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Directory: ./
File: include/crocoddyl/core/actions/lqr.hpp
Date: 2025-03-26 19:23:43
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1 ///////////////////////////////////////////////////////////////////////////////
2 // BSD 3-Clause License
3 //
4 // Copyright (C) 2019-2025, 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 EIGEN_MAKE_ALIGNED_OPERATOR_NEW
50 ✗ CROCODDYL_DERIVED_CAST(ActionModelBase, ActionModelLQRTpl)
51
52 typedef _Scalar Scalar;
53 typedef ActionDataAbstractTpl<Scalar> ActionDataAbstract;
54 typedef ActionModelAbstractTpl<Scalar> Base;
55 typedef ActionDataLQRTpl<Scalar> Data;
56 typedef StateVectorTpl<Scalar> StateVector;
57 typedef MathBaseTpl<Scalar> MathBase;
58 typedef typename MathBase::VectorXs VectorXs;
59 typedef typename MathBase::MatrixXs MatrixXs;
60
61 /**
62 * @brief Initialize the LQR action model
63 *
64 * @param[in] A State matrix
65 * @param[in] B Input matrix
66 * @param[in] Q State weight matrix
67 * @param[in] R Input weight matrix
68 * @param[in] N State-input weight matrix
69 */
70 ActionModelLQRTpl(const MatrixXs& A, const MatrixXs& B, const MatrixXs& Q,
71 const MatrixXs& R, const MatrixXs& N);
72
73 /**
74 * @brief Initialize the LQR action model
75 *
76 * @param[in] A State matrix
77 * @param[in] B Input matrix
78 * @param[in] Q State weight matrix
79 * @param[in] R Input weight matrix
80 * @param[in] N State-input weight matrix
81 * @param[in] f Dynamics drift
82 * @param[in] q State weight vector
83 * @param[in] r Input weight vector
84 */
85 ActionModelLQRTpl(const MatrixXs& A, const MatrixXs& B, const MatrixXs& Q,
86 const MatrixXs& R, const MatrixXs& N, const VectorXs& f,
87 const VectorXs& q, const VectorXs& r);
88
89 /**
90 * @brief Initialize the LQR action model
91 *
92 * @param[in] A State matrix
93 * @param[in] B Input matrix
94 * @param[in] Q State weight matrix
95 * @param[in] R Input weight matrix
96 * @param[in] N State-input weight matrix
97 * @param[in] G State-input inequality constraint matrix
98 * @param[in] H State-input equality constraint matrix
99 * @param[in] f Dynamics drift
100 * @param[in] q State weight vector
101 * @param[in] r Input weight vector
102 * @param[in] g State-input inequality constraint bias
103 * @param[in] h State-input equality constraint bias
104 */
105 ActionModelLQRTpl(const MatrixXs& A, const MatrixXs& B, const MatrixXs& Q,
106 const MatrixXs& R, const MatrixXs& N, const MatrixXs& G,
107 const MatrixXs& H, const VectorXs& f, const VectorXs& q,
108 const VectorXs& r, const VectorXs& g, const VectorXs& h);
109
110 /**
111 * @brief Initialize the LQR action model
112 *
113 * @param[in] nx Dimension of state vector
114 * @param[in] nu Dimension of control vector
115 * @param[in] drif_free Enable / disable the bias term of the linear dynamics
116 * (default true)
117 */
118 ActionModelLQRTpl(const std::size_t nx, const std::size_t nu,
119 const bool drift_free = true);
120
121 /** @brief Copy constructor */
122 ActionModelLQRTpl(const ActionModelLQRTpl& copy);
123
124 420 virtual ~ActionModelLQRTpl() = default;
125
126 virtual void calc(const std::shared_ptr<ActionDataAbstract>& data,
127 const Eigen::Ref<const VectorXs>& x,
128 const Eigen::Ref<const VectorXs>& u) override;
129 virtual void calc(const std::shared_ptr<ActionDataAbstract>& data,
130 const Eigen::Ref<const VectorXs>& x) override;
131 virtual void calcDiff(const std::shared_ptr<ActionDataAbstract>& data,
132 const Eigen::Ref<const VectorXs>& x,
133 const Eigen::Ref<const VectorXs>& u) override;
134 virtual void calcDiff(const std::shared_ptr<ActionDataAbstract>& data,
135 const Eigen::Ref<const VectorXs>& x) override;
136 virtual std::shared_ptr<ActionDataAbstract> createData() override;
137
138 /**
139 * @brief Cast the LQR model to a different scalar type.
140 *
141 * It is useful for operations requiring different precision or scalar types.
142 *
143 * @tparam NewScalar The new scalar type to cast to.
