Solve a quadratic program with a specific structure. qp_as = Quadratic Programming / Active Set. More...

#include <qp_as.h>

Inheritance diagram for qp_as:

Public Member Functions
	qp_as (const int N_, const double, const double, const double, const double, const double, const bool, const unsigned int, const bool)
	Constructor: initialization of the constant parameters. More...

	~qp_as ()

void	set_parameters (const double , const double , const double, const double , const double , const double , const double , const double *)
	Initializes quadratic problem. More...

void	solve (vector< double > &)
	Solve QP problem. More...

void	form_init_fp (const double , const double , const double , const bool, double )
	Generates an initial feasible point. More...

Public Member Functions inherited from AS::problem_parameters
	problem_parameters (const int, const double, const double, const double, const double)

	~problem_parameters ()

void	set_state_parameters (const double , const double , const double)
	Initializes quadratic problem. More...

Public Attributes
double *	X

unsigned int	added_constraints_num

unsigned int	removed_constraints_num

unsigned int	active_set_size

bool	constraint_removal_on

unsigned int	max_added_constraints_num

Public Attributes inherited from AS::problem_parameters
int	N

state_parameters *	spar

double	h_initial
	Height of the CoM at initial state divided by the gravity, this initial state precede the first state in the preview window. More...

double	i2Q [3]

double	i2P

Private Member Functions
int	check_blocking_constraints ()
	Checks for blocking constraints. More...

int	choose_excl_constr (const double *)
	Selects a constraint for removal from active set. More...

double	compute_obj ()
	Compute value of the objective function. More...

Private Attributes
AS::chol_solve	chol
	An instance of AS::chol_solve class. More...

const double *	zref_x

const double *	zref_y

double	tol
	tolerance More...

bool	obj_computation_on

vector< AS::constraint >	active_set
	A set of active constraints. More...

vector< AS::constraint >	constraints
	Vector of constraints. More...

double *	dX

double	alpha

Detailed Description

Solve a quadratic program with a specific structure. qp_as = Quadratic Programming / Active Set.

Definition at line 37 of file qp_as.h.

Constructor & Destructor Documentation

◆ qp_as()

qp_as::qp_as	(	const int	N_,
		const double	gain_position,
		const double	gain_velocity,
		const double	gain_acceleration,
		const double	gain_jerk,
		const double	tol_,
		const bool	obj_computation_on_,
		const unsigned int	max_added_constraints_num_,
		const bool	constraint_removal_on_
	)

Constructor: initialization of the constant parameters.

Parameters

[in]	N_	Number of sampling times in a preview window
[in]	gain_position	Position gain
[in]	gain_velocity	Velocity gain
[in]	gain_acceleration	Acceleration gain
[in]	gain_jerk	Jerk gain
[in]	tol_	tolerance
[in]	obj_computation_on_	enable computation of the objective function
[in]	max_added_constraints_num_	limit on the number of the added constraints
[in]	constraint_removal_on_	enable constraint removal

Definition at line 36 of file qp_as.cpp.

◆ ~qp_as()

qp_as::~qp_as ( )

Destructor

Definition at line 66 of file qp_as.cpp.

Member Function Documentation

◆ check_blocking_constraints()

int qp_as::check_blocking_constraints ( )

private

Checks for blocking constraints.

Returns: sequential number of constraint to be added, -1 if no constraints.

Definition at line 159 of file qp_as.cpp.

◆ choose_excl_constr()

int qp_as::choose_excl_constr ( const double * lambda )

private

Selects a constraint for removal from active set.

Parameters

[in] lambda vector of Lagrange multipliers corresponding to inequality constraints.

Returns: index of constraint in the active set, -1 if no constraint can be removed.

Attention: If a constraint for removal is selected, then it is removed from the active set (active_set).

Definition at line 226 of file qp_as.cpp.

◆ compute_obj()

double qp_as::compute_obj ( )

private

Compute value of the objective function.

Returns: value of the objective function.

Definition at line 343 of file qp_as.cpp.

