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 box q_box_lower <= q <= q_box_upper (or equivalently s_box_lower <= s <= s_box_upper).

Hence for each of the rational we will introduce Lagrangian multipliers for the polytopic constraint s - s_box_lower >= 0, s_box_upper - s >= 0.

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

Public Member Functions
	SeparatingPlaneLagrangians (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 > &	s_box_lower () const
	The Lagrangians for s - s_box_lower >= 0. More...

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

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

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

Constructor & Destructor Documentation

◆ SeparatingPlaneLagrangians()

SeparatingPlaneLagrangians ( int s_size )

explicit

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_s_box_lower()

VectorX<symbolic::Polynomial>& mutable_s_box_lower ( )

The Lagrangians for s - s_box_lower >= 0.

◆ mutable_s_box_upper()

VectorX<symbolic::Polynomial>& mutable_s_box_upper ( )

The Lagrangians for s_box_upper - s >= 0.

◆ s_box_lower()

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