| Directory: | ./ |
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| File: | include/crocoddyl/core/actions/lqr.hpp |
| Date: | 2025-01-30 11:01:55 |
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| Lines: | 16 | 24 | 66.7% |
| Branches: | 17 | 34 | 50.0% |
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| 1 | /////////////////////////////////////////////////////////////////////////////// | ||
| 2 | // BSD 3-Clause License | ||
| 3 | // | ||
| 4 | // Copyright (C) 2019-2024, LAAS-CNRS, University of Edinburgh | ||
| 5 | // Heriot-Watt University | ||
| 6 | // Copyright note valid unless otherwise stated in individual files. | ||
| 7 | // All rights reserved. | ||
| 8 | /////////////////////////////////////////////////////////////////////////////// | ||
| 9 | |||
| 10 | #ifndef CROCODDYL_CORE_ACTIONS_LQR_HPP_ | ||
| 11 | #define CROCODDYL_CORE_ACTIONS_LQR_HPP_ | ||
| 12 | |||
| 13 | #include <stdexcept> | ||
| 14 | |||
| 15 | #include "crocoddyl/core/action-base.hpp" | ||
| 16 | #include "crocoddyl/core/fwd.hpp" | ||
| 17 | #include "crocoddyl/core/states/euclidean.hpp" | ||
| 18 | |||
| 19 | namespace crocoddyl { | ||
| 20 | |||
| 21 | /** | ||
| 22 | * @brief Linear-quadratic regulator (LQR) action model | ||
| 23 | * | ||
| 24 | * A linear-quadratic regulator (LQR) action has a transition model of the form | ||
| 25 | * \f[ \begin{equation} | ||
| 26 | * \mathbf{x}^' = \mathbf{A x + B u + f}. | ||
| 27 | * \end{equation} \f] | ||
| 28 | * Its cost function is quadratic of the form: | ||
| 29 | * \f[ \begin{equation} | ||
| 30 | * \ell(\mathbf{x},\mathbf{u}) = \begin{bmatrix}1 | ||
| 31 | * \\ \mathbf{x} \\ \mathbf{u}\end{bmatrix}^T \begin{bmatrix}0 & | ||
| 32 | * \mathbf{q}^T & \mathbf{r}^T \\ \mathbf{q} & \mathbf{Q} | ||
| 33 | * & | ||
| 34 | * \mathbf{N}^T \\ | ||
| 35 | * \mathbf{r} & \mathbf{N} & \mathbf{R}\end{bmatrix} | ||
| 36 | * \begin{bmatrix}1 \\ \mathbf{x} \\ | ||
| 37 | * \mathbf{u}\end{bmatrix} | ||
| 38 | * \end{equation} \f] | ||
| 39 | * and the linear equality and inequality constraints has the form: | ||
| 40 | * \f[ \begin{aligned} | ||
| 41 | * \mathbf{g(x,u)} = \mathbf{G}\begin{bmatrix} \mathbf{x} \\ \mathbf{u} | ||
| 42 | * \end{bmatrix} [x,u] + \mathbf{g} \leq \mathbf{0} | ||
| 43 | * &\mathbf{h(x,u)} = \mathbf{H}\begin{bmatrix} \mathbf{x} \\ \mathbf{u} | ||
| 44 | * \end{bmatrix} [x,u] + \mathbf{h} \end{aligned} \f] | ||
| 45 | */ | ||
| 46 | template <typename _Scalar> | ||
| 47 | class ActionModelLQRTpl : public ActionModelAbstractTpl<_Scalar> { | ||
| 48 | public: | ||
| 49 | typedef _Scalar Scalar; | ||
| 50 | typedef ActionDataAbstractTpl<Scalar> ActionDataAbstract; | ||
| 51 | typedef ActionModelAbstractTpl<Scalar> Base; | ||
| 52 | typedef ActionDataLQRTpl<Scalar> Data; | ||
| 53 | typedef StateVectorTpl<Scalar> StateVector; | ||
| 54 | typedef MathBaseTpl<Scalar> MathBase; | ||
| 55 | typedef typename MathBase::VectorXs VectorXs; | ||
| 56 | typedef typename MathBase::MatrixXs MatrixXs; | ||
| 57 | |||
| 58 | /** | ||
| 59 | * @brief Initialize the LQR action model | ||
| 60 | * | ||
| 61 | * @param[in] A State matrix | ||
