| Directory: | ./ |
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| File: | include/crocoddyl/core/state-base.hpp |
| Date: | 2025-01-16 08:47:40 |
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| 1 | /////////////////////////////////////////////////////////////////////////////// | ||
| 2 | // BSD 3-Clause License | ||
| 3 | // | ||
| 4 | // Copyright (C) 2019-2020, LAAS-CNRS, University of Edinburgh, INRIA | ||
| 5 | // Copyright note valid unless otherwise stated in individual files. | ||
| 6 | // All rights reserved. | ||
| 7 | /////////////////////////////////////////////////////////////////////////////// | ||
| 8 | |||
| 9 | #ifndef CROCODDYL_CORE_STATE_BASE_HPP_ | ||
| 10 | #define CROCODDYL_CORE_STATE_BASE_HPP_ | ||
| 11 | |||
| 12 | #include <stdexcept> | ||
| 13 | #include <string> | ||
| 14 | #include <vector> | ||
| 15 | |||
| 16 | #include "crocoddyl/core/fwd.hpp" | ||
| 17 | #include "crocoddyl/core/mathbase.hpp" | ||
| 18 | #include "crocoddyl/core/utils/exception.hpp" | ||
| 19 | |||
| 20 | namespace crocoddyl { | ||
| 21 | |||
| 22 | enum Jcomponent { both = 0, first = 1, second = 2 }; | ||
| 23 | |||
| 24 | 61761 | inline bool is_a_Jcomponent(Jcomponent firstsecond) { | |
| 25 |
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61761 | return (firstsecond == first || firstsecond == second || firstsecond == both); |
| 26 | } | ||
| 27 | |||
| 28 | /** | ||
| 29 | * @brief Abstract class for the state representation | ||
| 30 | * | ||
| 31 | * A state is represented by its operators: difference, integrates, transport | ||
| 32 | * and their derivatives. The difference operator returns the value of | ||
| 33 | * \f$\mathbf{x}_{1}\ominus\mathbf{x}_{0}\f$ operation. Instead the integrate | ||
| 34 | * operator returns the value of \f$\mathbf{x}\oplus\delta\mathbf{x}\f$. These | ||
| 35 | * operators are used to compared two points on the state manifold | ||
| 36 | * \f$\mathcal{M}\f$ or to advance the state given a tangential velocity | ||
| 37 | * (\f$T_\mathbf{x} \mathcal{M}\f$). Therefore the points \f$\mathbf{x}\f$, | ||
| 38 | * \f$\mathbf{x}_{0}\f$ and \f$\mathbf{x}_{1}\f$ belong to the manifold | ||
| 39 | * \f$\mathcal{M}\f$; and \f$\delta\mathbf{x}\f$ or | ||
| 40 | * \f$\mathbf{x}_{1}\ominus\mathbf{x}_{0}\f$ lie on its tangential space. | ||
| 41 | * | ||
| 42 | * \sa `diff()`, `integrate()`, `Jdiff()`, `Jintegrate()` and | ||
| 43 | * `JintegrateTransport()` | ||
| 44 | */ | ||
| 45 | template <typename _Scalar> | ||
| 46 | class StateAbstractTpl { | ||
| 47 | public: | ||
| 48 | EIGEN_MAKE_ALIGNED_OPERATOR_NEW | ||
| 49 | |||
| 50 | typedef _Scalar Scalar; | ||
| 51 | typedef MathBaseTpl<Scalar> MathBase; | ||
| 52 | typedef typename MathBase::VectorXs VectorXs; | ||
| 53 | typedef typename MathBase::MatrixXs MatrixXs; | ||
| 54 | |||
| 55 | /** | ||
| 56 | * @brief Initialize the state dimensions | ||
| 57 | * | ||
| 58 | * @param[in] nx Dimension of state configuration tuple | ||
| 59 | * @param[in] ndx Dimension of state tangent vector | ||
| 60 | */ | ||
| 61 | StateAbstractTpl(const std::size_t nx, const std::size_t ndx); | ||
| 62 | StateAbstractTpl(); | ||
