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/////////////////////////////////////////////////////////////////////////////// |
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// BSD 3-Clause License |
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// |
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// Copyright (C) 2019-2023, LAAS-CNRS, University of Edinburgh, |
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// Heriot-Watt University |
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// Copyright note valid unless otherwise stated in individual files. |
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// All rights reserved. |
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/////////////////////////////////////////////////////////////////////////////// |
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#ifndef CROCODDYL_CORE_SOLVER_BASE_HPP_ |
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#define CROCODDYL_CORE_SOLVER_BASE_HPP_ |
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#include <vector> |
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#include "crocoddyl/core/optctrl/shooting.hpp" |
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#include "crocoddyl/core/utils/stop-watch.hpp" |
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namespace crocoddyl { |
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class CallbackAbstract; // forward declaration |
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static std::vector<Eigen::VectorXd> DEFAULT_VECTOR; |
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enum FeasibilityNorm { LInf = 0, L1 }; |
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/** |
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* @brief Abstract class for optimal control solvers |
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* |
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* A solver resolves an optimal control solver of the form |
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* \f{eqnarray*}{ |
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* \begin{Bmatrix} |
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* \mathbf{x}^*_0,\cdots,\mathbf{x}^*_{T} \\ |
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* \mathbf{u}^*_0,\cdots,\mathbf{u}^*_{T-1} |
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* \end{Bmatrix} = |
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* \arg\min_{\mathbf{x}_s,\mathbf{u}_s} && l_T (\mathbf{x}_T) + \sum_{k=0}^{T-1} |
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* l_k(\mathbf{x}_t,\mathbf{u}_t) \\ |
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* \operatorname{subject}\,\operatorname{to} && \mathbf{x}_0 = |
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* \mathbf{\tilde{x}}_0\\ |
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* && \mathbf{x}_{k+1} = \mathbf{f}_k(\mathbf{x}_k,\mathbf{u}_k)\\ |
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* && \mathbf{x}_k\in\mathcal{X}, \mathbf{u}_k\in\mathcal{U} |
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* \f} |
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* where \f$l_T(\mathbf{x}_T)\f$, \f$l_k(\mathbf{x}_t,\mathbf{u}_t)\f$ are the |
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* terminal and running cost functions, respectively, |
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* \f$\mathbf{f}_k(\mathbf{x}_k,\mathbf{u}_k)\f$ describes evolution of the |
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* system, and state and control admissible sets are defined by |
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* \f$\mathbf{x}_k\in\mathcal{X}\f$, \f$\mathbf{u}_k\in\mathcal{U}\f$. An action |
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* model, defined in the shooting problem, describes each node \f$k\f$. Inside |
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* the action model, we specialize the cost functions, the system evolution and |
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* the admissible sets. |
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* |
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* The main routines are `computeDirection()` and `tryStep()`. The former finds |
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* a search direction and typically computes the derivatives of each action |
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* model. The latter rollout the dynamics and cost (i.e., the action) to try the |
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* search direction found by `computeDirection`. Both functions used the current |
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* guess defined by `setCandidate()`. Finally, `solve()` function is used to |
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* define when the search direction and length are computed in each iterate. It |
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* also describes the globalization strategy (i.e., regularization) of the |
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* numerical optimization. |
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* |
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* \sa `solve()`, `computeDirection()`, `tryStep()`, `stoppingCriteria()` |
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*/ |
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class SolverAbstract { |
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public: |
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EIGEN_MAKE_ALIGNED_OPERATOR_NEW |
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/** |
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* @brief Initialize the solver |
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* |
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* @param[in] problem shooting problem |
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*/ |
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explicit SolverAbstract(boost::shared_ptr<ShootingProblem> problem); |
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virtual ~SolverAbstract(); |
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/** |
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* @brief Compute the optimal trajectory \f$\mathbf{x}^*_s,\mathbf{u}^*_s\f$ |
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* as lists of \f$T+1\f$ and \f$T\f$ terms |
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* |
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* From an initial guess \p init_xs, \p init_us (feasible or not), iterate |