| 62 | * @param[in] B Input matrix | ||
| 63 | * @param[in] Q State weight matrix | ||
| 64 | * @param[in] R Input weight matrix | ||
| 65 | * @param[in] N State-input weight matrix | ||
| 66 | */ | ||
| 67 | ActionModelLQRTpl(const MatrixXs& A, const MatrixXs& B, const MatrixXs& Q, | ||
| 68 | const MatrixXs& R, const MatrixXs& N); | ||
| 69 | |||
| 70 | /** | ||
| 71 | * @brief Initialize the LQR action model | ||
| 72 | * | ||
| 73 | * @param[in] A State matrix | ||
| 74 | * @param[in] B Input matrix | ||
| 75 | * @param[in] Q State weight matrix | ||
| 76 | * @param[in] R Input weight matrix | ||
| 77 | * @param[in] N State-input weight matrix | ||
| 78 | * @param[in] f Dynamics drift | ||
| 79 | * @param[in] q State weight vector | ||
| 80 | * @param[in] r Input weight vector | ||
| 81 | */ | ||
| 82 | ActionModelLQRTpl(const MatrixXs& A, const MatrixXs& B, const MatrixXs& Q, | ||
| 83 | const MatrixXs& R, const MatrixXs& N, const VectorXs& f, | ||
| 84 | const VectorXs& q, const VectorXs& r); | ||
| 85 | |||
| 86 | /** | ||
| 87 | * @brief Initialize the LQR action model | ||
| 88 | * | ||
| 89 | * @param[in] A State matrix | ||
| 90 | * @param[in] B Input matrix | ||
| 91 | * @param[in] Q State weight matrix | ||
| 92 | * @param[in] R Input weight matrix | ||
| 93 | * @param[in] N State-input weight matrix | ||
| 94 | * @param[in] G State-input inequality constraint matrix | ||
| 95 | * @param[in] H State-input equality constraint matrix | ||
| 96 | * @param[in] f Dynamics drift | ||
| 97 | * @param[in] q State weight vector | ||
| 98 | * @param[in] r Input weight vector | ||
| 99 | * @param[in] g State-input inequality constraint bias | ||
| 100 | * @param[in] h State-input equality constraint bias | ||
| 101 | */ | ||
| 102 | ActionModelLQRTpl(const MatrixXs& A, const MatrixXs& B, const MatrixXs& Q, | ||
| 103 | const MatrixXs& R, const MatrixXs& N, const MatrixXs& G, | ||
| 104 | const MatrixXs& H, const VectorXs& f, const VectorXs& q, | ||
| 105 | const VectorXs& r, const VectorXs& g, const VectorXs& h); | ||
| 106 | |||
| 107 | /** | ||
| 108 | * @brief Initialize the LQR action model | ||
| 109 | * | ||
| 110 | * @param[in] nx Dimension of state vector | ||
| 111 | * @param[in] nu Dimension of control vector | ||
| 112 | * @param[in] drif_free Enable / disable the bias term of the linear dynamics | ||
| 113 | * (default true) | ||
| 114 | */ | ||
| 115 | ActionModelLQRTpl(const std::size_t nx, const std::size_t nu, | ||
| 116 | const bool drift_free = true); | ||
| 117 | |||
| 118 | /** @brief Copy constructor */ | ||
| 119 | ActionModelLQRTpl(const ActionModelLQRTpl& copy); | ||
| 120 | |||
| 121 | virtual ~ActionModelLQRTpl(); | ||
| 122 | |||
| 123 | virtual void calc(const std::shared_ptr<ActionDataAbstract>& data, | ||
| 124 | const Eigen::Ref<const VectorXs>& x, | ||
| 125 | const Eigen::Ref<const VectorXs>& u); | ||
| 126 | virtual void calc(const std::shared_ptr<ActionDataAbstract>& data, | ||
| 127 | const Eigen::Ref<const VectorXs>& x); | ||
| 128 | virtual void calcDiff(const std::shared_ptr<ActionDataAbstract>& data, | ||
| 129 | const Eigen::Ref<const VectorXs>& x, | ||
