StaticFrictionConeConstraint Class Reference

Detailed Description

Formulates the nonlinear friction cone constraint |fₜ| ≤ μ*fₙ, where fₜ is the tangential contact force, fₙ is the normal contact force, and μ is the friction coefficient.

The mathematical formulation of this constraint is

0 ≤ μ*fᵀn
fᵀ((1+μ²)nnᵀ - I)f ≥ 0

where n is the unit length normal vector. This formulation is equivalent to |fₜ| ≤ μ*fₙ, but the constraint is differentiable everywhere (while |fₜ| ≤ μ*fₙ is not differentiable at fₜ = 0.)

The bound variables for this constraint is x = [q;λ], where q is the generalized position, and λ is the parameterization of the contact wrench.

#include <drake/multibody/optimization/static_friction_cone_constraint.h>

Public Member Functions
	StaticFrictionConeConstraint (const ContactWrenchEvaluator *contact_wrench_evaluator)
	~StaticFrictionConeConstraint () override
template<typename T >
void	DecomposeX (const Eigen::Ref< const VectorX< T >> &x, VectorX< T > *q, VectorX< T > *lambda) const
	Given the bound variable x, decompose it into the generalized position q, and λ as a parameterization of the contact wrench. More...
Does not allow copy, move, or assignment
	StaticFrictionConeConstraint (const StaticFrictionConeConstraint &)=delete
StaticFrictionConeConstraint &	operator= (const StaticFrictionConeConstraint &)=delete
	StaticFrictionConeConstraint (StaticFrictionConeConstraint &&)=delete
StaticFrictionConeConstraint &	operator= (StaticFrictionConeConstraint &&)=delete
Public Member Functions inherited from Constraint
template<typename DerivedLB , typename DerivedUB >
	Constraint (int num_constraints, int num_vars, const Eigen::MatrixBase< DerivedLB > &lb, const Eigen::MatrixBase< DerivedUB > &ub, const std::string &description="")
	Constructs a constraint which has num_constraints rows, with an input num_vars x 1 vector. More...
	Constraint (int num_constraints, int num_vars)
	Constructs a constraint which has num_constraints rows, with an input num_vars x 1 vector, with no bounds. More...
bool	CheckSatisfied (const Eigen::Ref< const Eigen::VectorXd > &x, double tol=1E-6) const
	Return whether this constraint is satisfied by the given value, x. More...
bool	CheckSatisfied (const Eigen::Ref< const AutoDiffVecXd > &x, double tol=1E-6) const
symbolic::Formula	CheckSatisfied (const Eigen::Ref< const VectorX< symbolic::Variable >> &x) const
const Eigen::VectorXd &	lower_bound () const
const Eigen::VectorXd &	upper_bound () const
int	num_constraints () const
	Number of rows in the output constraint. More...
	Constraint (const Constraint &)=delete
Constraint &	operator= (const Constraint &)=delete
	Constraint (Constraint &&)=delete
Constraint &	operator= (Constraint &&)=delete
Public Member Functions inherited from EvaluatorBase
virtual	~EvaluatorBase ()
void	Eval (const Eigen::Ref< const Eigen::VectorXd > &x, Eigen::VectorXd *y) const
	Evaluates the expression. More...
void	Eval (const Eigen::Ref< const AutoDiffVecXd > &x, AutoDiffVecXd *y) const
	Evaluates the expression. More...
void	Eval (const Eigen::Ref< const VectorX< symbolic::Variable >> &x, VectorX< symbolic::Expression > *y) const
	Evaluates the expression. More...
void	set_description (const std::string &description)
	Set a human-friendly description for the evaluator. More...
const std::string &	get_description () const
	Getter for a human-friendly description for the evaluator. More...
std::ostream &	Display (std::ostream &os, const VectorX< symbolic::Variable > &vars) const
	Formats this evaluator into the given stream using vars for the bound decision variable names. More...
std::ostream &	Display (std::ostream &os) const
	Formats this evaluator into the given stream, without displaying the decision variables it is bound to. More...
std::string	ToLatex (const VectorX< symbolic::Variable > &vars, int precision=3) const
	Returns a LaTeX string describing this evaluator. More...
int	num_vars () const
	Getter for the number of variables, namely the number of rows in x, as used in Eval(x, y). More...
int	num_outputs () const
	Getter for the number of outputs, namely the number of rows in y, as used in Eval(x, y). More...
void	SetGradientSparsityPattern (const std::vector< std::pair< int, int >> &gradient_sparsity_pattern)
	Set the sparsity pattern of the gradient matrix ∂y/∂x (the gradient of y value in Eval, w.r.t x in Eval) . More...
const std::optional< std::vector< std::pair< int, int > > > &	gradient_sparsity_pattern () const
	Returns the vector of (row_index, col_index) that contains all the entries in the gradient of Eval function (∂y/∂x) whose value could be non-zero, namely if ∂yᵢ/∂xⱼ could be non-zero, then the pair (i, j) is in gradient_sparsity_pattern. More...
	EvaluatorBase (const EvaluatorBase &)=delete
EvaluatorBase &	operator= (const EvaluatorBase &)=delete
	EvaluatorBase (EvaluatorBase &&)=delete
EvaluatorBase &	operator= (EvaluatorBase &&)=delete