| 63 | virtual ~StateAbstractTpl(); | ||
| 64 | |||
| 65 | /** | ||
| 66 | * @brief Generate a zero state | ||
| 67 | */ | ||
| 68 | virtual VectorXs zero() const = 0; | ||
| 69 | |||
| 70 | /** | ||
| 71 | * @brief Generate a random state | ||
| 72 | */ | ||
| 73 | virtual VectorXs rand() const = 0; | ||
| 74 | |||
| 75 | /** | ||
| 76 | * @brief Compute the state manifold differentiation. | ||
| 77 | * | ||
| 78 | * The state differentiation is defined as: | ||
| 79 | * \f{equation*}{ | ||
| 80 | * \delta\mathbf{x} = \mathbf{x}_{1} \ominus \mathbf{x}_{0}, | ||
| 81 | * \f} | ||
| 82 | * where \f$\mathbf{x}_{1}\f$, \f$\mathbf{x}_{0}\f$ are the current and | ||
| 83 | * previous state which lie in a manifold \f$\mathcal{M}\f$, and | ||
| 84 | * \f$\delta\mathbf{x} \in T_\mathbf{x} \mathcal{M}\f$ is the rate of change | ||
| 85 | * in the state in the tangent space of the manifold. | ||
| 86 | * | ||
| 87 | * @param[in] x0 Previous state point (size `nx`) | ||
| 88 | * @param[in] x1 Current state point (size `nx`) | ||
| 89 | * @param[out] dxout Difference between the current and previous state points | ||
| 90 | * (size `ndx`) | ||
| 91 | */ | ||
| 92 | virtual void diff(const Eigen::Ref<const VectorXs>& x0, | ||
| 93 | const Eigen::Ref<const VectorXs>& x1, | ||
| 94 | Eigen::Ref<VectorXs> dxout) const = 0; | ||
| 95 | |||
| 96 | /** | ||
| 97 | * @brief Compute the state manifold integration. | ||
| 98 | * | ||
| 99 | * The state integration is defined as: | ||
| 100 | * \f{equation*}{ | ||
| 101 | * \mathbf{x}_{next} = \mathbf{x} \oplus \delta\mathbf{x}, | ||
| 102 | * \f} | ||
| 103 | * where \f$\mathbf{x}\f$, \f$\mathbf{x}_{next}\f$ are the current and next | ||
| 104 | * state which lie in a manifold \f$\mathcal{M}\f$, and \f$\delta\mathbf{x} | ||
| 105 | * \in T_\mathbf{x} \mathcal{M}\f$ is the rate of change in the state in the | ||
| 106 | * tangent space of the manifold. | ||
| 107 | * | ||
| 108 | * @param[in] x State point (size `nx`) | ||
| 109 | * @param[in] dx Velocity vector (size `ndx`) | ||
| 110 | * @param[out] xout Next state point (size `nx`) | ||
| 111 | */ | ||
| 112 | virtual void integrate(const Eigen::Ref<const VectorXs>& x, | ||
| 113 | const Eigen::Ref<const VectorXs>& dx, | ||
| 114 | Eigen::Ref<VectorXs> xout) const = 0; | ||
| 115 | |||
| 116 | /** | ||
| 117 | * @brief Compute the Jacobian of the state manifold differentiation. | ||
| 118 | * | ||
| 119 | * The state differentiation is defined as: | ||
| 120 | * \f{equation*}{ | ||
| 121 | * \delta\mathbf{x} = \mathbf{x}_{1} \ominus \mathbf{x}_{0}, | ||
| 122 | * \f} | ||
| 123 | * where \f$\mathbf{x}_{1}\f$, \f$\mathbf{x}_{0}\f$ are the current and | ||
| 124 | * previous state which lie in a manifold \f$\mathcal{M}\f$, and | ||
| 125 | * \f$\delta\mathbf{x} \in T_\mathbf{x} \mathcal{M}\f$ is the rate of change | ||
| 126 | * in the state in the tangent space of the manifold. | ||
| 127 | * | ||
| 128 | * The Jacobians lie in the tangent space of manifold, i.e. | ||
| 129 | * \f$\mathbb{R}^{\textrm{ndx}\times\textrm{ndx}}\f$. Note that the state is | ||
| 130 | * represented as a tuple of `nx` values and its dimension is `ndx`. Calling | ||