| 130 | const Eigen::Ref<const VectorXs>& u); | ||
| 131 | virtual void calcDiff(const std::shared_ptr<ActionDataAbstract>& data, | ||
| 132 | const Eigen::Ref<const VectorXs>& x); | ||
| 133 | virtual std::shared_ptr<ActionDataAbstract> createData(); | ||
| 134 | virtual bool checkData(const std::shared_ptr<ActionDataAbstract>& data); | ||
| 135 | |||
| 136 | /** | ||
| 137 | * @brief Create a random LQR model | ||
| 138 | * | ||
| 139 | * @param[in] nx State dimension | ||
| 140 | * @param[in] nu Control dimension | ||
| 141 | * @param[in] ng Inequality constraint dimension (default 0) | ||
| 142 | * @param[in] nh Equality constraint dimension (defaul 0) | ||
| 143 | */ | ||
| 144 | static ActionModelLQRTpl Random(const std::size_t nx, const std::size_t nu, | ||
| 145 | const std::size_t ng = 0, | ||
| 146 | const std::size_t nh = 0); | ||
| 147 | |||
| 148 | /** @brief Return the state matrix */ | ||
| 149 | const MatrixXs& get_A() const; | ||
| 150 | |||
| 151 | /** @brief Return the input matrix */ | ||
| 152 | const MatrixXs& get_B() const; | ||
| 153 | |||
| 154 | /** @brief Return the dynamics drift */ | ||
| 155 | const VectorXs& get_f() const; | ||
| 156 | |||
| 157 | /** @brief Return the state weight matrix */ | ||
| 158 | const MatrixXs& get_Q() const; | ||
| 159 | |||
| 160 | /** @brief Return the input weight matrix */ | ||
| 161 | const MatrixXs& get_R() const; | ||
| 162 | |||
| 163 | /** @brief Return the state-input weight matrix */ | ||
| 164 | const MatrixXs& get_N() const; | ||
| 165 | |||
| 166 | /** @brief Return the state-input inequality constraint matrix */ | ||
| 167 | const MatrixXs& get_G() const; | ||
| 168 | |||
| 169 | /** @brief Return the state-input equality constraint matrix */ | ||
| 170 | const MatrixXs& get_H() const; | ||
| 171 | |||
| 172 | /** @brief Return the state weight vector */ | ||
| 173 | const VectorXs& get_q() const; | ||
| 174 | |||
| 175 | /** @brief Return the input weight vector */ | ||
| 176 | const VectorXs& get_r() const; | ||
| 177 | |||
| 178 | /** @brief Return the state-input inequality constraint bias */ | ||
| 179 | const VectorXs& get_g() const; | ||
| 180 | |||
| 181 | /** @brief Return the state-input equality constraint bias */ | ||
| 182 | const VectorXs& get_h() const; | ||
| 183 | |||
| 184 | /** | ||
| 185 | * @brief Modify the LQR action model | ||
| 186 | * | ||
| 187 | * @param[in] A State matrix | ||
| 188 | * @param[in] B Input matrix | ||
| 189 | * @param[in] Q State weight matrix | ||
| 190 | * @param[in] R Input weight matrix | ||
| 191 | * @param[in] N State-input weight matrix | ||
| 192 | * @param[in] G State-input inequality constraint matrix | ||
| 193 | * @param[in] H State-input equality constraint matrix | ||
| 194 | * @param[in] f Dynamics drift | ||
| 195 | * @param[in] q State weight vector | ||
| 196 | * @param[in] r Input weight vector | ||
| 197 | * @param[in] g State-input inequality constraint bias | ||
| 198 | * @param[in] h State-input equality constraint bias | ||
| 199 | */ | ||
| 200 | void set_LQR(const MatrixXs& A, const MatrixXs& B, const MatrixXs& Q, | ||