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* over `computeDirection()` and `tryStep()` until `stoppingCriteria()` is |
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* below threshold. It also describes the globalization strategy used during |
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* the numerical optimization. |
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* |
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* @param[in] init_xs initial guess for state trajectory with \f$T+1\f$ |
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* elements (default []) |
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* @param[in] init_us initial guess for control trajectory with \f$T\f$ |
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* elements (default []) |
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* @param[in] maxiter maximum allowed number of iterations (default 100) |
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* @param[in] is_feasible true if the \p init_xs are obtained from |
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* integrating the \p init_us (rollout) (default false) |
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* @param[in] init_reg initial guess for the regularization value. Very |
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* low values are typical used with very good guess points (default 1e-9). |
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* @return A boolean that describes if convergence was reached. |
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*/ |
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virtual bool solve( |
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const std::vector<Eigen::VectorXd>& init_xs = DEFAULT_VECTOR, |
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const std::vector<Eigen::VectorXd>& init_us = DEFAULT_VECTOR, |
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const std::size_t maxiter = 100, const bool is_feasible = false, |
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const double reg_init = NAN) = 0; |
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/** |
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* @brief Compute the search direction |
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* \f$(\delta\mathbf{x}^k,\delta\mathbf{u}^k)\f$ for the current guess |
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* \f$(\mathbf{x}^k_s,\mathbf{u}^k_s)\f$. |
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* |
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* You must call `setCandidate()` first in order to define the current guess. |
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* A current guess defines a state and control trajectory |
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* \f$(\mathbf{x}^k_s,\mathbf{u}^k_s)\f$ of \f$T+1\f$ and \f$T\f$ elements, |
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* respectively. |
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* |
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* @param[in] recalc true for recalculating the derivatives at current state |
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* and control |
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* @return The search direction \f$(\delta\mathbf{x},\delta\mathbf{u})\f$ and |
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* the dual lambdas as lists of \f$T+1\f$, \f$T\f$ and \f$T+1\f$ lengths, |
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* respectively |
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*/ |
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virtual void computeDirection(const bool recalc) = 0; |
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/** |
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* @brief Try a predefined step length \f$\alpha\f$ and compute its cost |
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* improvement \f$dV\f$. |
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* |
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* It uses the search direction found by `computeDirection()` to try a |
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* determined step length \f$\alpha\f$. Therefore, it assumes that we have run |
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* `computeDirection()` first. Additionally, it returns the cost improvement |
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* \f$dV\f$ along the predefined step length \f$\alpha\f$. |
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* |
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* @param[in] steplength applied step length (\f$0\leq\alpha\leq1\f$) |
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* @return the cost improvement |
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*/ |
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virtual double tryStep(const double steplength = 1) = 0; |
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/** |
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* @brief Return a positive value that quantifies the algorithm termination |
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* |
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* These values typically represents the gradient norm which tell us that it's |
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* been reached the local minima. The stopping criteria strictly speaking |
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* depends on the search direction (calculated by `computeDirection()`) but |
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* it could also depend on the chosen step length, tested by `tryStep()`. |
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*/ |
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virtual double stoppingCriteria() = 0; |
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/** |
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* @brief Return the expected improvement \f$dV_{exp}\f$ from a given current |
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* search direction \f$(\delta\mathbf{x}^k,\delta\mathbf{u}^k)\f$ |
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* |
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* For computing the expected improvement, you need to compute the search |
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* direction first via `computeDirection()`. |
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*/ |
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virtual const Eigen::Vector2d& expectedImprovement() = 0; |
