Directory: | ./ |
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File: | include/crocoddyl/core/integrator/rk.hpp |
Date: | 2025-03-26 19:23:43 |
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1 | /////////////////////////////////////////////////////////////////////////////// | ||
2 | // BSD 3-Clause License | ||
3 | // | ||
4 | // Copyright (C) 2019-2025, University of Edinburgh, University of Trento, | ||
5 | // LAAS-CNRS, IRI: CSIC-UPC, Heriot-Watt University | ||
6 | // Copyright note valid unless otherwise stated in individual files. | ||
7 | // All rights reserved. | ||
8 | /////////////////////////////////////////////////////////////////////////////// | ||
9 | |||
10 | #ifndef CROCODDYL_CORE_INTEGRATOR_RK_HPP_ | ||
11 | #define CROCODDYL_CORE_INTEGRATOR_RK_HPP_ | ||
12 | |||
13 | #include "crocoddyl/core/fwd.hpp" | ||
14 | #include "crocoddyl/core/integ-action-base.hpp" | ||
15 | |||
16 | namespace crocoddyl { | ||
17 | |||
18 | enum RKType { two = 2, three = 3, four = 4 }; | ||
19 | |||
20 | /** | ||
21 | * @brief Standard RK integrator | ||
22 | * | ||
23 | * It applies a standard RK integration schemes to a differential (i.e., | ||
24 | * continuous time) action model. The available integrators are: RK2, RK3, and | ||
25 | * RK4. | ||
26 | * | ||
27 | * This standard RK scheme introduces also the possibility to parametrize the | ||
28 | * control trajectory inside an integration step, for instance using | ||
29 | * polynomials. This requires introducing some notation to clarify the | ||
30 | * difference between the control inputs of the differential model and the | ||
31 | * control inputs to the integrated model. We have decided to use | ||
32 | * \f$\mathbf{w}\f$ to refer to the control inputs of the differential model and | ||
33 | * \f$\mathbf{u}\f$ for the control inputs of the integrated action model. | ||
34 | * | ||
35 | * \sa `IntegratedActionModelAbstractTpl`, `calc()`, `calcDiff()`, | ||
36 | * `createData()` | ||
37 | */ | ||
38 | template <typename _Scalar> | ||
39 | class IntegratedActionModelRKTpl | ||
40 | : public IntegratedActionModelAbstractTpl<_Scalar> { | ||
41 | public: | ||
42 | EIGEN_MAKE_ALIGNED_OPERATOR_NEW | ||
43 | ✗ | CROCODDYL_DERIVED_CAST(ActionModelBase, IntegratedActionModelRKTpl) | |
44 | |||
45 | typedef _Scalar Scalar; | ||
46 | typedef MathBaseTpl<Scalar> MathBase; | ||
47 | typedef IntegratedActionModelAbstractTpl<Scalar> Base; | ||
48 | typedef IntegratedActionDataRKTpl<Scalar> Data; | ||
49 | typedef ActionDataAbstractTpl<Scalar> ActionDataAbstract; | ||
50 | typedef DifferentialActionModelAbstractTpl<Scalar> | ||
51 | DifferentialActionModelAbstract; | ||
52 | typedef DifferentialActionDataAbstractTpl<Scalar> | ||
53 | DifferentialActionDataAbstract; | ||
54 | typedef ControlParametrizationModelAbstractTpl<Scalar> | ||
55 | ControlParametrizationModelAbstract; | ||
56 | typedef ControlParametrizationDataAbstractTpl<Scalar> | ||
57 | ControlParametrizationDataAbstract; | ||
58 | typedef typename MathBase::VectorXs VectorXs; | ||
59 | typedef typename MathBase::MatrixXs MatrixXs; | ||
60 | |||
61 | /** | ||
62 | * @brief Initialize the RK integrator | ||
63 | * | ||
64 | * @param[in] model Differential action model | ||
65 | * @param[in] control Control parametrization | ||
66 | * @param[in] rktype Type of RK integrator | ||
67 | * @param[in] time_step Step time (default 1e-3) | ||
68 | * @param[in] with_cost_residual Compute cost residual (default true) | ||
69 | */ | ||
70 | IntegratedActionModelRKTpl( | ||
71 | std::shared_ptr<DifferentialActionModelAbstract> model, | ||
72 | std::shared_ptr<ControlParametrizationModelAbstract> control, | ||
73 | const RKType rktype, const Scalar time_step = Scalar(1e-3), | ||
74 | const bool with_cost_residual = true); | ||
75 | |||
76 | /** | ||
77 | * @brief Initialize the RK integrator | ||
78 | * | ||
79 | * This initialization uses `ControlParametrizationPolyZeroTpl` for the | ||
80 | * control parametrization. | ||
81 | * | ||
82 | * @param[in] model Differential action model | ||
83 | * @param[in] rktype Type of RK integrator | ||