144 * @return ActionModelLQRTpl<NewScalar> A action model with the
145 * new scalar type.
146 */
147 template <typename NewScalar>
148 ActionModelLQRTpl<NewScalar> cast() const;
149
150 virtual bool checkData(
151 const std::shared_ptr<ActionDataAbstract>& data) override;
152
153 /**
154 * @brief Create a random LQR model
155 *
156 * @param[in] nx State dimension
157 * @param[in] nu Control dimension
158 * @param[in] ng Inequality constraint dimension (default 0)
159 * @param[in] nh Equality constraint dimension (defaul 0)
160 */
161 static ActionModelLQRTpl Random(const std::size_t nx, const std::size_t nu,
162 const std::size_t ng = 0,
163 const std::size_t nh = 0);
164
165 /** @brief Return the state matrix */
166 const MatrixXs& get_A() const;
167
168 /** @brief Return the input matrix */
169 const MatrixXs& get_B() const;
170
171 /** @brief Return the dynamics drift */
172 const VectorXs& get_f() const;
173
174 /** @brief Return the state weight matrix */
175 const MatrixXs& get_Q() const;
176
177 /** @brief Return the input weight matrix */
178 const MatrixXs& get_R() const;
179
180 /** @brief Return the state-input weight matrix */
181 const MatrixXs& get_N() const;
182
183 /** @brief Return the state-input inequality constraint matrix */
184 const MatrixXs& get_G() const;
185
186 /** @brief Return the state-input equality constraint matrix */
187 const MatrixXs& get_H() const;
188
189 /** @brief Return the state weight vector */
190 const VectorXs& get_q() const;
191
192 /** @brief Return the input weight vector */
193 const VectorXs& get_r() const;
194
195 /** @brief Return the state-input inequality constraint bias */
196 const VectorXs& get_g() const;
197
198 /** @brief Return the state-input equality constraint bias */
199 const VectorXs& get_h() const;
200
201 /**
202 * @brief Modify the LQR action model
203 *
204 * @param[in] A State matrix
205 * @param[in] B Input matrix
206 * @param[in] Q State weight matrix
207 * @param[in] R Input weight matrix
208 * @param[in] N State-input weight matrix
209 * @param[in] G State-input inequality constraint matrix
210 * @param[in] H State-input equality constraint matrix
211 * @param[in] f Dynamics drift
212 * @param[in] q State weight vector
213 * @param[in] r Input weight vector
214 * @param[in] g State-input inequality constraint bias
215 * @param[in] h State-input equality constraint bias
216 */
217 void set_LQR(const MatrixXs& A, const MatrixXs& B, const MatrixXs& Q,
218 const MatrixXs& R, const MatrixXs& N, const MatrixXs& G,
219 const MatrixXs& H, const VectorXs& f, const VectorXs& q,
220 const VectorXs& r, const VectorXs& g, const VectorXs& h);
221
222 ✗ DEPRECATED("Use get_A", const MatrixXs& get_Fx() const { return get_A(); })
223 ✗ DEPRECATED("Use get_B", const MatrixXs& get_Fu() const { return get_B(); })
224 ✗ DEPRECATED("Use get_f", const VectorXs& get_f0() const { return get_f(); })
225 ✗ DEPRECATED("Use get_q", const VectorXs& get_lx() const { return get_q(); })
226 ✗ DEPRECATED("Use get_r", const VectorXs& get_lu() const { return get_r(); })
227 ✗ DEPRECATED("Use get_Q", const MatrixXs& get_Lxx() const { return get_Q(); })
228 ✗ DEPRECATED("Use get_R", const MatrixXs& get_Lxu() const { return get_R(); })
229 ✗ DEPRECATED("Use get_N", const MatrixXs& get_Luu() const { return get_N(); })
230 ✗ DEPRECATED(
231 "Use set_LQR", void set_Fx(const MatrixXs& A) {
232 set_LQR(A, B_, Q_, R_, N_, G_, H_, f_, q_, r_, g_, h_);
233 })
234 ✗ DEPRECATED(
235 "Use set_LQR", void set_Fu(const MatrixXs& B) {
236 set_LQR(A_, B, Q_, R_, N_, G_, H_, f_, q_, r_, g_, h_);
237 })
238 ✗ DEPRECATED(
239 "Use set_LQR", void set_f0(const VectorXs& f) {
240 set_LQR(A_, B_, Q_, R_, N_, G_, H_, f, q_, r_, g_, h_);
241 })
242 ✗ DEPRECATED(
243 "Use set_LQR", void set_lx(const VectorXs& q) {
244 set_LQR(A_, B_, Q_, R_, N_, G_, H_, f_, q, r_, g_, h_);
245 })
246 ✗ DEPRECATED(
247 "Use set_LQR", void set_lu(const VectorXs& r) {
248 set_LQR(A_, B_, Q_, R_, N_, G_, H_, f_, q_, r, g_, h_);
249 })
250 ✗ DEPRECATED(