| 201 | const MatrixXs& R, const MatrixXs& N, const MatrixXs& G, | ||
| 202 | const MatrixXs& H, const VectorXs& f, const VectorXs& q, | ||
| 203 | const VectorXs& r, const VectorXs& g, const VectorXs& h); | ||
| 204 | |||
| 205 | DEPRECATED("Use get_A", const MatrixXs& get_Fx() const { return get_A(); }) | ||
| 206 | DEPRECATED("Use get_B", const MatrixXs& get_Fu() const { return get_B(); }) | ||
| 207 | DEPRECATED("Use get_f", const VectorXs& get_f0() const { return get_f(); }) | ||
| 208 | DEPRECATED("Use get_q", const VectorXs& get_lx() const { return get_q(); }) | ||
| 209 | DEPRECATED("Use get_r", const VectorXs& get_lu() const { return get_r(); }) | ||
| 210 | DEPRECATED("Use get_Q", const MatrixXs& get_Lxx() const { return get_Q(); }) | ||
| 211 | DEPRECATED("Use get_R", const MatrixXs& get_Lxu() const { return get_R(); }) | ||
| 212 | DEPRECATED("Use get_N", const MatrixXs& get_Luu() const { return get_N(); }) | ||
| 213 | ✗ | DEPRECATED( | |
| 214 | "Use set_LQR", void set_Fx(const MatrixXs& A) { | ||
| 215 | set_LQR(A, B_, Q_, R_, N_, G_, H_, f_, q_, r_, g_, h_); | ||
| 216 | }) | ||
| 217 | ✗ | DEPRECATED( | |
| 218 | "Use set_LQR", void set_Fu(const MatrixXs& B) { | ||
| 219 | set_LQR(A_, B, Q_, R_, N_, G_, H_, f_, q_, r_, g_, h_); | ||
| 220 | }) | ||
| 221 | ✗ | DEPRECATED( | |
| 222 | "Use set_LQR", void set_f0(const VectorXs& f) { | ||
| 223 | set_LQR(A_, B_, Q_, R_, N_, G_, H_, f, q_, r_, g_, h_); | ||
| 224 | }) | ||
| 225 | ✗ | DEPRECATED( | |
| 226 | "Use set_LQR", void set_lx(const VectorXs& q) { | ||
| 227 | set_LQR(A_, B_, Q_, R_, N_, G_, H_, f_, q, r_, g_, h_); | ||
| 228 | }) | ||
| 229 | ✗ | DEPRECATED( | |
| 230 | "Use set_LQR", void set_lu(const VectorXs& r) { | ||
| 231 | set_LQR(A_, B_, Q_, R_, N_, G_, H_, f_, q_, r, g_, h_); | ||
| 232 | }) | ||
| 233 | ✗ | DEPRECATED( | |
| 234 | "Use set_LQR", void set_Lxx(const MatrixXs& Q) { | ||
| 235 | set_LQR(A_, B_, Q, R_, N_, G_, H_, f_, q_, r_, g_, h_); | ||
| 236 | }) | ||
| 237 | ✗ | DEPRECATED( | |
| 238 | "Use set_LQR", void set_Luu(const MatrixXs& R) { | ||
| 239 | set_LQR(A_, B_, Q_, R, N_, G_, H_, f_, q_, r_, g_, h_); | ||
| 240 | }) | ||
| 241 | ✗ | DEPRECATED( | |
| 242 | "Use set_LQR", void set_Lxu(const MatrixXs& N) { | ||
| 243 | set_LQR(A_, B_, Q_, R_, N, G_, H_, f_, q_, r_, g_, h_); | ||
| 244 | }) | ||
| 245 | |||
| 246 | /** | ||
| 247 | * @brief Print relevant information of the LQR model | ||
| 248 | * | ||
| 249 | * @param[out] os Output stream object | ||
| 250 | */ | ||
| 251 | virtual void print(std::ostream& os) const; | ||
| 252 | |||
| 253 | protected: | ||
| 254 | using Base::ng_; //!< Equality constraint dimension | ||
| 255 | using Base::nh_; //!< Inequality constraint dimension | ||
| 256 | using Base::nu_; //!< Control dimension | ||
| 257 | using Base::state_; //!< Model of the state | ||
| 258 | |||
| 259 | private: | ||
| 260 | MatrixXs A_; | ||
| 261 | MatrixXs B_; | ||
| 262 | MatrixXs Q_; | ||
| 263 | MatrixXs R_; | ||
| 264 | MatrixXs N_; | ||
| 265 | MatrixXs G_; | ||
| 266 | MatrixXs H_; | ||
| 267 | VectorXs f_; | ||
| 268 | VectorXs q_; | ||
| 269 | VectorXs r_; | ||
| 270 | VectorXs g_; | ||
