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File: | include/crocoddyl/core/action-base.hpp |
Date: | 2025-01-16 08:47:40 |
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1 | /////////////////////////////////////////////////////////////////////////////// | ||
2 | // BSD 3-Clause License | ||
3 | // | ||
4 | // Copyright (C) 2019-2024, LAAS-CNRS, University of Edinburgh, | ||
5 | // University of Oxford, Heriot-Watt University | ||
6 | // Copyright note valid unless otherwise stated in individual files. | ||
7 | // All rights reserved. | ||
8 | /////////////////////////////////////////////////////////////////////////////// | ||
9 | |||
10 | #ifndef CROCODDYL_CORE_ACTION_BASE_HPP_ | ||
11 | #define CROCODDYL_CORE_ACTION_BASE_HPP_ | ||
12 | |||
13 | #include <boost/make_shared.hpp> | ||
14 | #include <boost/shared_ptr.hpp> | ||
15 | #include <stdexcept> | ||
16 | |||
17 | #include "crocoddyl/core/fwd.hpp" | ||
18 | #include "crocoddyl/core/state-base.hpp" | ||
19 | #include "crocoddyl/core/utils/math.hpp" | ||
20 | |||
21 | namespace crocoddyl { | ||
22 | |||
23 | /** | ||
24 | * @brief Abstract class for action model | ||
25 | * | ||
26 | * An action model combines dynamics, cost functions and constraints. Each node, | ||
27 | * in our optimal control problem, is described through an action model. Every | ||
28 | * time that we want describe a problem, we need to provide ways of computing | ||
29 | * the dynamics, cost functions, constraints and their derivatives. All these is | ||
30 | * described inside the action model. | ||
31 | * | ||
32 | * Concretely speaking, the action model describes a time-discrete action model | ||
33 | * with a first-order ODE along a cost function, i.e. | ||
34 | * - the state \f$\mathbf{z}\in\mathcal{Z}\f$ lies in a manifold described with | ||
35 | * a `nx`-tuple, | ||
36 | * - the state rate \f$\mathbf{\dot{x}}\in T_{\mathbf{q}}\mathcal{Q}\f$ is the | ||
37 | * tangent vector to the state manifold with `ndx` dimension, | ||
38 | * - the control input \f$\mathbf{u}\in\mathbb{R}^{nu}\f$ is an Euclidean | ||
39 | * vector | ||
40 | * - \f$\mathbf{r}(\cdot)\f$ and \f$a(\cdot)\f$ are the residual and activation | ||
41 | * functions (see `ResidualModelAbstractTpl` and `ActivationModelAbstractTpl`, | ||
42 | * respetively), | ||
43 | * - \f$\mathbf{g}(\cdot)\in\mathbb{R}^{ng}\f$ and | ||
44 | * \f$\mathbf{h}(\cdot)\in\mathbb{R}^{nh}\f$ are the inequality and equality | ||
45 | * vector functions, respectively. | ||
46 | * | ||
47 | * The computation of these equations are carried out out inside `calc()` | ||
48 | * function. In short, this function computes the system acceleration, cost and | ||
49 | * constraints values (also called constraints violations). This procedure is | ||
50 | * equivalent to running a forward pass of the action model. | ||
51 | * | ||
52 | * However, during numerical optimization, we also need to run backward passes | ||
53 | * of the action model. These calculations are performed by `calcDiff()`. In | ||
54 | * short, this method builds a linear-quadratic approximation of the action | ||
55 | * model, i.e.: \f[ \begin{aligned} | ||
56 | * &\delta\mathbf{x}_{k+1} = | ||
57 | * \mathbf{f_x}\delta\mathbf{x}_k+\mathbf{f_u}\delta\mathbf{u}_k, | ||
58 | * &\textrm{(dynamics)}\\ | ||
59 | * &\ell(\delta\mathbf{x}_k,\delta\mathbf{u}_k) = \begin{bmatrix}1 | ||
60 | * \\ \delta\mathbf{x}_k \\ \delta\mathbf{u}_k\end{bmatrix}^T \begin{bmatrix}0 & | ||
61 | * \mathbf{\ell_x}^T & \mathbf{\ell_u}^T \\ \mathbf{\ell_x} & \mathbf{\ell_{xx}} | ||