84 | * @param[in] time_step Step time (default 1e-3) | ||
85 | * @param[in] with_cost_residual Compute cost residual (default true) | ||
86 | */ | ||
87 | IntegratedActionModelRKTpl( | ||
88 | std::shared_ptr<DifferentialActionModelAbstract> model, | ||
89 | const RKType rktype, const Scalar time_step = Scalar(1e-3), | ||
90 | const bool with_cost_residual = true); | ||
91 | 1668 | virtual ~IntegratedActionModelRKTpl() = default; | |
92 | |||
93 | /** | ||
94 | * @brief Integrate the differential action model using RK scheme | ||
95 | * | ||
96 | * @param[in] data RK integrator data | ||
97 | * @param[in] x State point \f$\mathbf{x}\in\mathbb{R}^{ndx}\f$ | ||
98 | * @param[in] u Control input \f$\mathbf{u}\in\mathbb{R}^{nu}\f$ | ||
99 | */ | ||
100 | virtual void calc(const std::shared_ptr<ActionDataAbstract>& data, | ||
101 | const Eigen::Ref<const VectorXs>& x, | ||
102 | const Eigen::Ref<const VectorXs>& u) override; | ||
103 | |||
104 | /** | ||
105 | * @brief Integrate the total cost value for nodes that depends only on the | ||
106 | * state using RK scheme | ||
107 | * | ||
108 | * It computes the total cost and defines the next state as the current one. | ||
109 | * This function is used in the terminal nodes of an optimal control problem. | ||
110 | * | ||
111 | * @param[in] data RK integrator data | ||
112 | * @param[in] x State point \f$\mathbf{x}\in\mathbb{R}^{ndx}\f$ | ||
113 | */ | ||
114 | virtual void calc(const std::shared_ptr<ActionDataAbstract>& data, | ||
115 | const Eigen::Ref<const VectorXs>& x) override; | ||
116 | |||
117 | /** | ||
118 | * @brief Compute the partial derivatives of the RK integrator | ||
119 | * | ||
120 | * @param[in] data RK integrator data | ||
121 | * @param[in] x State point \f$\mathbf{x}\in\mathbb{R}^{ndx}\f$ | ||
122 | * @param[in] u Control input \f$\mathbf{u}\in\mathbb{R}^{nu}\f$ | ||
123 | */ | ||
124 | virtual void calcDiff(const std::shared_ptr<ActionDataAbstract>& data, | ||
125 | const Eigen::Ref<const VectorXs>& x, | ||
126 | const Eigen::Ref<const VectorXs>& u) override; | ||
127 | |||
128 | /** | ||
129 | * @brief Compute the partial derivatives of the cost | ||
130 | * | ||
131 | * It updates the derivatives of the cost function with respect to the state | ||
132 | * only. This function is used in the terminal nodes of an optimal control | ||
133 | * problem. | ||
134 | * | ||
135 | * @param[in] data RK integrator data | ||
136 | * @param[in] x State point \f$\mathbf{x}\in\mathbb{R}^{ndx}\f$ | ||
137 | */ | ||
138 | virtual void calcDiff(const std::shared_ptr<ActionDataAbstract>& data, | ||
139 | const Eigen::Ref<const VectorXs>& x) override; | ||
140 | |||
141 | /** | ||
142 | * @brief Create the RK integrator data | ||
143 | * | ||
144 | * @return the RK integrator data | ||
145 | */ | ||
146 | virtual std::shared_ptr<ActionDataAbstract> createData() override; | ||
147 | |||
148 | /** | ||
149 | * @brief Cast the RK integrated-action model to a different scalar type. | ||
150 | * | ||
151 | * It is useful for operations requiring different precision or scalar types. | ||
152 | * | ||
153 | * @tparam NewScalar The new scalar type to cast to. | ||
154 | * @return IntegratedActionModelRKTpl<NewScalar> An action model with the | ||
155 | * new scalar type. | ||
156 | */ | ||
157 | template <typename NewScalar> | ||
158 | IntegratedActionModelRKTpl<NewScalar> cast() const; | ||
159 | |||
160 | /** | ||
161 | * @brief Checks that a specific data belongs to this model | ||
162 | */ | ||
163 | virtual bool checkData( | ||
164 | const std::shared_ptr<ActionDataAbstract>& data) override; | ||
165 | |||
166 | /** | ||
167 | * @brief Computes the quasic static commands | ||
168 | * | ||
169 | * The quasic static commands are the ones produced for a the reference | ||
170 | * posture as an equilibrium point, i.e. for | ||
171 | * \f$\mathbf{f^q_x}\delta\mathbf{q}+\mathbf{f_u}\delta\mathbf{u}=\mathbf{0}\f$ | ||
172 | * | ||
173 | * @param[in] data RK integrator data | ||
174 | * @param[out] u Quasic static commands | ||
175 | * @param[in] x State point (velocity has to be zero) | ||