| 131 | * \f$\boldsymbol{\Delta}(\mathbf{x}_{0}, \mathbf{x}_{1}) \f$, the difference | ||
| 132 | * function, these Jacobians satisfy the following relationships: | ||
| 133 | * - | ||
| 134 | * \f$\boldsymbol{\Delta}(\mathbf{x}_{0},\mathbf{x}_{0}\oplus\delta\mathbf{y}) | ||
| 135 | * - \boldsymbol{\Delta}(\mathbf{x}_{0},\mathbf{x}_{1}) = | ||
| 136 | * \mathbf{J}_{\mathbf{x}_{1}}\delta\mathbf{y} + | ||
| 137 | * \mathbf{o}(\mathbf{x}_{0})\f$. | ||
| 138 | * - | ||
| 139 | * \f$\boldsymbol{\Delta}(\mathbf{x}_{0}\oplus\delta\mathbf{y},\mathbf{x}_{1}) | ||
| 140 | * - \boldsymbol{\Delta}(\mathbf{x}_{0},\mathbf{x}_{1}) = | ||
| 141 | * \mathbf{J}_{\mathbf{x}_{0}}\delta\mathbf{y} + | ||
| 142 | * \mathbf{o}(\mathbf{x}_{0})\f$, | ||
| 143 | * | ||
| 144 | * where \f$\mathbf{J}_{\mathbf{x}_{1}}\f$ and | ||
| 145 | * \f$\mathbf{J}_{\mathbf{x}_{0}}\f$ are the Jacobian with respect to the | ||
| 146 | * current and previous state, respectively. | ||
| 147 | * | ||
| 148 | * @param[in] x0 Previous state point (size `nx`) | ||
| 149 | * @param[in] x1 Current state point (size `nx`) | ||
| 150 | * @param[out] Jfirst Jacobian of the difference operation relative to | ||
| 151 | * the previous state point (size `ndx`\f$\times\f$`ndx`) | ||
| 152 | * @param[out] Jsecond Jacobian of the difference operation relative to | ||
| 153 | * the current state point (size `ndx`\f$\times\f$`ndx`) | ||
| 154 | * @param[in] firstsecond Argument (either x0 and / or x1) with respect to | ||
| 155 | * which the differentiation is performed. | ||
| 156 | */ | ||
| 157 | virtual void Jdiff(const Eigen::Ref<const VectorXs>& x0, | ||
| 158 | const Eigen::Ref<const VectorXs>& x1, | ||
| 159 | Eigen::Ref<MatrixXs> Jfirst, Eigen::Ref<MatrixXs> Jsecond, | ||
| 160 | const Jcomponent firstsecond = both) const = 0; | ||
| 161 | |||
| 162 | /** | ||
| 163 | * @brief Compute the Jacobian of the state manifold integration. | ||
| 164 | * | ||
| 165 | * The state integration is defined as: | ||
| 166 | * \f{equation*}{ | ||
| 167 | * \mathbf{x}_{next} = \mathbf{x} \oplus \delta\mathbf{x}, | ||
| 168 | * \f} | ||
| 169 | * where \f$\mathbf{x}\f$, \f$\mathbf{x}_{next}\f$ are the current and next | ||
| 170 | * state which lie in a manifold \f$\mathcal{M}\f$, and \f$\delta\mathbf{x} | ||
| 171 | * \in T_\mathbf{x} \mathcal{M}\f$ is the rate of change in the state in the | ||
| 172 | * tangent space of the manifold. | ||
| 173 | * | ||
| 174 | * The Jacobians lie in the tangent space of manifold, i.e. | ||
| 175 | * \f$\mathbb{R}^{\textrm{ndx}\times\textrm{ndx}}\f$. Note that the state is | ||
| 176 | * represented as a tuple of `nx` values and its dimension is `ndx`. Calling | ||
| 177 | * \f$ \mathbf{f}(\mathbf{x}, \delta\mathbf{x}) \f$, the integrate function, | ||
| 178 | * these Jacobians satisfy the following relationships: | ||
| 179 | * - | ||
| 180 | * \f$\mathbf{f}(\mathbf{x}\oplus\delta\mathbf{y},\delta\mathbf{x})\ominus\mathbf{f}(\mathbf{x},\delta\mathbf{x}) | ||
| 181 | * = \mathbf{J}_\mathbf{x}\delta\mathbf{y} + \mathbf{o}(\delta\mathbf{x})\f$. | ||
| 182 | * - | ||
| 183 | * \f$\mathbf{f}(\mathbf{x},\delta\mathbf{x}+\delta\mathbf{y})\ominus\mathbf{f}(\mathbf{x},\delta\mathbf{x}) | ||
