1 |
|
|
/////////////////////////////////////////////////////////////////////////////// |
2 |
|
|
// BSD 3-Clause License |
3 |
|
|
// |
4 |
|
|
// Copyright (C) 2019-2022, 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_INTEGRATOR_EULER_HPP_ |
11 |
|
|
#define CROCODDYL_CORE_INTEGRATOR_EULER_HPP_ |
12 |
|
|
|
13 |
|
|
#include "crocoddyl/core/fwd.hpp" |
14 |
|
|
#include "crocoddyl/core/integ-action-base.hpp" |
15 |
|
|
|
16 |
|
|
namespace crocoddyl { |
17 |
|
|
|
18 |
|
|
/** |
19 |
|
|
* @brief Symplectic Euler integrator |
20 |
|
|
* |
21 |
|
|
* It applies a symplectic Euler integration scheme to a differential (i.e., |
22 |
|
|
* continuous time) action model. |
23 |
|
|
* |
24 |
|
|
* This symplectic Euler scheme introduces also the possibility to parametrize |
25 |
|
|
* the control trajectory inside an integration step, for instance using |
26 |
|
|
* polynomials. This requires introducing some notation to clarify the |
27 |
|
|
* difference between the control inputs of the differential model and the |
28 |
|
|
* control inputs to the integrated model. We have decided to use |
29 |
|
|
* \f$\mathbf{w}\f$ to refer to the control inputs of the differential model and |
30 |
|
|
* \f$\mathbf{u}\f$ for the control inputs of the integrated action model. Note |
31 |
|
|
* that the zero-order (e.g., `ControlParametrizationModelPolyZeroTpl`) are the |
32 |
|
|
* only ones that make sense to use within this integrator. |
33 |
|
|
* |
34 |
|
|
* \sa `calc()`, `calcDiff()`, `createData()` |
35 |
|
|
*/ |
36 |
|
|
template <typename _Scalar> |
37 |
|
|
class IntegratedActionModelEulerTpl |
38 |
|
|
: public IntegratedActionModelAbstractTpl<_Scalar> { |
39 |
|
|
public: |
40 |
|
|
EIGEN_MAKE_ALIGNED_OPERATOR_NEW |
41 |
|
|
|
42 |
|
|
typedef _Scalar Scalar; |
43 |
|
|
typedef MathBaseTpl<Scalar> MathBase; |
44 |
|
|
typedef IntegratedActionModelAbstractTpl<Scalar> Base; |
45 |
|
|
typedef IntegratedActionDataEulerTpl<Scalar> Data; |
46 |
|
|
typedef ActionDataAbstractTpl<Scalar> ActionDataAbstract; |
47 |
|
|
typedef DifferentialActionModelAbstractTpl<Scalar> |
48 |
|
|
DifferentialActionModelAbstract; |
49 |
|
|
typedef ControlParametrizationModelAbstractTpl<Scalar> |
50 |
|
|
ControlParametrizationModelAbstract; |
51 |
|
|
typedef ControlParametrizationDataAbstractTpl<Scalar> |
52 |
|
|
ControlParametrizationDataAbstract; |
53 |
|
|
typedef typename MathBase::VectorXs VectorXs; |
54 |
|
|
typedef typename MathBase::MatrixXs MatrixXs; |
55 |
|
|
|
56 |
|
|
/** |
57 |
|
|
* @brief Initialize the symplectic Euler integrator |
58 |
|
|
* |
59 |
|
|
* @param[in] model Differential action model |
60 |
|
|
* @param[in] control Control parametrization |
61 |
|
|
* @param[in] time_step Step time (default 1e-3) |
62 |
|
|
* @param[in] with_cost_residual Compute cost residual (default true) |
63 |
|
|
*/ |
64 |
|
|
IntegratedActionModelEulerTpl( |
65 |
|
|
boost::shared_ptr<DifferentialActionModelAbstract> model, |
66 |
|
|
boost::shared_ptr<ControlParametrizationModelAbstract> control, |
67 |
|
|
const Scalar time_step = Scalar(1e-3), |
68 |
|
|
const bool with_cost_residual = true); |
69 |
|
|
|
70 |
|
|
/** |
71 |
|
|
* @brief Initialize the symplectic Euler integrator |
72 |
|
|
* |
73 |
|
|
* This initialization uses `ControlParametrizationPolyZeroTpl` for the |
74 |
|
|
* control parametrization. |
75 |
|
|
* |
76 |
|
|
* @param[in] model Differential action model |
77 |
|
|
* @param[in] time_step Step time (default 1e-3) |
78 |
|
|
* @param[in] with_cost_residual Compute cost residual (default true) |
79 |
|
|
*/ |
80 |
|
|
IntegratedActionModelEulerTpl( |
81 |
|
|
boost::shared_ptr<DifferentialActionModelAbstract> model, |
82 |
|
|