176 | * @param[in] maxiter Maximum allowed number of iterations | ||
177 | * @param[in] tol Tolerance | ||
178 | */ | ||
179 | virtual void quasiStatic(const std::shared_ptr<ActionDataAbstract>& data, | ||
180 | Eigen::Ref<VectorXs> u, | ||
181 | const Eigen::Ref<const VectorXs>& x, | ||
182 | const std::size_t maxiter = 100, | ||
183 | const Scalar tol = Scalar(1e-9)) override; | ||
184 | |||
185 | /** | ||
186 | * @brief Return the number of nodes of the integrator | ||
187 | */ | ||
188 | std::size_t get_ni() const; | ||
189 | |||
190 | /** | ||
191 | * @brief Print relevant information of the RK integrator model | ||
192 | * | ||
193 | * @param[out] os Output stream object | ||
194 | */ | ||
195 | virtual void print(std::ostream& os) const override; | ||
196 | |||
197 | protected: | ||
198 | using Base::control_; //!< Control parametrization | ||
199 | using Base::differential_; //!< Differential action model | ||
200 | using Base::ng_; //!< Number of inequality constraints | ||
201 | using Base::nh_; //!< Number of equality constraints | ||
202 | using Base::nu_; //!< Dimension of the control | ||
203 | using Base::state_; //!< Model of the state | ||
204 | using Base::time_step2_; //!< Square of the time step used for integration | ||
205 | using Base::time_step_; //!< Time step used for integration | ||
206 | using Base::with_cost_residual_; //!< Flag indicating whether a cost residual | ||
207 | //!< is used | ||
208 | |||
209 | private: | ||
210 | /** | ||
211 | * @brief Modify the RK type | ||
212 | */ | ||
213 | void set_rk_type(const RKType rktype); | ||
214 | |||
215 | RKType rk_type_; | ||
216 | std::vector<Scalar> rk_c_; | ||
217 | std::size_t ni_; | ||
218 | }; | ||
219 | |||
220 | template <typename _Scalar> | ||
221 | struct IntegratedActionDataRKTpl | ||
222 | : public IntegratedActionDataAbstractTpl<_Scalar> { | ||
223 | EIGEN_MAKE_ALIGNED_OPERATOR_NEW | ||
224 | |||
225 | typedef _Scalar Scalar; | ||
226 | typedef MathBaseTpl<Scalar> MathBase; | ||
227 | typedef IntegratedActionDataAbstractTpl<Scalar> Base; | ||
228 | typedef DifferentialActionDataAbstractTpl<Scalar> | ||
229 | DifferentialActionDataAbstract; | ||
230 | typedef ControlParametrizationDataAbstractTpl<Scalar> | ||
231 | ControlParametrizationDataAbstract; | ||
232 | typedef typename MathBase::VectorXs VectorXs; | ||
233 | typedef typename MathBase::MatrixXs MatrixXs; | ||
234 | |||
235 | template <template <typename Scalar> class Model> | ||
236 | 31571 | explicit IntegratedActionDataRKTpl(Model<Scalar>* const model) | |
237 | : Base(model), | ||
238 |
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31571 | integral(model->get_ni(), Scalar(0.)), |
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31571 | dx(model->get_state()->get_ndx()), |
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31571 | ki(model->get_ni(), VectorXs::Zero(model->get_state()->get_ndx())), |
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31571 | y(model->get_ni(), VectorXs::Zero(model->get_state()->get_nx())), |
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31571 | ws(model->get_ni(), VectorXs::Zero(model->get_control()->get_nw())), |
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31571 | dx_rk(model->get_ni(), VectorXs::Zero(model->get_state()->get_ndx())), |
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63142 | dki_dx(model->get_ni(), MatrixXs::Zero(model->get_state()->get_ndx(), |
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31571 | model->get_state()->get_ndx())), |
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63142 | dki_du(model->get_ni(), |
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31571 | MatrixXs::Zero(model->get_state()->get_ndx(), model->get_nu())), |
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63142 | dyi_dx(model->get_ni(), MatrixXs::Zero(model->get_state()->get_ndx(), |
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31571 | model->get_state()->get_ndx())), |
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63142 | dyi_du(model->get_ni(), |