Additional Inherited Members
Protected Member Functions inherited from Constraint
void	UpdateLowerBound (const Eigen::Ref< const Eigen::VectorXd > &new_lb)
	Updates the lower bound. More...
void	UpdateUpperBound (const Eigen::Ref< const Eigen::VectorXd > &new_ub)
	Updates the upper bound. More...
void	set_bounds (const Eigen::Ref< const Eigen::VectorXd > &new_lb, const Eigen::Ref< const Eigen::VectorXd > &new_ub)
	Set the upper and lower bounds of the constraint. More...
virtual bool	DoCheckSatisfied (const Eigen::Ref< const Eigen::VectorXd > &x, const double tol) const
virtual bool	DoCheckSatisfied (const Eigen::Ref< const AutoDiffVecXd > &x, const double tol) const
virtual symbolic::Formula	DoCheckSatisfied (const Eigen::Ref< const VectorX< symbolic::Variable >> &x) const
Protected Member Functions inherited from EvaluatorBase
	EvaluatorBase (int num_outputs, int num_vars, const std::string &description="")
	Constructs a evaluator. More...
virtual std::ostream &	DoDisplay (std::ostream &os, const VectorX< symbolic::Variable > &vars) const
	NVI implementation of Display. More...
virtual std::string	DoToLatex (const VectorX< symbolic::Variable > &vars, int precision) const
void	set_num_outputs (int num_outputs)

Constructor & Destructor Documentation

StaticFrictionConeConstraint() [1/3]

StaticFrictionConeConstraint ( const StaticFrictionConeConstraint &  )

delete

StaticFrictionConeConstraint() [2/3]

StaticFrictionConeConstraint ( StaticFrictionConeConstraint &&  )

delete

StaticFrictionConeConstraint() [3/3]

StaticFrictionConeConstraint

(

const ContactWrenchEvaluator *

contact_wrench_evaluator

)

Parameters

contact_wrench_evaluator.

The evaluator takes in the generalized position q, and a parameterization of the contact wrench λ, and evaluates the contact wrench from body A to body B applied at the witness point of geometry B expressed in the world frame, i.e., computes the contact wrench F_Cb_W at the witness point p_WCb_W (see SignedDistancePair for the definition of witness point), and F_Ca_W = -F_Cb_W (assuming Ca and Cb are at the same spatial location).

Note

although contact_wrench_evaluator computes both the contact force and torque in the wrench, we only constrain the contact force to be within the friction cone, and leave the torque unconstrained.

~StaticFrictionConeConstraint()

~StaticFrictionConeConstraint ( )

override

Member Function Documentation

DecomposeX()

void DecomposeX	(	const Eigen::Ref< const VectorX< T >> &	x,
		VectorX< T > *	q,
		VectorX< T > *	lambda
	)		const

Given the bound variable x, decompose it into the generalized position q, and λ as a parameterization of the contact wrench.

x = [q; λ].

operator=() [1/2]

StaticFrictionConeConstraint& operator= ( const StaticFrictionConeConstraint &  )

delete

operator=() [2/2]

StaticFrictionConeConstraint& operator= ( StaticFrictionConeConstraint &&  )

delete

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

• drake/multibody/optimization/static_friction_cone_constraint.h