◆ form_init_fp()

void qp_as::form_init_fp	(	const double *	x_coord,
		const double *	y_coord,
		const double *	init_state,
		const bool	tilde_state,
		double *	X_
	)

Generates an initial feasible point.

Parameters

[in]	x_coord	x coordinates of points satisfying constraints
[in]	y_coord	y coordinates of points satisfying constraints
[in]	init_state	current state
[in]	tilde_state	if true the state is interpreted as X_tilde.
[in,out]	X_	initial guess / solution of optimization problem

Definition at line 141 of file qp_as.cpp.

◆ set_parameters()

void qp_as::set_parameters	(	const double *	T_,
		const double *	h_,
		const double	h_initial_,
		const double *	angle,
		const double *	zref_x_,
		const double *	zref_y_,
		const double *	lb,
		const double *	ub
	)

Initializes quadratic problem.

Parameters

[in]	T_	Sampling time (for the moment it is assumed to be constant) [sec.]
[in]	h_	Height of the Center of Mass divided by gravity
[in]	h_initial_	current h
[in]	angle	Rotation angle for each state in the preview window
[in]	zref_x_	reference values of z_x
[in]	zref_y_	reference values of z_y
[in]	lb	array of lower constraints for z_x and z_y
[in]	ub	array of upper constraints for z_x and z_y

Definition at line 84 of file qp_as.cpp.

◆ solve()

void qp_as::solve ( vector< double > & obj_log )

Solve QP problem.

Parameters

[in,out] obj_log a vector of objective function values

Returns: number of activated constraints

Definition at line 258 of file qp_as.cpp.

Member Data Documentation

◆ active_set

vector<AS::constraint> qp_as::active_set

private

A set of active constraints.

Definition at line 111 of file qp_as.h.

◆ active_set_size

unsigned int qp_as::active_set_size

Definition at line 82 of file qp_as.h.

◆ added_constraints_num

unsigned int qp_as::added_constraints_num

Definition at line 80 of file qp_as.h.

◆ alpha

double qp_as::alpha

private

A number from 0 to 1, which controls depth of descent X = X + alpha*dX.

Definition at line 122 of file qp_as.h.

◆ chol

AS::chol_solve qp_as::chol

private

An instance of AS::chol_solve class.

Definition at line 98 of file qp_as.h.

◆ constraint_removal_on

bool qp_as::constraint_removal_on

Definition at line 84 of file qp_as.h.

◆ constraints

vector<AS::constraint> qp_as::constraints

private

Vector of constraints.

Definition at line 114 of file qp_as.h.

◆ dX

double* qp_as::dX

private

Feasible descent direction (to be used for updating X).

Definition at line 119 of file qp_as.h.

◆ max_added_constraints_num

unsigned int qp_as::max_added_constraints_num

Definition at line 85 of file qp_as.h.

◆ obj_computation_on

bool qp_as::obj_computation_on

private

Definition at line 107 of file qp_as.h.

◆ removed_constraints_num

unsigned int qp_as::removed_constraints_num

Definition at line 81 of file qp_as.h.

◆ tol

double qp_as::tol

private

tolerance

Definition at line 105 of file qp_as.h.

◆ X

double* qp_as::X

Variables for the QP (contain the states + control variables). Initial feasible point with respect to the equality and inequality constraints.

Definition at line 76 of file qp_as.h.

◆ zref_x

const double* qp_as::zref_x

private

Definition at line 101 of file qp_as.h.

◆ zref_y

const double* qp_as::zref_y

private

Definition at line 102 of file qp_as.h.

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

solver/qp_as.h
solver/qp_as.cpp

Public Member Functions

Public Attributes

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ qp_as()

◆ ~qp_as()

Member Function Documentation

◆ check_blocking_constraints()

◆ choose_excl_constr()

◆ compute_obj()

◆ form_init_fp()

◆ set_parameters()

◆ solve()

Member Data Documentation

◆ active_set

◆ active_set_size

◆ added_constraints_num

◆ alpha

◆ chol

◆ constraint_removal_on

◆ constraints

◆ dX

◆ max_added_constraints_num

◆ obj_computation_on

◆ removed_constraints_num

◆ tol

◆ X

◆ zref_x

◆ zref_y