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31571 | MatrixXs::Zero(model->get_state()->get_ndx(), model->get_nu())), |
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31571 | dli_dx(model->get_ni(), VectorXs::Zero(model->get_state()->get_ndx())), |
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31571 | dli_du(model->get_ni(), VectorXs::Zero(model->get_nu())), |
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63142 | ddli_ddx(model->get_ni(), |
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31571 | MatrixXs::Zero(model->get_state()->get_ndx(), |
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31571 | model->get_state()->get_ndx())), |
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63142 | ddli_ddw(model->get_ni(), |
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31571 | MatrixXs::Zero(model->get_control()->get_nw(), |
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31571 | model->get_control()->get_nw())), |
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63142 | ddli_ddu(model->get_ni(), |
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31571 | MatrixXs::Zero(model->get_nu(), model->get_nu())), |
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63142 | ddli_dxdw(model->get_ni(), |
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31571 | MatrixXs::Zero(model->get_state()->get_ndx(), |
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31571 | model->get_control()->get_nw())), |
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63142 | ddli_dxdu(model->get_ni(), MatrixXs::Zero(model->get_state()->get_ndx(), |
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31571 | model->get_nu())), |
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63142 | ddli_dwdu( |
268 | model->get_ni(), | ||
269 |
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31571 | MatrixXs::Zero(model->get_control()->get_nw(), model->get_nu())), |
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63142 | Luu_partialx(model->get_ni(), |
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31571 | MatrixXs::Zero(model->get_nu(), model->get_nu())), |
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63142 | Lxu_i(model->get_ni(), |
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31571 | MatrixXs::Zero(model->get_state()->get_ndx(), model->get_nu())), |
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63142 | Lxx_partialx(model->get_ni(), |
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31571 | MatrixXs::Zero(model->get_state()->get_ndx(), |
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31571 | model->get_state()->get_ndx())), |
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63142 | Lxx_partialu( |
278 | model->get_ni(), | ||
279 |
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63142 | MatrixXs::Zero(model->get_state()->get_ndx(), model->get_nu())) { |
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31571 | dx.setZero(); |
281 | |||
282 |
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128610 | for (std::size_t i = 0; i < model->get_ni(); ++i) { |
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97039 | differential.push_back(std::shared_ptr<DifferentialActionDataAbstract>( |
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97039 | model->get_differential()->createData())); |
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97039 | control.push_back(std::shared_ptr<ControlParametrizationDataAbstract>( |
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97039 | model->get_control()->createData())); |
287 | } | ||
288 | |||
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31571 | const std::size_t nv = model->get_state()->get_nv(); |
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31571 | dyi_dx[0].diagonal().setOnes(); |
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31571 | dki_dx[0].topRightCorner(nv, nv).diagonal().setOnes(); |
292 | 31571 | } | |
293 | 63102 | virtual ~IntegratedActionDataRKTpl() = default; | |
294 | |||
295 | std::vector<std::shared_ptr<DifferentialActionDataAbstract> > | ||