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/** |
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* @brief Resizing the solver data |
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* |
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* If the shooting problem has changed after construction, then this function |
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* resizes all the data before starting resolve the problem. |
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*/ |
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virtual void resizeData(); |
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/** |
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* @brief Compute the dynamic feasibility |
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* \f$\|\mathbf{f}_{\mathbf{s}}\|_{\infty,1}\f$ for the current guess |
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* \f$(\mathbf{x}^k,\mathbf{u}^k)\f$ |
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* |
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* The feasibility can be computed using different norms (e.g, |
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* \f$\ell_\infty\f$ or \f$\ell_1\f$ norms). By default we use the |
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* \f$\ell_\infty\f$ norm, however, we can change the type of norm using |
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* `set_feasnorm`. Note that \f$\mathbf{f}_{\mathbf{s}}\f$ are the gaps on the |
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* dynamics, which are computed at each node as |
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* \f$\mathbf{x}^{'}-\mathbf{f}(\mathbf{x},\mathbf{u})\f$. |
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*/ |
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double computeDynamicFeasibility(); |
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/** |
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* @brief Compute the feasibility of the inequality constraints for the |
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* current guess |
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* |
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* The feasibility can be computed using different norms (e.g, |
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* \f$\ell_\infty\f$ or \f$\ell_1\f$ norms). By default we use the |
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* \f$\ell_\infty\f$ norm, however, we can change the type of norm using |
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* `set_feasnorm`. |
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*/ |
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double computeInequalityFeasibility(); |
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/** |
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* @brief Compute the feasibility of the equality constraints for the current |
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* guess |
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* |
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* The feasibility can be computed using different norms (e.g, |
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* \f$\ell_\infty\f$ or \f$\ell_1\f$ norms). By default we use the |
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* \f$\ell_\infty\f$ norm, however, we can change the type of norm using |
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* `set_feasnorm`. |
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*/ |
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double computeEqualityFeasibility(); |
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/** |
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* @brief Set the solver candidate trajectories |
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* \f$(\mathbf{x}_s,\mathbf{u}_s)\f$ |
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* |
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* The solver candidates are defined as a state and control trajectories |
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* \f$(\mathbf{x}_s,\mathbf{u}_s)\f$ of \f$T+1\f$ and \f$T\f$ elements, |
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* respectively. Additionally, we need to define the dynamic feasibility of |
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* the \f$(\mathbf{x}_s,\mathbf{u}_s)\f$ pair. Note that the trajectories are |
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* feasible if \f$\mathbf{x}_s\f$ is the resulting trajectory from the system |
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* rollout with \f$\mathbf{u}_s\f$ inputs. |
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* |
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* @param[in] xs state trajectory of \f$T+1\f$ elements (default []) |
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* @param[in] us control trajectory of \f$T\f$ elements (default []) |
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* @param[in] isFeasible true if the \p xs are obtained from integrating the |
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* \p us (rollout) |
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*/ |
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void setCandidate( |
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const std::vector<Eigen::VectorXd>& xs_warm = DEFAULT_VECTOR, |
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const std::vector<Eigen::VectorXd>& us_warm = DEFAULT_VECTOR, |
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const bool is_feasible = false); |
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/** |
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* @brief Set a list of callback functions using for the solver diagnostic |
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* |
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* Each iteration, the solver calls these set of functions in order to allowed |
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* user the diagnostic of its performance. |
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* |
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* @param callbacks set of callback functions |
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*/ |
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void setCallbacks( |
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const std::vector<boost::shared_ptr<CallbackAbstract> >& callbacks); |
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/** |