| 271 | VectorXs h_; | ||
| 272 | MatrixXs L_; | ||
| 273 | bool drift_free_; | ||
| 274 | bool updated_lqr_; | ||
| 275 | }; | ||
| 276 | |||
| 277 | template <typename _Scalar> | ||
| 278 | struct ActionDataLQRTpl : public ActionDataAbstractTpl<_Scalar> { | ||
| 279 | typedef _Scalar Scalar; | ||
| 280 | typedef MathBaseTpl<Scalar> MathBase; | ||
| 281 | typedef ActionDataAbstractTpl<Scalar> Base; | ||
| 282 | typedef typename MathBase::VectorXs VectorXs; | ||
| 283 | |||
| 284 | template <template <typename Scalar> class Model> | ||
| 285 | 1617 | explicit ActionDataLQRTpl(Model<Scalar>* const model) | |
| 286 | : Base(model), | ||
| 287 |
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1617 | R_u_tmp(VectorXs::Zero(static_cast<Eigen::Index>(model->get_nu()))), |
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1617 | Q_x_tmp(VectorXs::Zero( |
| 289 | 3234 | static_cast<Eigen::Index>(model->get_state()->get_ndx()))) { | |
| 290 | // Setting the linear model and quadratic cost as they are constant | ||
| 291 | 1617 | const std::size_t nq = model->get_state()->get_nq(); | |
| 292 | 1617 | const std::size_t nu = model->get_nu(); | |
| 293 |
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1617 | Fx = model->get_A(); |
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1617 | Fu = model->get_B(); |
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1617 | Lxx = model->get_Q(); |
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1617 | Luu = model->get_R(); |
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1617 | Lxu = model->get_N(); |
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1617 | Gx = model->get_G().leftCols(2 * nq); |
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1617 | Gu = model->get_G().rightCols(nu); |
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1617 | Hx = model->get_H().leftCols(2 * nq); |
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1617 | Hu = model->get_H().rightCols(nu); |
| 302 | 1617 | } | |
| 303 | |||
| 304 | using Base::cost; | ||
| 305 | using Base::Fu; | ||
| 306 | using Base::Fx; | ||
| 307 | using Base::Gu; | ||
| 308 | using Base::Gx; | ||
| 309 | using Base::Hu; | ||
| 310 | using Base::Hx; | ||
| 311 | using Base::Lu; | ||
| 312 | using Base::Luu; | ||
| 313 | using Base::Lx; | ||
| 314 | using Base::Lxu; | ||
| 315 | using Base::Lxx; | ||
| 316 | using Base::r; | ||
| 317 | using Base::xnext; | ||
| 318 | |||
| 319 | VectorXs R_u_tmp; // Temporary variable for storing Hessian-vector product | ||
| 320 | // (size: nu) | ||
| 321 | VectorXs Q_x_tmp; // Temporary variable for storing Hessian-vector product | ||
| 322 | // (size: nx) | ||
| 323 | }; | ||
| 324 | |||
| 325 | } // namespace crocoddyl | ||
| 326 | |||
| 327 | /* --- Details -------------------------------------------------------------- */ | ||
| 328 | /* --- Details -------------------------------------------------------------- */ | ||
| 329 | /* --- Details -------------------------------------------------------------- */ | ||
| 330 | #include "crocoddyl/core/actions/lqr.hxx" | ||
| 331 | |||
| 332 | #endif // CROCODDYL_CORE_ACTIONS_LQR_HPP_ | ||
| 333 |