firstsecond = both, |
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const AssignmentOp op = setto) const = 0; |
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/** |
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* @brief Parallel transport from integrate(x, dx) to x. |
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* |
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* This function performs the parallel transportation of an input matrix whose |
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* columns are expressed in the tangent space at |
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* \f$\mathbf{x}\oplus\delta\mathbf{x}\f$ to the tangent space at |
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* \f$\mathbf{x}\f$ point. |
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* |
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* @param[in] x State point (size `nx`). |
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* @param[in] dx Velocity vector (size `ndx`) |
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* @param[out] Jin Input matrix (number of rows = `nv`). |
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* @param[in] firstsecond Argument (either x or dx) with respect to which the |
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* differentiation of Jintegrate is performed. |
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*/ |
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virtual void JintegrateTransport(const Eigen::Ref<const VectorXs>& x, |
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const Eigen::Ref<const VectorXs>& dx, |
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Eigen::Ref<MatrixXs> Jin, |
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const Jcomponent firstsecond) const = 0; |
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/** |
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* @copybrief diff() |
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* |
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* @param[in] x0 Previous state point (size `nx`) |
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* @param[in] x1 Current state point (size `nx`) |
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* @return Difference between the current and previous state points (size |
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* `ndx`) |
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*/ |
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VectorXs diff_dx(const Eigen::Ref<const VectorXs>& x0, |
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const Eigen::Ref<const VectorXs>& x1); |
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/** |
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* @copybrief integrate() |
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* |
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* @param[in] x State point (size `nx`) |
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* @param[in] dx Velocity vector (size `ndx`) |
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* @return Next state point (size `nx`) |
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*/ |
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VectorXs integrate_x(const Eigen::Ref<const VectorXs>& x, |
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const Eigen::Ref<const VectorXs>& dx); |
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/** |
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* @copybrief jdiff() |
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* |
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* @param[in] x0 Previous state point (size `nx`) |
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* @param[in] x1 Current state point (size `nx`) |
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* @return Jacobians |
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*/ |
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std::vector<MatrixXs> Jdiff_Js(const Eigen::Ref<const VectorXs>& x0, |
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const Eigen::Ref<const VectorXs>& x1, |
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const Jcomponent firstsecond = both); |
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/** |
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* @copybrief Jintegrate() |
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* |
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* @param[in] x State point (size `nx`) |
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* @param[in] dx Velocity vector (size `ndx`) |
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* @return Jacobians |
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*/ |
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std::vector<MatrixXs> Jintegrate_Js(const Eigen::Ref<const VectorXs>& x, |
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const Eigen::Ref<const VectorXs>& dx, |
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const Jcomponent firstsecond = both); |
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/** |
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* @brief Print information on the state 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 state 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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/** |
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* @brief Return the dimension of the state tuple |
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*/ |
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std::size_t get_nx() const; |
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/** |
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* @brief Return the dimension of the tangent space of the state manifold |
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*/ |
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std::size_t get_ndx() const; |
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/** |
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* @brief Return the dimension of the configuration tuple |
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*/ |
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std::size_t get_nq() const; |
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/** |
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* @brief Return the dimension of tangent space of the configuration manifold |
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*/ |
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std::size_t get_nv() const; |
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/** |
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* @brief Return the state lower bound |
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*/ |
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const VectorXs& get_lb() const; |
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/** |
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* @brief Return the state upper bound |
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*/ |
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const VectorXs& get_ub() const; |
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/** |
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* @brief Indicate if the state has defined limits |
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*/ |
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bool get_has_limits() const; |
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/** |
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* @brief Modify the state lower bound |
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*/ |
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void set_lb(const VectorXs& lb); |
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/** |
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* @brief Modify the state upper bound |
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*/ |
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void set_ub(const VectorXs& ub); |
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protected: |
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void update_has_limits(); |
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std::size_t nx_; //!< State dimension |
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std::size_t ndx_; //!< State rate dimension |
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std::size_t nq_; //!< Configuration dimension |
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std::size_t nv_; //!< Velocity dimension |
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VectorXs lb_; //!< Lower state limits |
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VectorXs ub_; //!< Upper state limits |
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bool has_limits_; //!< Indicates whether any of the state limits is finite |
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}; |
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| 343 |
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} // namespace crocoddyl |
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| 345 |
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/* --- Details -------------------------------------------------------------- */ |
| 346 |
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/* --- Details -------------------------------------------------------------- */ |
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/* --- Details -------------------------------------------------------------- */ |
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#include "crocoddyl/core/state-base.hxx" |
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| 350 |
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CROCODDYL_DECLARE_EXTERN_TEMPLATE_CLASS(crocoddyl::StateAbstractTpl) |
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| 352 |
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#endif // CROCODDYL_CORE_STATE_BASE_HPP_ |
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