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* @brief Return the list of callback functions using for diagnostic |
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*/ |
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const std::vector<boost::shared_ptr<CallbackAbstract> >& getCallbacks() const; |
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/** |
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* @brief Return the shooting problem |
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*/ |
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const boost::shared_ptr<ShootingProblem>& get_problem() const; |
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/** |
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* @brief Return the state trajectory \f$\mathbf{x}_s\f$ |
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*/ |
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const std::vector<Eigen::VectorXd>& get_xs() const; |
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/** |
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* @brief Return the control trajectory \f$\mathbf{u}_s\f$ |
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*/ |
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const std::vector<Eigen::VectorXd>& get_us() const; |
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/** |
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* @brief Return the dynamic infeasibility \f$\mathbf{f}_{s}\f$ |
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*/ |
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const std::vector<Eigen::VectorXd>& get_fs() const; |
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/** |
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* @brief Return the feasibility status of the |
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* \f$(\mathbf{x}_s,\mathbf{u}_s)\f$ trajectory |
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*/ |
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bool get_is_feasible() const; |
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/** |
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* @brief Return the cost for the current guess |
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*/ |
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double get_cost() const; |
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/** |
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* @brief Return the merit for the current guess |
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*/ |
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double get_merit() const; |
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/** |
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* @brief Return the stopping-criteria value computed by `stoppingCriteria()` |
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*/ |
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double get_stop() const; |
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/** |
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* @brief Return the linear and quadratic terms of the expected improvement |
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*/ |
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const Eigen::Vector2d& get_d() const; |
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/** |
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* @brief Return the reduction in the cost function \f$\Delta V\f$ |
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*/ |
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double get_dV() const; |
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/** |
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* @brief Return the reduction in the merit function \f$\Delta\Phi\f$ |
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*/ |
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double get_dPhi() const; |
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/** |
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* @brief Return the expected reduction in the cost function \f$\Delta |
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* V_{exp}\f$ |
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*/ |
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double get_dVexp() const; |
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/** |
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* @brief Return the expected reduction in the merit function |
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* \f$\Delta\Phi_{exp}\f$ |
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*/ |
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double get_dPhiexp() const; |
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/** |
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* @brief Return the reduction in the feasibility |
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*/ |
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double get_dfeas() const; |
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/** |
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* @brief Return the total feasibility for the current guess |
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*/ |
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double get_feas() const; |
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/** |
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* @brief Return the dynamic feasibility for the current guess |
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*/ |
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double get_ffeas() const; |
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/** |
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* @brief Return the inequality feasibility for the current guess |
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*/ |
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double get_gfeas() const; |
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/** |
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* @brief Return the equality feasibility for the current guess |
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*/ |
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double get_hfeas() const; |
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/** |
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* @brief Return the dynamic feasibility for the current step length |
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*/ |
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double get_ffeas_try() const; |
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/** |