const Scalar time_step = Scalar(1e-3), |
83 |
|
|
const bool with_cost_residual = true); |
84 |
|
|
virtual ~IntegratedActionModelEulerTpl(); |
85 |
|
|
|
86 |
|
|
/** |
87 |
|
|
* @brief Integrate the differential action model using symplectic Euler |
88 |
|
|
* scheme |
89 |
|
|
* |
90 |
|
|
* @param[in] data Symplectic Euler data |
91 |
|
|
* @param[in] x State point \f$\mathbf{x}\in\mathbb{R}^{ndx}\f$ |
92 |
|
|
* @param[in] u Control input \f$\mathbf{u}\in\mathbb{R}^{nu}\f$ |
93 |
|
|
*/ |
94 |
|
|
virtual void calc(const boost::shared_ptr<ActionDataAbstract>& data, |
95 |
|
|
const Eigen::Ref<const VectorXs>& x, |
96 |
|
|
const Eigen::Ref<const VectorXs>& u); |
97 |
|
|
|
98 |
|
|
/** |
99 |
|
|
* @brief Integrate the total cost value for nodes that depends only on the |
100 |
|
|
* state using symplectic Euler scheme |
101 |
|
|
* |
102 |
|
|
* It computes the total cost and defines the next state as the current one. |
103 |
|
|
* This function is used in the terminal nodes of an optimal control problem. |
104 |
|
|
* |
105 |
|
|
* @param[in] data Symplectic Euler data |
106 |
|
|
* @param[in] x State point \f$\mathbf{x}\in\mathbb{R}^{ndx}\f$ |
107 |
|
|
*/ |
108 |
|
|
virtual void calc(const boost::shared_ptr<ActionDataAbstract>& data, |
109 |
|
|
const Eigen::Ref<const VectorXs>& x); |
110 |
|
|
|
111 |
|
|
/** |
112 |
|
|
* @brief Compute the partial derivatives of the symplectic Euler integrator |
113 |
|
|
* |
114 |
|
|
* @param[in] data Symplectic Euler data |
115 |
|
|
* @param[in] x State point \f$\mathbf{x}\in\mathbb{R}^{ndx}\f$ |
116 |
|
|
* @param[in] u Control input \f$\mathbf{u}\in\mathbb{R}^{nu}\f$ |
117 |
|
|
*/ |
118 |
|
|
virtual void calcDiff(const boost::shared_ptr<ActionDataAbstract>& data, |
119 |
|
|
const Eigen::Ref<const VectorXs>& x, |
120 |
|
|
const Eigen::Ref<const VectorXs>& u); |
121 |
|
|
|
122 |
|
|
/** |
123 |
|
|
* @brief Compute the partial derivatives of the cost |
124 |
|
|
* |
125 |
|
|
* It updates the derivatives of the cost function with respect to the state |
126 |
|
|
* only. This function is used in the terminal nodes of an optimal control |
127 |
|
|
* problem. |
128 |
|
|
* |
129 |
|
|
* @param[in] data Symplectic Euler data |
130 |
|
|
* @param[in] x State point \f$\mathbf{x}\in\mathbb{R}^{ndx}\f$ |
131 |
|
|
*/ |
132 |
|
|
virtual void calcDiff(const boost::shared_ptr<ActionDataAbstract>& data, |
133 |
|
|
const Eigen::Ref<const VectorXs>& x); |
134 |
|
|
|
135 |
|
|
/** |
136 |
|
|
* @brief Create the symplectic Euler data |
137 |
|
|
* |
138 |
|
|
* @return the symplectic Euler data |
139 |
|
|
*/ |
140 |
|
|
virtual boost::shared_ptr<ActionDataAbstract> createData(); |
141 |
|
|
|
142 |
|
|
/** |
143 |
|
|
* @brief Checks that a specific data belongs to this model |
144 |
|
|
*/ |
145 |
|
|
virtual bool checkData(const boost::shared_ptr<ActionDataAbstract>& data); |
146 |
|
|
|
147 |
|
|
/** |
148 |
|
|
* @brief Computes the quasic static commands |
149 |
|
|
* |
150 |
|
|
* The quasic static commands are the ones produced for a the reference |
151 |
|
|
* posture as an equilibrium point, i.e. for |
152 |
|
|
* \f$\mathbf{f^q_x}\delta\mathbf{q}+\mathbf{f_u}\delta\mathbf{u}=\mathbf{0}\f$ |
153 |
|
|
* |
154 |
|
|
* @param[in] data Symplectic Euler data |
155 |
|
|
* @param[out] u Quasic static commands |
156 |
|
|
* @param[in] x State point (velocity has to be zero) |
157 |
|
|
* @param[in] maxiter Maximum allowed number of iterations |
158 |
|
|
* @param[in] tol Tolerance |
159 |
|
|
*/ |
160 |
|
|
virtual void quasiStatic(const boost::shared_ptr<ActionDataAbstract>& data, |
161 |
|
|
Eigen::Ref<VectorXs> u, |
162 |
|
|
const Eigen::Ref<const VectorXs>& x, |
163 |
|
|
const std::size_t maxiter = 100, |