251 "Use set_LQR", void set_Lxx(const MatrixXs& Q) {
252 set_LQR(A_, B_, Q, R_, N_, G_, H_, f_, q_, r_, g_, h_);
253 })
254 ✗ DEPRECATED(
255 "Use set_LQR", void set_Luu(const MatrixXs& R) {
256 set_LQR(A_, B_, Q_, R, N_, G_, H_, f_, q_, r_, g_, h_);
257 })
258 ✗ DEPRECATED(
259 "Use set_LQR", void set_Lxu(const MatrixXs& N) {
260 set_LQR(A_, B_, Q_, R_, N, G_, H_, f_, q_, r_, g_, h_);
261 })
262
263 /**
264 * @brief Print relevant information of the LQR model
265 *
266 * @param[out] os Output stream object
267 */
268 virtual void print(std::ostream& os) const override;
269
270 protected:
271 using Base::ng_; //!< Equality constraint dimension
272 using Base::nh_; //!< Inequality constraint dimension
273 using Base::nu_; //!< Control dimension
274 using Base::state_; //!< Model of the state
275
276 private:
277 MatrixXs A_;
278 MatrixXs B_;
279 MatrixXs Q_;
280 MatrixXs R_;
281 MatrixXs N_;
282 MatrixXs G_;
283 MatrixXs H_;
284 VectorXs f_;
285 VectorXs q_;
286 VectorXs r_;
287 VectorXs g_;
288 VectorXs h_;
289 MatrixXs L_;
290 bool drift_free_;
291 bool updated_lqr_;
292 };
293
294 template <typename _Scalar>
295 struct ActionDataLQRTpl : public ActionDataAbstractTpl<_Scalar> {
296 typedef _Scalar Scalar;
297 typedef MathBaseTpl<Scalar> MathBase;
298 typedef ActionDataAbstractTpl<Scalar> Base;
299 typedef typename MathBase::VectorXs VectorXs;
300
301 template <template <typename Scalar> class Model>
302 1648 explicit ActionDataLQRTpl(Model<Scalar>* const model)
303 : Base(model),
304
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 1648 R_u_tmp(VectorXs::Zero(static_cast<Eigen::Index>(model->get_nu()))),
305
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 1648 Q_x_tmp(VectorXs::Zero(
306
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 3296 static_cast<Eigen::Index>(model->get_state()->get_ndx()))) {
307 // Setting the linear model and quadratic cost as they are constant
308
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 1648 const std::size_t nq = model->get_state()->get_nq();
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 1648 const std::size_t nu = model->get_nu();
310
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 1648 Fx = model->get_A();
311
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 1648 Fu = model->get_B();
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 1648 Lxx = model->get_Q();
313
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 1648 Luu = model->get_R();
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 1648 Lxu = model->get_N();
315
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 1648 Gx = model->get_G().leftCols(2 * nq);
316
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 1648 Gu = model->get_G().rightCols(nu);
317
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 1648 Hx = model->get_H().leftCols(2 * nq);
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 1648 Hu = model->get_H().rightCols(nu);
319 1648 }
320 3205 virtual ~ActionDataLQRTpl() = default;
321
322 using Base::cost;
323 using Base::Fu;
324 using Base::Fx;
325 using Base::Gu;
326 using Base::Gx;
327 using Base::Hu;
328 using Base::Hx;
329 using Base::Lu;
330 using Base::Luu;
331 using Base::Lx;
332 using Base::Lxu;
333 using Base::Lxx;
334 using Base::r;
335 using Base::xnext;
336
337 VectorXs R_u_tmp; // Temporary variable for storing Hessian-vector product
338 // (size: nu)
339 VectorXs Q_x_tmp; // Temporary variable for storing Hessian-vector product
340 // (size: nx)
341 };
342
343 } // namespace crocoddyl
344
345 /* --- Details -------------------------------------------------------------- */
346 /* --- Details -------------------------------------------------------------- */
347 /* --- Details -------------------------------------------------------------- */
348 #include "crocoddyl/core/actions/lqr.hxx"
349
350 CROCODDYL_DECLARE_EXTERN_TEMPLATE_CLASS(crocoddyl::ActionModelLQRTpl)
351 CROCODDYL_DECLARE_EXTERN_TEMPLATE_STRUCT(crocoddyl::ActionDataLQRTpl)
352
353 #endif // CROCODDYL_CORE_ACTIONS_LQR_HPP_
354