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* @brief Return the inequality feasibility for the current step length |
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*/ |
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double get_gfeas_try() const; |
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/** |
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* @brief Return the equality feasibility for the current step length |
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*/ |
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double get_hfeas_try() const; |
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/** |
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* @brief Return the primal-variable regularization |
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*/ |
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double get_preg() const; |
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/** |
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* @brief Return the dual-variable regularization |
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*/ |
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double get_dreg() const; |
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DEPRECATED("Use get_preg for primal-variable regularization", |
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double get_xreg() const;) |
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DEPRECATED("Use get_preg for primal-variable regularization", |
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double get_ureg() const;) |
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/** |
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* @brief Return the step length \f$\alpha\f$ |
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*/ |
| 357 |
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double get_steplength() const; |
| 358 |
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| 359 |
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/** |
| 360 |
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* @brief Return the threshold used for accepting a step |
| 361 |
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*/ |
| 362 |
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double get_th_acceptstep() const; |
| 363 |
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| 364 |
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/** |
| 365 |
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* @brief Return the tolerance for stopping the algorithm |
| 366 |
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*/ |
| 367 |
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double get_th_stop() const; |
| 368 |
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| 369 |
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/** |
| 370 |
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* @brief Return the threshold for accepting a gap as non-zero |
| 371 |
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*/ |
| 372 |
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double get_th_gaptol() const; |
| 373 |
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| 374 |
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/** |
| 375 |
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* @brief Return the type of norm used to evaluate the dynamic and constraints |
| 376 |
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* feasibility |
| 377 |
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*/ |
| 378 |
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FeasibilityNorm get_feasnorm() const; |
| 379 |
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| 380 |
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/** |
| 381 |
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* @brief Return the number of iterations performed by the solver |
| 382 |
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*/ |
| 383 |
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std::size_t get_iter() const; |
| 384 |
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| 385 |
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/** |
| 386 |
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* @brief Modify the state trajectory \f$\mathbf{x}_s\f$ |
| 387 |
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*/ |
| 388 |
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void set_xs(const std::vector<Eigen::VectorXd>& xs); |
| 389 |
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| 390 |
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/** |
| 391 |
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* @brief Modify the control trajectory \f$\mathbf{u}_s\f$ |
| 392 |
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*/ |
| 393 |
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void set_us(const std::vector<Eigen::VectorXd>& us); |
| 394 |
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| 395 |
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/** |
| 396 |
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* @brief Modify the primal-variable regularization value |
| 397 |
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*/ |
| 398 |
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void set_preg(const double preg); |
| 399 |
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| 400 |
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/** |
| 401 |
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* @brief Modify the dual-variable regularization value |
| 402 |
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*/ |
| 403 |
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void set_dreg(const double dreg); |
| 404 |
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| 405 |
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DEPRECATED("Use set_preg for primal-variable regularization", |
| 406 |
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void set_xreg(const double xreg);) |
| 407 |
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DEPRECATED("Use set_preg for primal-variable regularization", |
| 408 |
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void set_ureg(const double ureg);) |
| 409 |
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| 410 |
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/** |
| 411 |
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* @brief Modify the threshold used for accepting step |
| 412 |
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*/ |
| 413 |
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void set_th_acceptstep(const double th_acceptstep); |