62 | * & | ||
63 | * \mathbf{\ell_{ux}}^T \\ | ||
64 | * \mathbf{\ell_u} & \mathbf{\ell_{ux}} & \mathbf{\ell_{uu}}\end{bmatrix} | ||
65 | * \begin{bmatrix}1 \\ \delta\mathbf{x}_k \\ | ||
66 | * \delta\mathbf{u}_k\end{bmatrix}, &\textrm{(cost)}\\ | ||
67 | * &\mathbf{g}(\delta\mathbf{x}_k,\delta\mathbf{u}_k)<\mathbf{0}, | ||
68 | * &\textrm{(inequality constraint)}\\ | ||
69 | * &\mathbf{h}(\delta\mathbf{x}_k,\delta\mathbf{u}_k)=\mathbf{0}, | ||
70 | * &\textrm{(equality constraint)} \end{aligned} \f] where | ||
71 | * - \f$\mathbf{f_x}\in\mathbb{R}^{ndx\times ndx}\f$ and | ||
72 | * \f$\mathbf{f_u}\in\mathbb{R}^{ndx\times nu}\f$ are the Jacobians of the | ||
73 | * dynamics, | ||
74 | * - \f$\mathbf{\ell_x}\in\mathbb{R}^{ndx}\f$ and | ||
75 | * \f$\mathbf{\ell_u}\in\mathbb{R}^{nu}\f$ are the Jacobians of the cost | ||
76 | * function, | ||
77 | * - \f$\mathbf{\ell_{xx}}\in\mathbb{R}^{ndx\times ndx}\f$, | ||
78 | * \f$\mathbf{\ell_{xu}}\in\mathbb{R}^{ndx\times nu}\f$ and | ||
79 | * \f$\mathbf{\ell_{uu}}\in\mathbb{R}^{nu\times nu}\f$ are the Hessians of the | ||
80 | * cost function, | ||
81 | * - \f$\mathbf{g_x}\in\mathbb{R}^{ng\times ndx}\f$ and | ||
82 | * \f$\mathbf{g_u}\in\mathbb{R}^{ng\times nu}\f$ are the Jacobians of the | ||
83 | * inequality constraints, and | ||
84 | * - \f$\mathbf{h_x}\in\mathbb{R}^{nh\times ndx}\f$ and | ||
85 | * \f$\mathbf{h_u}\in\mathbb{R}^{nh\times nu}\f$ are the Jacobians of the | ||
86 | * equality constraints. | ||
87 | * | ||
88 | * Additionally, it is important to note that `calcDiff()` computes the | ||
89 | * derivatives using the latest stored values by `calc()`. Thus, we need to | ||
90 | * first run `calc()`. | ||
91 | * | ||
92 | * \sa `calc()`, `calcDiff()`, `createData()` | ||
93 | */ | ||
94 | template <typename _Scalar> | ||
95 | class ActionModelAbstractTpl { | ||
96 | public: | ||
97 | EIGEN_MAKE_ALIGNED_OPERATOR_NEW | ||
98 | |||
99 | typedef _Scalar Scalar; | ||
100 | typedef MathBaseTpl<Scalar> MathBase; | ||
101 | typedef ActionDataAbstractTpl<Scalar> ActionDataAbstract; | ||
102 | typedef StateAbstractTpl<Scalar> StateAbstract; | ||
103 | typedef typename MathBase::VectorXs VectorXs; | ||
104 | |||
105 | /** | ||
106 | * @brief Initialize the action model | ||
107 | * | ||
108 | * @param[in] state State description | ||
109 | * @param[in] nu Dimension of control vector | ||
110 | * @param[in] nr Dimension of cost-residual vector | ||
111 | * @param[in] ng Number of inequality constraints (default 0) | ||
112 | * @param[in] nh Number of equality constraints (default 0) | ||
113 | * @param[in] ng_T Number of inequality terminal constraints (default 0) | ||
114 | * @param[in] nh_T Number of equality terminal constraints (default 0) | ||
115 | */ | ||
116 | ActionModelAbstractTpl(boost::shared_ptr<StateAbstract> state, | ||
117 | const std::size_t nu, const std::size_t nr = 0, | ||
118 | const std::size_t ng = 0, const std::size_t nh = 0, | ||
119 | const std::size_t ng_T = 0, | ||
120 | const std::size_t nh_T = 0); | ||
121 | virtual ~ActionModelAbstractTpl(); | ||
122 | |||
123 | /** | ||
124 | * @brief Compute the next state and cost value | ||
125 | * | ||
126 | * @param[in] data Action data | ||
127 | * @param[in] x State point \f$\mathbf{x}\in\mathbb{R}^{ndx}\f$ | ||
128 | * @param[in] u Control input \f$\mathbf{u}\in\mathbb{R}^{nu}\f$ | ||
129 | */ | ||
130 | virtual void calc(const boost::shared_ptr<ActionDataAbstract>& data, | ||
131 | const Eigen::Ref<const VectorXs>& x, | ||
132 | const Eigen::Ref<const VectorXs>& u) = 0; | ||
133 | |||