| 184 | * = \mathbf{J}_{\delta\mathbf{x}}\delta\mathbf{y} + | ||
| 185 | * \mathbf{o}(\delta\mathbf{x})\f$, | ||
| 186 | * | ||
| 187 | * where \f$\mathbf{J}_{\delta\mathbf{x}}\f$ and \f$\mathbf{J}_{\mathbf{x}}\f$ | ||
| 188 | * are the Jacobian with respect to the state and velocity, respectively. | ||
| 189 | * | ||
| 190 | * @param[in] x State point (size `nx`) | ||
| 191 | * @param[in] dx Velocity vector (size `ndx`) | ||
| 192 | * @param[out] Jfirst Jacobian of the integration operation relative to | ||
| 193 | * the state point (size `ndx`\f$\times\f$`ndx`) | ||
| 194 | * @param[out] Jsecond Jacobian of the integration operation relative to | ||
| 195 | * the velocity vector (size `ndx`\f$\times\f$`ndx`) | ||
| 196 | * @param[in] firstsecond Argument (either x and / or dx) with respect to | ||
| 197 | * which the differentiation is performed | ||
| 198 | * @param[in] op Assignment operator which sets, adds, or removes | ||
| 199 | * the given Jacobian matrix | ||
| 200 | */ | ||
| 201 | virtual void Jintegrate(const Eigen::Ref<const VectorXs>& x, | ||
| 202 | const Eigen::Ref<const VectorXs>& dx, | ||
| 203 | Eigen::Ref<MatrixXs> Jfirst, | ||
| 204 | Eigen::Ref<MatrixXs> Jsecond, | ||
| 205 | const Jcomponent firstsecond = both, | ||
| 206 | const AssignmentOp op = setto) const = 0; | ||
| 207 | |||
| 208 | /** | ||
| 209 | * @brief Parallel transport from integrate(x, dx) to x. | ||
| 210 | * | ||
| 211 | * This function performs the parallel transportation of an input matrix whose | ||
| 212 | * columns are expressed in the tangent space at | ||
| 213 | * \f$\mathbf{x}\oplus\delta\mathbf{x}\f$ to the tangent space at | ||
| 214 | * \f$\mathbf{x}\f$ point. | ||
| 215 | * | ||
| 216 | * @param[in] x State point (size `nx`). | ||
| 217 | * @param[in] dx Velocity vector (size `ndx`) | ||
| 218 | * @param[out] Jin Input matrix (number of rows = `nv`). | ||
| 219 | * @param[in] firstsecond Argument (either x or dx) with respect to which the | ||
| 220 | * differentiation of Jintegrate is performed. | ||
| 221 | */ | ||
| 222 | virtual void JintegrateTransport(const Eigen::Ref<const VectorXs>& x, | ||
| 223 | const Eigen::Ref<const VectorXs>& dx, | ||
| 224 | Eigen::Ref<MatrixXs> Jin, | ||
| 225 | const Jcomponent firstsecond) const = 0; | ||
| 226 | |||
| 227 | /** | ||
| 228 | * @copybrief diff() | ||
| 229 | * | ||
| 230 | * @param[in] x0 Previous state point (size `nx`) | ||
| 231 | * @param[in] x1 Current state point (size `nx`) | ||
| 232 | * @return Difference between the current and previous state points (size | ||
| 233 | * `ndx`) | ||
| 234 | */ | ||
| 235 | VectorXs diff_dx(const Eigen::Ref<const VectorXs>& x0, | ||
| 236 | const Eigen::Ref<const VectorXs>& x1); | ||
| 237 | |||
| 238 | /** | ||
| 239 | * @copybrief integrate() | ||
| 240 | * | ||
| 241 | * @param[in] x State point (size `nx`) | ||
| 242 | * @param[in] dx Velocity vector (size `ndx`) | ||
| 243 | * @return Next state point (size `nx`) | ||
| 244 | */ | ||
| 245 | VectorXs integrate_x(const Eigen::Ref<const VectorXs>& x, | ||
| 246 | const Eigen::Ref<const VectorXs>& dx); | ||
| 247 | |||
| 248 | /** | ||
