qp_ip Class Reference

Solve a quadratic program with a specific structure. qp_ip = Quadratic Programming / Interior-point method. More...

#include <qp_ip.h>

Inheritance diagram for qp_ip:

List of all members.

Public Member Functions
	qp_ip (const int N_, const double, const double, const double, const double, const double)
	Constructor: initialization of the constant parameters.
	~qp_ip ()
void	set_parameters (const double *, const double *, const double, const double *, const double *, const double *, const double *, const double *)
	Initializes quadratic problem.
void	set_ip_parameters (const double, const double, const double, const double, const int, const double)
	Set parameters of interior-point method.
int	solve ()
	Solve QP using interior-point method.
Private Member Functions
void	init_alpha ()
	tolerance of the outer loop
double	form_bs_alpha_grad_dX ()
	Forms bs_alpha * grad' * dX.
double	form_phi_X_tmp (const double)
	Forms phi(X+alpha*dX)
bool	solve_onestep (const double)
	One step of interior point method.
void	form_g (const double *, const double *)
	Forms vector g.
void	form_grad_i2hess_logbar (const double)
	Compute gradient of phi, varying elements of i2hess, logarithmic barrier of phi.
void	form_i2hess_grad ()
	Finish initialization of i2hess_grad = -i2hess*grad.
void	form_phi_X ()
	Compute phi_X for initial point, phi_X must already store logarithmic barrier term.
Private Attributes
double *	g
	2*N non-zero elements of vector g.
double *	i2hess
	Inverted hessian: non-repeating diagonal elements 1:3:N*SMPC_NUM_STATE_VAR, 2*N in total.
double *	i2hess_grad
	Inverted hessian * gradient (N*SMPC_NUM_VAR vector)
double *	grad
	N*SMPC_NUM_VAR gradient vector
double	phi_X
	Value of phi(X), where phi is the cost function + log barrier.
chol_solve_ip	chol
	An instance of chol_solve_ip class.
double	t
double	mu
	logarithmic barrier parameter
double	bs_alpha
	multiplier of t, >1.
double	bs_beta
	backtracking search parameter alpha
int	max_iter
	backtracking search parameter beta
double	tol_out
	maximum number of internal loop iterations
double	Q [3]
	Diagonal elements of H.
double	P
	Diagonal elements of H.
const double *	lb
	lower and upper bounds
const double *	ub
	lower and upper bounds

---

Detailed Description

Solve a quadratic program with a specific structure. qp_ip = Quadratic Programming / Interior-point method.

Definition at line 36 of file qp_ip.h.

---

Constructor & Destructor Documentation

qp_ip::qp_ip	(	const int	N_,
		const double	Alpha,
		const double	Beta,
		const double	Gamma,
		const double	regularization,
		const double	tol_
	)

Constructor: initialization of the constant parameters.

Parameters:

[in]	N_	Number of sampling times in a preview window
[in]	Alpha	Velocity gain
[in]	Beta	Position gain
[in]	Gamma	Jerk gain
[in]	regularization	regularization
[in]	tol_	tolerance

Definition at line 34 of file qp_ip.cpp.

qp_ip::~qp_ip

(

)

Destructor

Definition at line 57 of file qp_ip.cpp.

---

Member Function Documentation

double qp_ip::form_bs_alpha_grad_dX

(

)

[private]

Forms bs_alpha * grad' * dX.

Returns:

result of multiplication.

Definition at line 281 of file qp_ip.cpp.

void qp_ip::form_g	(	const double *	zref_x,
		const double *	zref_y
	)		[private]

Forms vector g.

Parameters:

[in]	zref_x	x coordinates of reference ZMP positions
[in]	zref_y	y coordinates of reference ZMP positions

Definition at line 108 of file qp_ip.cpp.

void qp_ip::form_grad_i2hess_logbar

(

const double

kappa

)

[private]

Compute gradient of phi, varying elements of i2hess, logarithmic barrier of phi.

Parameters:

[in]

kappa

1/t, a logarithmic barrier multiplicator.

Definition at line 136 of file qp_ip.cpp.

void qp_ip::form_i2hess_grad

(

)

[private]

Finish initialization of i2hess_grad = -i2hess*grad.