296 | differential; //!< List of differential model data | ||
297 | std::vector<std::shared_ptr<ControlParametrizationDataAbstract> > | ||
298 | control; //!< List of control parametrization data | ||
299 | std::vector<Scalar> integral; | ||
300 | VectorXs dx; //!< State rate | ||
301 | std::vector<VectorXs> ki; //!< List of RK terms related to system dynamics | ||
302 | std::vector<VectorXs> | ||
303 | y; //!< List of states where f is evaluated in the RK integration | ||
304 | std::vector<VectorXs> ws; //!< Control inputs evaluated in the RK integration | ||
305 | std::vector<VectorXs> dx_rk; | ||
306 | |||
307 | std::vector<MatrixXs> | ||
308 | dki_dx; //!< List of partial derivatives of RK nodes with respect to the | ||
309 | //!< state of the RK integration. dki/dx | ||
310 | std::vector<MatrixXs> | ||
311 | dki_du; //!< List of partial derivatives of RK nodes with respect to the | ||
312 | //!< control parameters of the RK integration. dki/du | ||
313 | |||
314 | std::vector<MatrixXs> | ||
315 | dyi_dx; //!< List of partial derivatives of RK dynamics with respect to | ||
316 | //!< the state of the RK integrator. dyi/dx | ||
317 | std::vector<MatrixXs> | ||
318 | dyi_du; //!< List of partial derivatives of RK dynamics with respect to | ||
319 | //!< the control parameters of the RK integrator. dyi/du | ||
320 | |||
321 | std::vector<VectorXs> | ||
322 | dli_dx; //!< List of partial derivatives of the cost with respect to the | ||
323 | //!< state of the RK integration. dli_dx | ||
324 | std::vector<VectorXs> | ||
325 | dli_du; //!< List of partial derivatives of the cost with respect to the | ||
326 | //!< control input of the RK integration. dli_du | ||
327 | |||
328 | std::vector<MatrixXs> | ||
329 | ddli_ddx; //!< List of second partial derivatives of the cost with | ||
330 | //!< respect to the state of the RK integration. ddli_ddx | ||
331 | std::vector<MatrixXs> | ||
332 | ddli_ddw; //!< List of second partial derivatives of the cost with | ||
333 | //!< respect to the control parameters of the RK integration. | ||
334 | //!< ddli_ddw | ||
335 | std::vector<MatrixXs> ddli_ddu; //!< List of second partial derivatives of | ||
336 | //!< the cost with respect to the control | ||
337 | //!< input of the RK integration. ddli_ddu | ||
338 | std::vector<MatrixXs> | ||
339 | ddli_dxdw; //!< List of second partial derivatives of the cost with | ||
340 | //!< respect to the state and control input of the RK | ||
341 | //!< integration. ddli_dxdw | ||
342 | std::vector<MatrixXs> | ||
343 | ddli_dxdu; //!< List of second partial derivatives of the cost with | ||
344 | //!< respect to the state and control parameters of the RK | ||
345 | //!< integration. ddli_dxdu | ||
346 | std::vector<MatrixXs> | ||
347 | ddli_dwdu; //!< List of second partial derivatives of the cost with | ||
348 | //!< respect to the control parameters and inputs control of | ||
349 | //!< the RK integration. ddli_dwdu | ||
350 | |||
351 | std::vector<MatrixXs> Luu_partialx; | ||
352 | std::vector<MatrixXs> Lxu_i; | ||
353 | std::vector<MatrixXs> Lxx_partialx; | ||
354 | std::vector<MatrixXs> Lxx_partialu; | ||
355 | |||
356 | using Base::cost; | ||
357 | using Base::Fu; | ||
358 | using Base::Fx; | ||
359 | using Base::Lu; | ||
360 | using Base::Luu; | ||
361 | using Base::Lx; | ||
362 | using Base::Lxu; | ||
363 | using Base::Lxx; | ||
364 | using Base::r; | ||
365 | using Base::xnext; | ||
366 | }; | ||
367 | |||
368 | } // namespace crocoddyl | ||
369 | |||
370 | /* --- Details -------------------------------------------------------------- */ | ||
371 | /* --- Details -------------------------------------------------------------- */ | ||
372 | /* --- Details -------------------------------------------------------------- */ | ||
373 | #include "crocoddyl/core/integrator/rk.hxx" | ||
374 | |||
375 | CROCODDYL_DECLARE_EXTERN_TEMPLATE_CLASS(crocoddyl::IntegratedActionModelRKTpl) | ||
376 | CROCODDYL_DECLARE_EXTERN_TEMPLATE_STRUCT(crocoddyl::IntegratedActionDataRKTpl) | ||
377 | |||
378 | #endif // CROCODDYL_CORE_INTEGRATOR_RK4_HPP_ | ||
379 |