| 249 | * @copybrief jdiff() | ||
| 250 | * | ||
| 251 | * @param[in] x0 Previous state point (size `nx`) | ||
| 252 | * @param[in] x1 Current state point (size `nx`) | ||
| 253 | * @return Jacobians | ||
| 254 | */ | ||
| 255 | std::vector<MatrixXs> Jdiff_Js(const Eigen::Ref<const VectorXs>& x0, | ||
| 256 | const Eigen::Ref<const VectorXs>& x1, | ||
| 257 | const Jcomponent firstsecond = both); | ||
| 258 | |||
| 259 | /** | ||
| 260 | * @copybrief Jintegrate() | ||
| 261 | * | ||
| 262 | * @param[in] x State point (size `nx`) | ||
| 263 | * @param[in] dx Velocity vector (size `ndx`) | ||
| 264 | * @return Jacobians | ||
| 265 | */ | ||
| 266 | std::vector<MatrixXs> Jintegrate_Js(const Eigen::Ref<const VectorXs>& x, | ||
| 267 | const Eigen::Ref<const VectorXs>& dx, | ||
| 268 | const Jcomponent firstsecond = both); | ||
| 269 | |||
| 270 | /** | ||
| 271 | * @brief Return the dimension of the state tuple | ||
| 272 | */ | ||
| 273 | std::size_t get_nx() const; | ||
| 274 | |||
| 275 | /** | ||
| 276 | * @brief Return the dimension of the tangent space of the state manifold | ||
| 277 | */ | ||
| 278 | std::size_t get_ndx() const; | ||
| 279 | |||
| 280 | /** | ||
| 281 | * @brief Return the dimension of the configuration tuple | ||
| 282 | */ | ||
| 283 | std::size_t get_nq() const; | ||
| 284 | |||
| 285 | /** | ||
| 286 | * @brief Return the dimension of tangent space of the configuration manifold | ||
| 287 | */ | ||
| 288 | std::size_t get_nv() const; | ||
| 289 | |||
| 290 | /** | ||
| 291 | * @brief Return the state lower bound | ||
| 292 | */ | ||
| 293 | const VectorXs& get_lb() const; | ||
| 294 | |||
| 295 | /** | ||
| 296 | * @brief Return the state upper bound | ||
| 297 | */ | ||
| 298 | const VectorXs& get_ub() const; | ||
| 299 | |||
| 300 | /** | ||
| 301 | * @brief Indicate if the state has defined limits | ||
| 302 | */ | ||
| 303 | bool get_has_limits() const; | ||
| 304 | |||
| 305 | /** | ||
| 306 | * @brief Modify the state lower bound | ||
| 307 | */ | ||
| 308 | void set_lb(const VectorXs& lb); | ||
| 309 | |||
| 310 | /** | ||
| 311 | * @brief Modify the state upper bound | ||
| 312 | */ | ||
| 313 | void set_ub(const VectorXs& ub); | ||
| 314 | |||
| 315 | protected: | ||
| 316 | void update_has_limits(); | ||
| 317 | |||
| 318 | std::size_t nx_; //!< State dimension | ||
| 319 | std::size_t ndx_; //!< State rate dimension | ||
| 320 | std::size_t nq_; //!< Configuration dimension | ||
| 321 | std::size_t nv_; //!< Velocity dimension | ||
| 322 | VectorXs lb_; //!< Lower state limits | ||
| 323 | VectorXs ub_; //!< Upper state limits | ||
| 324 | bool has_limits_; //!< Indicates whether any of the state limits is finite | ||
| 325 | }; | ||
| 326 | |||
| 327 | } // namespace crocoddyl | ||
| 328 | |||
| 329 | /* --- Details -------------------------------------------------------------- */ | ||
| 330 | /* --- Details -------------------------------------------------------------- */ | ||
| 331 | /* --- Details -------------------------------------------------------------- */ | ||
| 332 | #include "crocoddyl/core/state-base.hxx" | ||
| 333 | |||
| 334 | #endif // CROCODDYL_CORE_STATE_BASE_HPP_ | ||
| 335 |