134 | /** | ||
135 | * @brief Compute the total cost value for nodes that depends only on the | ||
136 | * state | ||
137 | * | ||
138 | * It updates the total cost and the next state is not computed as it is not | ||
139 | * expected to change. This function is used in the terminal nodes of an | ||
140 | * optimal control problem. | ||
141 | * | ||
142 | * @param[in] data Action data | ||
143 | * @param[in] x State point \f$\mathbf{x}\in\mathbb{R}^{ndx}\f$ | ||
144 | */ | ||
145 | virtual void calc(const boost::shared_ptr<ActionDataAbstract>& data, | ||
146 | const Eigen::Ref<const VectorXs>& x); | ||
147 | |||
148 | /** | ||
149 | * @brief Compute the derivatives of the dynamics and cost functions | ||
150 | * | ||
151 | * It computes the partial derivatives of the dynamical system and the cost | ||
152 | * function. It assumes that `calc()` has been run first. This function builds | ||
153 | * a linear-quadratic approximation of the action model (i.e. dynamical system | ||
154 | * and cost function). | ||
155 | * | ||
156 | * @param[in] data Action data | ||
157 | * @param[in] x State point \f$\mathbf{x}\in\mathbb{R}^{ndx}\f$ | ||
158 | * @param[in] u Control input \f$\mathbf{u}\in\mathbb{R}^{nu}\f$ | ||
159 | */ | ||
160 | virtual void calcDiff(const boost::shared_ptr<ActionDataAbstract>& data, | ||
161 | const Eigen::Ref<const VectorXs>& x, | ||
162 | const Eigen::Ref<const VectorXs>& u) = 0; | ||
163 | |||
164 | /** | ||
165 | * @brief Compute the derivatives of the cost functions with respect to the | ||
166 | * state only | ||
167 | * | ||
168 | * It updates the derivatives of the cost function with respect to the state | ||
169 | * only. This function is used in the terminal nodes of an optimal control | ||
170 | * problem. | ||
171 | * | ||
172 | * @param[in] data Action data | ||
173 | * @param[in] x State point \f$\mathbf{x}\in\mathbb{R}^{ndx}\f$ | ||
174 | */ | ||
175 | virtual void calcDiff(const boost::shared_ptr<ActionDataAbstract>& data, | ||
176 | const Eigen::Ref<const VectorXs>& x); | ||
177 | |||
178 | /** | ||
179 | * @brief Create the action data | ||
180 | * | ||
181 | * @return the action data | ||
182 | */ | ||
183 | virtual boost::shared_ptr<ActionDataAbstract> createData(); | ||
184 | |||
185 | /** | ||
186 | * @brief Checks that a specific data belongs to this model | ||
187 | */ | ||
188 | virtual bool checkData(const boost::shared_ptr<ActionDataAbstract>& data); | ||
189 | |||
190 | /** | ||
191 | * @brief Computes the quasic static commands | ||
192 | * | ||
193 | * The quasic static commands are the ones produced for a the reference | ||
194 | * posture as an equilibrium point, i.e. for | ||
195 | * \f$\mathbf{f^q_x}\delta\mathbf{q}+\mathbf{f_u}\delta\mathbf{u}=\mathbf{0}\f$ | ||
196 | * | ||
197 | * @param[in] data Action data | ||
198 | * @param[out] u Quasic static commands | ||
199 | * @param[in] x State point (velocity has to be zero) | ||
200 | * @param[in] maxiter Maximum allowed number of iterations | ||
201 | * @param[in] tol Tolerance | ||
202 | */ | ||
203 | virtual void quasiStatic(const boost::shared_ptr<ActionDataAbstract>& data, | ||
204 | Eigen::Ref<VectorXs> u, | ||
205 | const Eigen::Ref<const VectorXs>& x, | ||
206 | const std::size_t maxiter = 100, | ||
207 | const Scalar tol = Scalar(1e-9)); | ||
208 | |||
209 | /** | ||
210 | * @copybrief quasicStatic() | ||
211 | * | ||
212 | * @copydetails quasicStatic() | ||
213 | * | ||
214 | * @param[in] data Action data | ||
215 | * @param[in] x State point (velocity has to be zero) | ||