| 414 |
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| 415 |
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/** |
| 416 |
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* @brief Modify the tolerance for stopping the algorithm |
| 417 |
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*/ |
| 418 |
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void set_th_stop(const double th_stop); |
| 419 |
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| 420 |
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/** |
| 421 |
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* @brief Modify the threshold for accepting a gap as non-zero |
| 422 |
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*/ |
| 423 |
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void set_th_gaptol(const double th_gaptol); |
| 424 |
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| 425 |
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/** |
| 426 |
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* @brief Modify the current norm used for computed the dynamic and constraint |
| 427 |
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* feasibility |
| 428 |
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*/ |
| 429 |
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void set_feasnorm(const FeasibilityNorm feas_norm); |
| 430 |
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| 431 |
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protected: |
| 432 |
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boost::shared_ptr<ShootingProblem> problem_; //!< optimal control problem |
| 433 |
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std::vector<Eigen::VectorXd> xs_; //!< State trajectory |
| 434 |
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std::vector<Eigen::VectorXd> us_; //!< Control trajectory |
| 435 |
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std::vector<Eigen::VectorXd> fs_; //!< Gaps/defects between shooting nodes |
| 436 |
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std::vector<boost::shared_ptr<CallbackAbstract> > |
| 437 |
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callbacks_; //!< Callback functions |
| 438 |
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bool is_feasible_; //!< Label that indicates is the iteration is feasible |
| 439 |
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bool was_feasible_; //!< Label that indicates in the previous iterate was |
| 440 |
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//!< feasible |
| 441 |
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double cost_; //!< Cost for the current guess |
| 442 |
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double merit_; //!< Merit for the current guess |
| 443 |
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double stop_; //!< Value computed by `stoppingCriteria()` |
| 444 |
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Eigen::Vector2d d_; //!< LQ approximation of the expected improvement |
| 445 |
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double dV_; //!< Reduction in the cost function computed by `tryStep()` |
| 446 |
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double dPhi_; //!< Reduction in the merit function computed by `tryStep()` |
| 447 |
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double dVexp_; //!< Expected reduction in the cost function |
| 448 |
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|
double dPhiexp_; //!< Expected reduction in the merit function |
| 449 |
|
|
double dfeas_; //!< Reduction in the feasibility |
| 450 |
|
|
double feas_; //!< Total feasibility for the current guess |
| 451 |
|
|
double |
| 452 |
|
|
ffeas_; //!< Feasibility of the dynamic constraints for the current guess |
| 453 |
|
|
double gfeas_; //!< Feasibility of the inequality constraints for the current |
| 454 |
|
|
//!< guess |
| 455 |
|
|
double hfeas_; //!< Feasibility of the equality constraints for the current |
| 456 |
|
|
//!< guess |
| 457 |
|
|
double ffeas_try_; //!< Feasibility of the dynamic constraints evaluated for |
| 458 |
|
|
//!< the current step length |
| 459 |
|
|
double gfeas_try_; //!< Feasibility of the inequality constraints evaluated |
| 460 |
|
|
//!< for the current step length |
| 461 |
|
|
double hfeas_try_; //!< Feasibility of the equality constraints evaluated for |
| 462 |
|
|
//!< the current step length |
| 463 |
|
|
double preg_; //!< Current primal-variable regularization value |
| 464 |
|
|
double dreg_; //!< Current dual-variable regularization value |
| 465 |
|
|
DEPRECATED("Use preg_ for primal-variable regularization", |
| 466 |
|
|
double xreg_;) //!< Current state regularization value |
| 467 |
|
|
DEPRECATED("Use dreg_ for primal-variable regularization", |
| 468 |
|
|
double ureg_;) //!< Current control regularization values |
| 469 |
|
|
double steplength_; //!< Current applied step length |
| 470 |
|
|
double th_acceptstep_; //!< Threshold used for accepting step |
| 471 |
|
|
double th_stop_; //!< Tolerance for stopping the algorithm |
| 472 |
|
|
double th_gaptol_; //!< Threshold limit to check non-zero gaps |
| 473 |
|
|
enum FeasibilityNorm feasnorm_; //!< Type of norm used to evaluate the |
| 474 |
|
|
//!< dynamics and constraints feasibility |
| 475 |
|
|
std::size_t iter_; //!< Number of iteration performed by the solver |
| 476 |
|
|
double tmp_feas_; //!< Temporal variables used for computed the feasibility |
| 477 |
|
|
std::vector<Eigen::VectorXd> g_adj_; //!< Adjusted inequality bound |
| 478 |
|
|
}; |
| 479 |
|
|
|
| 480 |
|
|
/** |
| 481 |
|
|
* @brief Abstract class for solver callbacks |
| 482 |
|
|
* |
| 483 |
|
|
* A callback is used to diagnostic the behaviour of our solver in each |
| 484 |
|
|
* iteration of it. For instance, it can be used to print values, record data or |
| 485 |
|
|
* display motions. |
| 486 |
|
|
*/ |
| 487 |
|
|
class CallbackAbstract { |
| 488 |
|
|
public: |
| 489 |
|
|
/** |
| 490 |
|
|
* @brief Initialize the callback function |
| 491 |
|
|
*/ |
| 492 |
|
26 |
CallbackAbstract() {} |
| 493 |
|
56 |
virtual ~CallbackAbstract() {} |
| 494 |
|
|
|
| 495 |
|
|
/** |
| 496 |
|
|
* @brief Run the callback function given a solver |
| 497 |
|
|
* |
| 498 |
|
|
* @param[in] solver solver to be diagnostic |
| 499 |
|
|
*/ |
| 500 |
|
|
virtual void operator()(SolverAbstract& solver) = 0; |
| 501 |
|
|
}; |
| 502 |
|
|
|
| 503 |
|
|
bool raiseIfNaN(const double value); |
| 504 |
|
|
|
| 505 |
|
|
} // namespace crocoddyl |
| 506 |
|
|
|
| 507 |
|
|
#endif // CROCODDYL_CORE_SOLVER_BASE_HPP_ |
| 508 |
|
|
|