A description of an MLCP (mixed linear complementarity problem, or mixed LCP) system to be solved. More...

#include <MlcpProblem.h>

Inheritance diagram for SurgSim::Math::MlcpProblem:

Public Types
typedef Eigen::Matrix< double, Eigen::Dynamic, Eigen::Dynamic >	Matrix

typedef Eigen::Matrix< double, Eigen::Dynamic, 1 >	Vector

Public Member Functions
virtual	~MlcpProblem ()
	Destructor.

size_t	getSize () const
	Gets the size of the system. More...

bool	isConsistent () const
	Checks if the sizes of various elements of the system are consistent with each other. More...

virtual void	setZero (size_t numDof, size_t numConstraintDof, size_t numConstraints)
	Resize an MlcpProblem and set to zero. More...

Static Public Member Functions
static MlcpProblem	Zero (size_t numDof, size_t numConstraintDof, size_t numConstraints)
	Initialize an MlcpProblem with zero values. More...

Public Attributes
Matrix	A
	Matrix \(\mathbf{A}\) used to describe the mixed LCP problem.

Vector	b
	Vector \(b\) used to describe the mixed LCP problem.

Vector	mu
	A vector of friction coefficients used to describe the mixed LCP problem. More...

std::vector< MlcpConstraintType >	constraintTypes
	A vector of constraint types used to describe the mixed LCP problem. More...

Detailed Description

A description of an MLCP (mixed linear complementarity problem, or mixed LCP) system to be solved.

A traditional (not mixed!) LCP problem is expressed as \(\mathbf{A}x + b = c\), where \(x\) is the vector of variables of interest to be determined, \(c\) is the vector of slack variables (transforming a system of inequalities into a system of equalities), and \(x\) and \(c\) are subject to the inequality conditions \(x_i \ge 0\), \(c_i \ge 0\), and \(x \perp c\) (i.e., \(x \cdot c = 0\)). Thus for each row \(i\), either

\((\mathbf{A}x+b)_i = \mathbf{A}_{i,*}\cdot x+b_i = c_i \ge 0\) and \(x_i = 0\) (the constraint is non-binding, so the variable of interest enforcing the constraint is zero); or
\((\mathbf{A}x+b)_i = \mathbf{A}_{i,*}\cdot x+b_i = c_i = 0\) and \(x_i > 0\) (the constraint is binding, so the variable of interest is nonzero to enforce the constraint).

Solving the problem produces the vector \(x\), from which \(c\) can also be computed if needed.

A mixed LCP problem is defined in the same way, except that for a certain subset of indices, the conditions are restricted further to require \(c_i\) to be zero, \(\mathbf{A}_{i,*}\cdot x+b_i = 0\). These are referred to as bilateral constraints, as opposed to the unilateral constraints in the LCP problem.

Friction is integrated directly into the problem, using the general approach described e.g. in:
Duriez, Christian; Dubois, F.; Kheddar, A.; Andriot, C., "Realistic haptic rendering of interacting deformable objects in virtual environments," IEEE Transactions on Visualization and Computer Graphics, vol.12, no.1, pp.36,47, Jan.-Feb. 2006.

See also: SurgSim::Physics::MlcpPhysicsProblem, MlcpSolution, MlcpSolver

Member Function Documentation

§ getSize()

size_t SurgSim::Math::MlcpProblem::getSize ( ) const

inline

Gets the size of the system.

Returns: the number of degrees of freedom of the system.

§ isConsistent()

bool SurgSim::Math::MlcpProblem::isConsistent ( ) const

inline

Checks if the sizes of various elements of the system are consistent with each other.

Returns: true if consistent, false otherwise.

§ setZero()

void SurgSim::Math::MlcpProblem::setZero	(	size_t	numDof,
		size_t	numConstraintDof,
		size_t	numConstraints
	)

virtual

Resize an MlcpProblem and set to zero.

Parameters

numDof	the total degrees of freedom.
numConstraintDof	the total constrained degrees of freedom.
numConstraints	the number of constraints.

Reimplemented in SurgSim::Physics::MlcpPhysicsProblem.

§ Zero()

MlcpProblem SurgSim::Math::MlcpProblem::Zero	(	size_t	numDof,
		size_t	numConstraintDof,
		size_t	numConstraints
	)

static

Initialize an MlcpProblem with zero values.

Parameters

numDof	the total degrees of freedom for the MlcpProblem to be constructed.
numConstraintDof	the total constrained degrees of freedom for the MlcpProblem to be constructed.
numConstraints	the number of constraints for the MlcpProblem to be constructed.

Returns: An MlcpProblem appropriately sized and initialized to zero.

Member Data Documentation

§ constraintTypes

std::vector<MlcpConstraintType> SurgSim::Math::MlcpProblem::constraintTypes

A vector of constraint types used to describe the mixed LCP problem.

Todo:: This API will change in the future to something more independent of physics.

§ mu

Vector SurgSim::Math::MlcpProblem::mu

A vector of friction coefficients used to describe the mixed LCP problem.

Todo:: This API will change in the future to something more independent of physics.

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

SurgSim/Math/MlcpProblem.h
SurgSim/Math/MlcpProblem.cpp

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes