Abstract class for optimal control solvers. More...

#include <solver-base.hpp>

Inheritance diagram for SolverAbstract:

Public Member Functions
EIGEN_MAKE_ALIGNED_OPERATOR_NEW	SolverAbstract (boost::shared_ptr< ShootingProblem > problem)
	Initialize the solver. More...

virtual void	computeDirection (const bool recalc)=0
	Compute the search direction \((\delta\mathbf{x}^k,\delta\mathbf{u}^k)\) for the current guess \((\mathbf{x}^k_s,\mathbf{u}^k_s)\). More...

double	computeDynamicFeasibility ()
	Compute the dynamic feasibility \(\\|\mathbf{f}_{\mathbf{s}}\\|_{\infty,1}\) for the current guess \((\mathbf{x}^k,\mathbf{u}^k)\). More...

double	computeEqualityFeasibility ()
	Compute the feasibility of the equality constraints for the current guess. More...

double	computeInequalityFeasibility ()
	Compute the feasibility of the inequality constraints for the current guess. More...

	DEPRECATED ("Use get_preg for primal-variable regularization", double get_xreg() const ;) DEPRECATED("Use get_preg for primal-variable regularization"

	DEPRECATED ("Use set_preg for primal-variable regularization", void set_xreg(const double xreg);) DEPRECATED("Use set_preg for primal-variable regularization"

virtual const Eigen::Vector2d &	expectedImprovement ()=0
	Return the expected improvement \(dV_{exp}\) from a given current search direction \((\delta\mathbf{x}^k,\delta\mathbf{u}^k)\). More...

double	get_cost () const
	Return the cost for the current guess.

const Eigen::Vector2d &	get_d () const
	Return the linear and quadratic terms of the expected improvement.

double	get_dfeas () const
	Return the reduction in the feasibility.

double	get_dPhi () const
	Return the reduction in the merit function \(\Delta\Phi\).

double	get_dPhiexp () const
	Return the expected reduction in the merit function \(\Delta\Phi_{exp}\).

double	get_dreg () const
	Return the dual-variable regularization.

double	get_dV () const
	Return the reduction in the cost function \(\Delta V\).

double	get_dVexp () const
	Return the expected reduction in the cost function \(\Delta V_{exp}\).

double	get_feas () const
	Return the total feasibility for the current guess.

FeasibilityNorm	get_feasnorm () const
	Return the type of norm used to evaluate the dynamic and constraints feasibility.

double	get_ffeas () const
	Return the dynamic feasibility for the current guess.

double	get_ffeas_try () const
	Return the dynamic feasibility for the current step length.

const std::vector< Eigen::VectorXd > &	get_fs () const
	Return the dynamic infeasibility \(\mathbf{f}_{s}\).

double	get_gfeas () const
	Return the inequality feasibility for the current guess.

double	get_gfeas_try () const
	Return the inequality feasibility for the current step length.

double	get_hfeas () const
	Return the equality feasibility for the current guess.

double	get_hfeas_try () const
	Return the equality feasibility for the current step length.

bool	get_is_feasible () const
	Return the feasibility status of the \((\mathbf{x}_s,\mathbf{u}_s)\) trajectory.

std::size_t	get_iter () const
	Return the number of iterations performed by the solver.

double	get_merit () const
	Return the merit for the current guess.

double	get_preg () const
	Return the primal-variable regularization.

const boost::shared_ptr< ShootingProblem > &	get_problem () const
	Return the shooting problem.

double	get_steplength () const
	Return the step length \(\alpha\).

double	get_stop () const
	Return the stopping-criteria value computed by `stoppingCriteria()`

double	get_th_acceptstep () const
	Return the threshold used for accepting a step.

double	get_th_gaptol () const
	Return the threshold for accepting a gap as non-zero.

double	get_th_stop () const
	Return the tolerance for stopping the algorithm.

double	get_ureg () const

const std::vector< Eigen::VectorXd > &	get_us () const
	Return the control trajectory \(\mathbf{u}_s\).

const std::vector< Eigen::VectorXd > &	get_xs () const
	Return the state trajectory \(\mathbf{x}_s\).

const std::vector< boost::shared_ptr< CallbackAbstract > > &	getCallbacks () const
	Return the list of callback functions using for diagnostic.

virtual void	resizeData ()
	Resizing the solver data. More...

void	set_dreg (const double dreg)
	Modify the dual-variable regularization value.

void	set_feasnorm (const FeasibilityNorm feas_norm)
	Modify the current norm used for computed the dynamic and constraint feasibility.

void	set_preg (const double preg)
	Modify the primal-variable regularization value.

void	set_th_acceptstep (const double th_acceptstep)
	Modify the threshold used for accepting step.

void	set_th_gaptol (const double th_gaptol)
	Modify the threshold for accepting a gap as non-zero.

void	set_th_stop (const double th_stop)
	Modify the tolerance for stopping the algorithm.

void	set_ureg (const double ureg)

void	set_us (const std::vector< Eigen::VectorXd > &us)
	Modify the control trajectory \(\mathbf{u}_s\).

void	set_xs (const std::vector< Eigen::VectorXd > &xs)
	Modify the state trajectory \(\mathbf{x}_s\).

void	setCallbacks (const std::vector< boost::shared_ptr< CallbackAbstract > > &callbacks)
	Set a list of callback functions using for the solver diagnostic. More...

void	setCandidate (const std::vector< Eigen::VectorXd > &xs_warm=DEFAULT_VECTOR, const std::vector< Eigen::VectorXd > &us_warm=DEFAULT_VECTOR, const bool is_feasible=false)
	Set the solver candidate trajectories \((\mathbf{x}_s,\mathbf{u}_s)\). More...

virtual bool	solve (const std::vector< Eigen::VectorXd > &init_xs=DEFAULT_VECTOR, const std::vector< Eigen::VectorXd > &init_us=DEFAULT_VECTOR, const std::size_t maxiter=100, const bool is_feasible=false, const double reg_init=NAN)=0
	Compute the optimal trajectory \(\mathbf{x}^_s,\mathbf{u}^_s\) as lists of \(T+1\) and \(T\) terms. More...

virtual double	stoppingCriteria ()=0
	Return a positive value that quantifies the algorithm termination. More...

virtual double	tryStep (const double steplength=1)=0
	Try a predefined step length \(\alpha\) and compute its cost improvement \(dV\). More...

Protected Member Functions
	DEPRECATED ("Use preg_ for primal-variable regularization", double xreg_;) DEPRECATED("Use dreg_ for primal-variable regularization"

Protected Attributes
std::vector< boost::shared_ptr< CallbackAbstract > >	callbacks_
	Callback functions.

double	cost_
	Cost for the current guess.

Eigen::Vector2d	d_
	LQ approximation of the expected improvement.

double	dfeas_
	Reduction in the feasibility.

double	dPhi_
	Reduction in the merit function computed by `tryStep()`

double	dPhiexp_
	Expected reduction in the merit function.

double	dreg_
	Current dual-variable regularization value.

double	dV_
	Reduction in the cost function computed by `tryStep()`

double	dVexp_
	Expected reduction in the cost function.

double	feas_
	Total feasibility for the current guess.

enum FeasibilityNorm	feasnorm_

double	ffeas_
	Feasibility of the dynamic constraints for the current guess.

double	ffeas_try_

std::vector< Eigen::VectorXd >	fs_
	Gaps/defects between shooting nodes.

double	gfeas_

double	gfeas_try_

double	hfeas_

double	hfeas_try_

bool	is_feasible_
	Label that indicates is the iteration is feasible.

std::size_t	iter_
	Number of iteration performed by the solver.

double	merit_
	Merit for the current guess.

double	preg_
	Current primal-variable regularization value.

boost::shared_ptr< ShootingProblem >	problem_
	optimal control problem

double	steplength_
	< Current control regularization values More...

double	stop_
	Value computed by `stoppingCriteria()`

double	th_acceptstep_
	Threshold used for accepting step.

double	th_gaptol_
	Threshold limit to check non-zero gaps.

double	th_stop_
	Tolerance for stopping the algorithm.

double	tmp_feas_
	Temporal variables used for computed the feasibility.

double	ureg_

std::vector< Eigen::VectorXd >	us_
	Control trajectory.

bool	was_feasible_

std::vector< Eigen::VectorXd >	xs_
	State trajectory.

Detailed Description

Abstract class for optimal control solvers.

A solver resolves an optimal control solver of the form

\begin{eqnarray*} \begin{Bmatrix} \mathbf{x}^*_0,\cdots,\mathbf{x}^*_{T} \\ \mathbf{u}^*_0,\cdots,\mathbf{u}^*_{T-1} \end{Bmatrix} = \arg\min_{\mathbf{x}_s,\mathbf{u}_s} && l_T (\mathbf{x}_T) + \sum_{k=0}^{T-1} l_k(\mathbf{x}_t,\mathbf{u}_t) \\ \operatorname{subject}\,\operatorname{to} && \mathbf{x}_0 = \mathbf{\tilde{x}}_0\\ && \mathbf{x}_{k+1} = \mathbf{f}_k(\mathbf{x}_k,\mathbf{u}_k)\\ && \mathbf{x}_k\in\mathcal{X}, \mathbf{u}_k\in\mathcal{U} \end{eqnarray*}

where \(l_T(\mathbf{x}_T)\), \(l_k(\mathbf{x}_t,\mathbf{u}_t)\) are the terminal and running cost functions, respectively, \(\mathbf{f}_k(\mathbf{x}_k,\mathbf{u}_k)\) describes evolution of the system, and state and control admissible sets are defined by \(\mathbf{x}_k\in\mathcal{X}\), \(\mathbf{u}_k\in\mathcal{U}\). An action model, defined in the shooting problem, describes each node \(k\). Inside the action model, we specialize the cost functions, the system evolution and the admissible sets.

The main routines are computeDirection() and tryStep(). The former finds a search direction and typically computes the derivatives of each action model. The latter rollout the dynamics and cost (i.e., the action) to try the search direction found by computeDirection. Both functions used the current guess defined by setCandidate(). Finally, solve() function is used to define when the search direction and length are computed in each iterate. It also describes the globalization strategy (i.e., regularization) of the numerical optimization.

See also: solve(), computeDirection(), tryStep(), stoppingCriteria()

Definition at line 61 of file solver-base.hpp.

Constructor & Destructor Documentation

◆ SolverAbstract()

SolverAbstract ( boost::shared_ptr< ShootingProblem > problem )

explicit

Initialize the solver.

Parameters

[in] problem shooting problem

Definition at line 19 of file solver-base.cpp.

Member Function Documentation

◆ solve()

virtual bool solve	(	const std::vector< Eigen::VectorXd > &	init_xs = `DEFAULT_VECTOR`,
		const std::vector< Eigen::VectorXd > &	init_us = `DEFAULT_VECTOR`,
		const std::size_t	maxiter = `100`,
		const bool	is_feasible = `false`,
		const double	reg_init = `NAN`
	)

pure virtual

Compute the optimal trajectory \(\mathbf{x}^*_s,\mathbf{u}^*_s\) as lists of \(T+1\) and \(T\) terms.

From an initial guess init_xs, init_us (feasible or not), iterate over computeDirection() and tryStep() until stoppingCriteria() is below threshold. It also describes the globalization strategy used during the numerical optimization.

Parameters

[in]	init_xs	initial guess for state trajectory with \(T+1\) elements (default [])
[in]	init_us	initial guess for control trajectory with \(T\) elements (default [])
[in]	maxiter	maximum allowed number of iterations (default 100)
[in]	is_feasible	true if the `init_xs` are obtained from integrating the `init_us` (rollout) (default false)
[in]	init_reg	initial guess for the regularization value. Very low values are typical used with very good guess points (default 1e-9).

Returns: A boolean that describes if convergence was reached.

Implemented in SolverKKT, and SolverIpopt.

◆ computeDirection()

virtual void computeDirection ( const bool recalc )

pure virtual

Compute the search direction \((\delta\mathbf{x}^k,\delta\mathbf{u}^k)\) for the current guess \((\mathbf{x}^k_s,\mathbf{u}^k_s)\).

You must call setCandidate() first in order to define the current guess. A current guess defines a state and control trajectory \((\mathbf{x}^k_s,\mathbf{u}^k_s)\) of \(T+1\) and \(T\) elements, respectively.

Parameters

[in] recalc true for recalculating the derivatives at current state and control

Returns: The search direction \((\delta\mathbf{x},\delta\mathbf{u})\) and the dual lambdas as lists of \(T+1\), \(T\) and \(T+1\) lengths, respectively

Implemented in SolverKKT.

◆ tryStep()

virtual double tryStep ( const double steplength = 1 )

pure virtual

Try a predefined step length \(\alpha\) and compute its cost improvement \(dV\).

It uses the search direction found by computeDirection() to try a determined step length \(\alpha\). Therefore, it assumes that we have run computeDirection() first. Additionally, it returns the cost improvement \(dV\) along the predefined step length \(\alpha\).

Parameters

[in] steplength applied step length ( \(0\leq\alpha\leq1\))

Returns: the cost improvement

Implemented in SolverKKT.

◆ stoppingCriteria()

virtual double stoppingCriteria ( )

pure virtual

Return a positive value that quantifies the algorithm termination.

These values typically represents the gradient norm which tell us that it's been reached the local minima. The stopping criteria strictly speaking depends on the search direction (calculated by computeDirection()) but it could also depend on the chosen step length, tested by tryStep().

Implemented in SolverKKT.

◆ expectedImprovement()

virtual const Eigen::Vector2d& expectedImprovement ( )

pure virtual

Return the expected improvement \(dV_{exp}\) from a given current search direction \((\delta\mathbf{x}^k,\delta\mathbf{u}^k)\).

For computing the expected improvement, you need to compute the search direction first via computeDirection().

Implemented in SolverKKT.

◆ resizeData()

void resizeData ( )

virtual

Resizing the solver data.

If the shooting problem has changed after construction, then this function resizes all the data before starting resolve the problem.

Reimplemented in SolverIpopt.

Definition at line 68 of file solver-base.cpp.

◆ computeDynamicFeasibility()

double computeDynamicFeasibility ( )

Compute the dynamic feasibility \(\|\mathbf{f}_{\mathbf{s}}\|_{\infty,1}\) for the current guess \((\mathbf{x}^k,\mathbf{u}^k)\).

The feasibility can be computed using different norms (e.g, \(\ell_\infty\) or \(\ell_1\) norms). By default we use the \(\ell_\infty\) norm, however, we can change the type of norm using set_feasnorm. Note that \(\mathbf{f}_{\mathbf{s}}\) are the gaps on the dynamics, which are computed at each node as \(\mathbf{x}^{'}-\mathbf{f}(\mathbf{x},\mathbf{u})\).

Definition at line 79 of file solver-base.cpp.

◆ computeInequalityFeasibility()

double computeInequalityFeasibility ( )

Compute the feasibility of the inequality constraints for the current guess.

The feasibility can be computed using different norms (e.g, \(\ell_\infty\) or \(\ell_1\) norms). By default we use the \(\ell_\infty\) norm, however, we can change the type of norm using set_feasnorm.

Definition at line 121 of file solver-base.cpp.

◆ computeEqualityFeasibility()

double computeEqualityFeasibility ( )

Compute the feasibility of the equality constraints for the current guess.

The feasibility can be computed using different norms (e.g, \(\ell_\infty\) or \(\ell_1\) norms). By default we use the \(\ell_\infty\) norm, however, we can change the type of norm using set_feasnorm.

Definition at line 156 of file solver-base.cpp.

◆ setCandidate()

void setCandidate	(	const std::vector< Eigen::VectorXd > &	xs_warm = `DEFAULT_VECTOR`,
		const std::vector< Eigen::VectorXd > &	us_warm = `DEFAULT_VECTOR`,
		const bool	is_feasible = `false`
	)

Set the solver candidate trajectories \((\mathbf{x}_s,\mathbf{u}_s)\).

The solver candidates are defined as a state and control trajectories \((\mathbf{x}_s,\mathbf{u}_s)\) of \(T+1\) and \(T\) elements, respectively. Additionally, we need to define the dynamic feasibility of the \((\mathbf{x}_s,\mathbf{u}_s)\) pair. Note that the trajectories are feasible if \(\mathbf{x}_s\) is the resulting trajectory from the system rollout with \(\mathbf{u}_s\) inputs.

Parameters

[in]	xs	state trajectory of \(T+1\) elements (default [])
[in]	us	control trajectory of \(T\) elements (default [])
[in]	isFeasible	true if the `xs` are obtained from integrating the `us` (rollout)

Definition at line 191 of file solver-base.cpp.

◆ setCallbacks()

void setCallbacks ( const std::vector< boost::shared_ptr< CallbackAbstract > > & callbacks )

Set a list of callback functions using for the solver diagnostic.

Each iteration, the solver calls these set of functions in order to allowed user the diagnostic of its performance.

Parameters

callbacks set of callback functions

Definition at line 263 of file solver-base.cpp.

Member Data Documentation

◆ was_feasible_

bool was_feasible_

protected

Label that indicates in the previous iterate was feasible

Definition at line 439 of file solver-base.hpp.

◆ gfeas_

double gfeas_

protected

Feasibility of the inequality constraints for the current guess

Definition at line 453 of file solver-base.hpp.

◆ hfeas_

double hfeas_

protected

Feasibility of the equality constraints for the current guess

Definition at line 455 of file solver-base.hpp.

◆ ffeas_try_

double ffeas_try_

protected

Feasibility of the dynamic constraints evaluated for the current step length

Definition at line 457 of file solver-base.hpp.

◆ gfeas_try_

double gfeas_try_

protected

Feasibility of the inequality constraints evaluated for the current step length

Definition at line 459 of file solver-base.hpp.

◆ hfeas_try_

double hfeas_try_

protected

Feasibility of the equality constraints evaluated for the current step length

Definition at line 461 of file solver-base.hpp.

◆ steplength_

double steplength_

protected

< Current control regularization values

Current applied step length

Definition at line 469 of file solver-base.hpp.

◆ feasnorm_

enum FeasibilityNorm feasnorm_

protected

Type of norm used to evaluate the dynamics and constraints feasibility

Definition at line 472 of file solver-base.hpp.

The documentation for this class was generated from the following files:

/root/robotpkg/optimization/py-crocoddyl/work/crocoddyl-2.1.0/include/crocoddyl/core/solver-base.hpp
/root/robotpkg/optimization/py-crocoddyl/work/crocoddyl-2.1.0/src/core/solver-base.cpp

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ SolverAbstract()

Member Function Documentation

◆ solve()

◆ computeDirection()

◆ tryStep()

◆ stoppingCriteria()

◆ expectedImprovement()

◆ resizeData()

◆ computeDynamicFeasibility()

◆ computeInequalityFeasibility()

◆ computeEqualityFeasibility()

◆ setCandidate()

◆ setCallbacks()

Member Data Documentation

◆ was_feasible_

◆ gfeas_

◆ hfeas_

◆ ffeas_try_

◆ gfeas_try_

◆ hfeas_try_

◆ steplength_

◆ feasnorm_