Definition at line 183 of file qp_ip.cpp.

void qp_ip::form_phi_X

(

)

[private]

Compute phi_X for initial point, phi_X must already store logarithmic barrier term.

Definition at line 207 of file qp_ip.cpp.

double qp_ip::form_phi_X_tmp

(

const double

kappa

)

[private]

Forms phi(X+alpha*dX)

Parameters:

[in]

kappa

logarithmic barrier multiplicator.

Returns:

a value of phi.

Definition at line 301 of file qp_ip.cpp.

void qp_ip::init_alpha

(

)

[private]

tolerance of the outer loop

Find initial value of alpha.

Note:

sets alpha to 0, if it is too small.

Definition at line 234 of file qp_ip.cpp.

void qp_ip::set_ip_parameters	(	const double	t_,
		const double	mu_,
		const double	bs_alpha_,
		const double	bs_beta_,
		const int	max_iter_,
		const double	tol_out_
	)

Set parameters of interior-point method.

Parameters:

[in]	t_	logarithmic barrier parameter
[in]	mu_	multiplier of t, >1.
[in]	bs_alpha_	backtracking search parameter alpha
[in]	bs_beta_	backtracking search parameter beta
[in]	max_iter_	maximum number of internal loop iterations
[in]	tol_out_	tolerance of the outer loop

Definition at line 354 of file qp_ip.cpp.

void qp_ip::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_
	)		[virtual]

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 bounds for z_x and z_y
[in]	ub_	array of upper bounds for z_x and z_y

Implements qp_solver.

Definition at line 81 of file qp_ip.cpp.

int qp_ip::solve

(

)

[virtual]

Solve QP using interior-point method.

Returns:

0 if ok, negative number otherwise.

Implements qp_solver.

Definition at line 377 of file qp_ip.cpp.

bool qp_ip::solve_onestep

(

const double

kappa

)

[private]

One step of interior point method.

Parameters:

[in]

kappa

logarithmic barrier multiplier

Returns:

true if a step was made, false if alpha or dX are too small.

Definition at line 406 of file qp_ip.cpp.

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Member Data Documentation

double qp_ip::bs_alpha [private]

multiplier of t, >1.

Definition at line 108 of file qp_ip.h.

double qp_ip::bs_beta [private]

backtracking search parameter alpha

Definition at line 109 of file qp_ip.h.

chol_solve_ip qp_ip::chol [private]

An instance of chol_solve_ip class.

Definition at line 96 of file qp_ip.h.

double* qp_ip::g [private]

2*N non-zero elements of vector g.

Definition at line 72 of file qp_ip.h.

double* qp_ip::grad [private]

N*SMPC_NUM_VAR gradient vector

Definition at line 82 of file qp_ip.h.

double* qp_ip::i2hess [private]

Inverted hessian: non-repeating diagonal elements 1:3:N*SMPC_NUM_STATE_VAR, 2*N in total.

Definition at line 76 of file qp_ip.h.

double* qp_ip::i2hess_grad [private]

Inverted hessian * gradient (N*SMPC_NUM_VAR vector)

Definition at line 79 of file qp_ip.h.

const double* qp_ip::lb [private]

lower and upper bounds

Definition at line 101 of file qp_ip.h.

int qp_ip::max_iter [private]

backtracking search parameter beta

Definition at line 110 of file qp_ip.h.

double qp_ip::mu [private]

logarithmic barrier parameter

Definition at line 107 of file qp_ip.h.

double qp_ip::P [private]

Diagonal elements of H.

Definition at line 91 of file qp_ip.h.

double qp_ip::phi_X [private]

Value of phi(X), where phi is the cost function + log barrier.

Definition at line 85 of file qp_ip.h.

double qp_ip::Q[3] [private]

Diagonal elements of H.

Definition at line 90 of file qp_ip.h.

double qp_ip::t [private]

Definition at line 106 of file qp_ip.h.

double qp_ip::tol_out [private]

maximum number of internal loop iterations

Definition at line 111 of file qp_ip.h.

const double* qp_ip::ub [private]

lower and upper bounds

Definition at line 102 of file qp_ip.h.

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

• solver/qp_ip.h
• solver/qp_ip.cpp