Detailed Description

When searching for the separating plane, we want to certify that the numerator of a rational is non-negative in the C-space region C*s<=d, s_lower <= s <= s_upper.

Hence for each of the rational we will introduce Lagrangian multipliers for the polytopic constraint d-C*s >= 0, s - s_lower >= 0, s_upper - s >= 0.

#include <drake/geometry/optimization/cspace_free_polytope.h>

Public Member Functions
	SeparatingPlaneLagrangians (int C_rows, int s_size)

SeparatingPlaneLagrangians	GetSolution (const solvers::MathematicalProgramResult &result) const
	Substitutes the decision variables in each Lagrangians with its value in result, returns the substitution result. More...

const VectorX< symbolic::Polynomial > &	polytope () const
	The Lagrangians for d - C*s >= 0. More...

VectorX< symbolic::Polynomial > &	mutable_polytope ()
	The Lagrangians for d - C*s >= 0. More...

const VectorX< symbolic::Polynomial > &	s_lower () const
	The Lagrangians for s - s_lower >= 0. More...

VectorX< symbolic::Polynomial > &	mutable_s_lower ()
	The Lagrangians for s - s_lower >= 0. More...

const VectorX< symbolic::Polynomial > &	s_upper () const
	The Lagrangians for s_upper - s >= 0. More...

VectorX< symbolic::Polynomial > &	mutable_s_upper ()
	The Lagrangians for s_upper - s >= 0. More...

Constructor & Destructor Documentation

◆ SeparatingPlaneLagrangians()

SeparatingPlaneLagrangians	(	int	C_rows,
		int	s_size
	)

Member Function Documentation

◆ GetSolution()

SeparatingPlaneLagrangians GetSolution ( const solvers::MathematicalProgramResult & result ) const

Substitutes the decision variables in each Lagrangians with its value in result, returns the substitution result.

◆ mutable_polytope()

VectorX<symbolic::Polynomial>& mutable_polytope ( )

The Lagrangians for d - C*s >= 0.

◆ mutable_s_lower()

VectorX<symbolic::Polynomial>& mutable_s_lower ( )

The Lagrangians for s - s_lower >= 0.

◆ mutable_s_upper()

VectorX<symbolic::Polynomial>& mutable_s_upper ( )

The Lagrangians for s_upper - s >= 0.

◆ polytope()

const VectorX<symbolic::Polynomial>& polytope ( ) const