216 | * @param[in] maxiter Maximum allowed number of iterations | ||
217 | * @param[in] tol Tolerance | ||
218 | * @return Quasic static commands | ||
219 | */ | ||
220 | VectorXs quasiStatic_x(const boost::shared_ptr<ActionDataAbstract>& data, | ||
221 | const VectorXs& x, const std::size_t maxiter = 100, | ||
222 | const Scalar tol = Scalar(1e-9)); | ||
223 | |||
224 | /** | ||
225 | * @brief Return the dimension of the control input | ||
226 | */ | ||
227 | std::size_t get_nu() const; | ||
228 | |||
229 | /** | ||
230 | * @brief Return the dimension of the cost-residual vector | ||
231 | */ | ||
232 | std::size_t get_nr() const; | ||
233 | |||
234 | /** | ||
235 | * @brief Return the number of inequality constraints | ||
236 | */ | ||
237 | virtual std::size_t get_ng() const; | ||
238 | |||
239 | /** | ||
240 | * @brief Return the number of equality constraints | ||
241 | */ | ||
242 | virtual std::size_t get_nh() const; | ||
243 | |||
244 | /** | ||
245 | * @brief Return the number of inequality terminal constraints | ||
246 | */ | ||
247 | virtual std::size_t get_ng_T() const; | ||
248 | |||
249 | /** | ||
250 | * @brief Return the number of equality terminal constraints | ||
251 | */ | ||
252 | virtual std::size_t get_nh_T() const; | ||
253 | |||
254 | /** | ||
255 | * @brief Return the state | ||
256 | */ | ||
257 | const boost::shared_ptr<StateAbstract>& get_state() const; | ||
258 | |||
259 | /** | ||
260 | * @brief Return the lower bound of the inequality constraints | ||
261 | */ | ||
262 | virtual const VectorXs& get_g_lb() const; | ||
263 | |||
264 | /** | ||
265 | * @brief Return the upper bound of the inequality constraints | ||
266 | */ | ||
267 | virtual const VectorXs& get_g_ub() const; | ||
268 | |||
269 | /** | ||
270 | * @brief Return the control lower bound | ||
271 | */ | ||
272 | const VectorXs& get_u_lb() const; | ||
273 | |||
274 | /** | ||
275 | * @brief Return the control upper bound | ||
276 | */ | ||
277 | const VectorXs& get_u_ub() const; | ||
278 | |||
279 | /** | ||
280 | * @brief Indicates if there are defined control limits | ||
281 | */ | ||
282 | bool get_has_control_limits() const; | ||
283 | |||
284 | /** | ||
285 | * @brief Modify the lower bound of the inequality constraints | ||
286 | */ | ||
287 | void set_g_lb(const VectorXs& g_lb); | ||
288 | |||
289 | /** | ||
290 | * @brief Modify the upper bound of the inequality constraints | ||
291 | */ | ||
292 | void set_g_ub(const VectorXs& g_ub); | ||
293 | |||
294 | /** | ||
295 | * @brief Modify the control lower bounds | ||
296 | */ | ||
297 | void set_u_lb(const VectorXs& u_lb); | ||
298 | |||
299 | /** | ||
300 | * @brief Modify the control upper bounds | ||
301 | */ | ||
302 | void set_u_ub(const VectorXs& u_ub); | ||
303 | |||
304 | /** | ||
305 | * @brief Print information on the action model | ||
306 | */ | ||
307 | template <class Scalar> | ||
308 | friend std::ostream& operator<<(std::ostream& os, | ||
309 | const ActionModelAbstractTpl<Scalar>& model); | ||
310 | |||
311 | /** | ||
312 | * @brief Print relevant information of the action model | ||
313 | * | ||
314 | * @param[out] os Output stream object | ||
315 | */ | ||
316 | virtual void print(std::ostream& os) const; | ||
317 | |||
318 | protected: | ||
319 | std::size_t nu_; //!< Control dimension | ||
320 | std::size_t nr_; //!< Dimension of the cost residual | ||
321 | std::size_t ng_; //!< Number of inequality constraints | ||
322 | std::size_t nh_; //!< Number of equality constraints | ||
323 | std::size_t ng_T_; //!< Number of inequality terminal constraints | ||