164 |
|
|
const Scalar tol = Scalar(1e-9)); |
165 |
|
|
|
166 |
|
|
/** |
167 |
|
|
* @brief Print relevant information of the Euler integrator model |
168 |
|
|
* |
169 |
|
|
* @param[out] os Output stream object |
170 |
|
|
*/ |
171 |
|
|
virtual void print(std::ostream& os) const; |
172 |
|
|
|
173 |
|
|
protected: |
174 |
|
|
using Base::control_; //!< Control parametrization |
175 |
|
|
using Base::differential_; //!< Differential action model |
176 |
|
|
using Base::ng_; //!< Number of inequality constraints |
177 |
|
|
using Base::nh_; //!< Number of equality constraints |
178 |
|
|
using Base::nu_; //!< Dimension of the control |
179 |
|
|
using Base::state_; //!< Model of the state |
180 |
|
|
using Base::time_step2_; //!< Square of the time step used for integration |
181 |
|
|
using Base::time_step_; //!< Time step used for integration |
182 |
|
|
using Base::with_cost_residual_; //!< Flag indicating whether a cost residual |
183 |
|
|
//!< is used |
184 |
|
|
}; |
185 |
|
|
|
186 |
|
|
template <typename _Scalar> |
187 |
|
|
struct IntegratedActionDataEulerTpl |
188 |
|
|
: public IntegratedActionDataAbstractTpl<_Scalar> { |
189 |
|
|
EIGEN_MAKE_ALIGNED_OPERATOR_NEW |
190 |
|
|
|
191 |
|
|
typedef _Scalar Scalar; |
192 |
|
|
typedef MathBaseTpl<Scalar> MathBase; |
193 |
|
|
typedef IntegratedActionDataAbstractTpl<Scalar> Base; |
194 |
|
|
typedef DifferentialActionDataAbstractTpl<Scalar> |
195 |
|
|
DifferentialActionDataAbstract; |
196 |
|
|
typedef ControlParametrizationDataAbstractTpl<Scalar> |
197 |
|
|
ControlParametrizationDataAbstract; |
198 |
|
|
typedef typename MathBase::VectorXs VectorXs; |
199 |
|
|
typedef typename MathBase::MatrixXs MatrixXs; |
200 |
|
|
|
201 |
|
|
template <template <typename Scalar> class Model> |
202 |
|
7410 |
explicit IntegratedActionDataEulerTpl(Model<Scalar>* const model) |
203 |
✓✗✓✗
✓✗ |
7410 |
: Base(model) { |
204 |
✓✗ |
7410 |
differential = model->get_differential()->createData(); |
205 |
✓✗ |
7410 |
control = model->get_control()->createData(); |
206 |
|
7410 |
const std::size_t ndx = model->get_state()->get_ndx(); |
207 |
|
7410 |
const std::size_t nv = model->get_state()->get_nv(); |
208 |
✓✗✓✗
|
7410 |
dx = VectorXs::Zero(ndx); |
209 |
✓✗✓✗
|
7410 |
da_du = MatrixXs::Zero(nv, model->get_nu()); |
210 |
✓✗✓✗
|
7410 |
Lwu = MatrixXs::Zero(model->get_control()->get_nw(), model->get_nu()); |
211 |
|
7410 |
} |
212 |
|
14824 |
virtual ~IntegratedActionDataEulerTpl() {} |
213 |
|
|
|
214 |
|
|
boost::shared_ptr<DifferentialActionDataAbstract> |
215 |
|
|
differential; //!< Differential model data |
216 |
|
|
boost::shared_ptr<ControlParametrizationDataAbstract> |
217 |
|
|
control; //!< Control parametrization data |
218 |
|
|
VectorXs dx; |
219 |
|
|
MatrixXs da_du; |
220 |
|
|
MatrixXs Lwu; //!< Hessian of the cost function with respect to the control |
221 |
|
|
//!< input (w) and control parameters (u) |
222 |
|
|
|
223 |
|
|
using Base::cost; |
224 |
|
|
using Base::Fu; |
225 |
|
|
using Base::Fx; |
226 |
|
|
using Base::Lu; |
227 |
|
|
using Base::Luu; |
228 |
|
|
using Base::Lx; |
229 |
|
|
using Base::Lxu; |
230 |
|
|
using Base::Lxx; |
231 |
|
|
using Base::r; |
232 |
|
|
using Base::xnext; |
233 |
|
|
}; |
234 |
|
|
|
235 |
|
|
} // namespace crocoddyl |
236 |
|
|
|
237 |
|
|
/* --- Details -------------------------------------------------------------- */ |
238 |
|
|
/* --- Details -------------------------------------------------------------- */ |
239 |
|
|
/* --- Details -------------------------------------------------------------- */ |
240 |
|
|
#include "crocoddyl/core/integrator/euler.hxx" |
241 |
|
|
|
242 |
|
|
#endif // CROCODDYL_CORE_INTEGRATOR_EULER_HPP_ |