324 | std::size_t nh_T_; //!< Number of equality terminal constraints | ||
325 | boost::shared_ptr<StateAbstract> state_; //!< Model of the state | ||
326 | VectorXs unone_; //!< Neutral state | ||
327 | VectorXs g_lb_; //!< Lower bound of the inequality constraints | ||
328 | VectorXs g_ub_; //!< Lower bound of the inequality constraints | ||
329 | VectorXs u_lb_; //!< Lower control limits | ||
330 | VectorXs u_ub_; //!< Upper control limits | ||
331 | bool has_control_limits_; //!< Indicates whether any of the control limits is | ||
332 | //!< finite | ||
333 | |||
334 | /** | ||
335 | * @brief Update the status of the control limits (i.e. if there are defined | ||
336 | * limits) | ||
337 | */ | ||
338 | void update_has_control_limits(); | ||
339 | |||
340 | template <class Scalar> | ||
341 | friend class ConstraintModelManagerTpl; | ||
342 | }; | ||
343 | |||
344 | template <typename _Scalar> | ||
345 | struct ActionDataAbstractTpl { | ||
346 | EIGEN_MAKE_ALIGNED_OPERATOR_NEW | ||
347 | |||
348 | typedef _Scalar Scalar; | ||
349 | typedef MathBaseTpl<Scalar> MathBase; | ||
350 | typedef typename MathBase::VectorXs VectorXs; | ||
351 | typedef typename MathBase::MatrixXs MatrixXs; | ||
352 | |||
353 | template <template <typename Scalar> class Model> | ||
354 | 93157 | explicit ActionDataAbstractTpl(Model<Scalar>* const model) | |
355 | 93157 | : cost(Scalar(0.)), | |
356 |
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93157 | xnext(model->get_state()->get_nx()), |
357 |
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186314 | model->get_nu()) { |
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396 | 93157 | } | |
397 | 48098 | virtual ~ActionDataAbstractTpl() {} | |
398 | |||
399 | Scalar cost; //!< cost value | ||
400 | VectorXs xnext; //!< evolution state | ||
401 | MatrixXs Fx; //!< Jacobian of the dynamics w.r.t. the state \f$\mathbf{x}\f$ | ||
402 | MatrixXs | ||
403 | Fu; //!< Jacobian of the dynamics w.r.t. the control \f$\mathbf{u}\f$ | ||
404 | VectorXs r; //!< Cost residual | ||
405 | VectorXs Lx; //!< Jacobian of the cost w.r.t. the state \f$\mathbf{x}\f$ | ||
406 | VectorXs Lu; //!< Jacobian of the cost w.r.t. the control \f$\mathbf{u}\f$ | ||
407 | MatrixXs Lxx; //!< Hessian of the cost w.r.t. the state \f$\mathbf{x}\f$ | ||
408 | MatrixXs Lxu; //!< Hessian of the cost w.r.t. the state \f$\mathbf{x}\f$ and | ||
409 | //!< control \f$\mathbf{u}\f$ | ||
410 | MatrixXs Luu; //!< Hessian of the cost w.r.t. the control \f$\mathbf{u}\f$ | ||
411 | VectorXs g; //!< Inequality constraint values | ||
412 | MatrixXs Gx; //!< Jacobian of the inequality constraint w.r.t. the state | ||
413 | //!< \f$\mathbf{x}\f$ | ||
414 | MatrixXs Gu; //!< Jacobian of the inequality constraint w.r.t. the control | ||
415 | //!< \f$\mathbf{u}\f$ | ||
416 | VectorXs h; //!< Equality constraint values | ||
417 | MatrixXs Hx; //!< Jacobian of the equality constraint w.r.t. the state | ||
418 | //!< \f$\mathbf{x}\f$ | ||
419 | MatrixXs Hu; //!< Jacobian of the equality constraint w.r.t. the control | ||
420 | //!< \f$\mathbf{u}\f$ | ||
421 | }; | ||
422 | |||
423 | } // namespace crocoddyl | ||
424 | |||
425 | /* --- Details -------------------------------------------------------------- */ | ||
426 | /* --- Details -------------------------------------------------------------- */ | ||
427 | /* --- Details -------------------------------------------------------------- */ | ||
428 | #include "crocoddyl/core/action-base.hxx" | ||
429 | |||
430 | #endif // CROCODDYL_CORE_ACTION_BASE_HPP_ | ||
431 |