CIrisCollisionGeometry Class Reference

Detailed Description

This class contains the necessary information about the collision geometry used in C-IRIS.

Most notably it transcribes the geometric condition that the collision geometry is on one side of the plane to mathematical constraints. For the detailed algorithm please refer to the paper Certified Polyhedral Decompositions of Collision-Free Configuration Space by Hongkai Dai*, Alexandre Amice*, Peter Werner, Annan Zhang and Russ Tedrake.

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

Public Member Functions
	CIrisCollisionGeometry (const Shape *geometry, multibody::BodyIndex body_index, GeometryId id, math::RigidTransformd X_BG)
const Shape &	geometry () const
multibody::BodyIndex	body_index () const
GeometryId	id () const
const math::RigidTransformd &	X_BG () const
void	OnPlaneSide (const Vector3< symbolic::Polynomial > &a, const symbolic::Polynomial &b, const multibody::RationalForwardKinematics::Pose< symbolic::Polynomial > &X_AB_multilinear, const multibody::RationalForwardKinematics &rational_forward_kin, PlaneSide plane_side, const VectorX< symbolic::Variable > &y_slack, std::vector< symbolic::RationalFunction > *rationals) const
	Impose the constraint that the geometry is on a given side of the plane {x | aᵀx+b=0}. More...
CIrisGeometryType	type () const
int	num_rationals () const
	Returns the number of rationals in the condition "this geometry is on one side of the plane. More...
Implements CopyConstructible, CopyAssignable, MoveConstructible, MoveAssignable
	CIrisCollisionGeometry (const CIrisCollisionGeometry &)=default
CIrisCollisionGeometry &	operator= (const CIrisCollisionGeometry &)=default
	CIrisCollisionGeometry (CIrisCollisionGeometry &&)=default
CIrisCollisionGeometry &	operator= (CIrisCollisionGeometry &&)=default

Constructor & Destructor Documentation

CIrisCollisionGeometry() [1/3]

CIrisCollisionGeometry ( const CIrisCollisionGeometry &  )

default

CIrisCollisionGeometry() [2/3]

CIrisCollisionGeometry ( CIrisCollisionGeometry &&  )

default

CIrisCollisionGeometry() [3/3]

CIrisCollisionGeometry	(	const Shape *	geometry,
		multibody::BodyIndex	body_index,
		GeometryId	id,
		math::RigidTransformd	X_BG
	)

Parameters

geometry	The actual geometry object. geometry must outlive this CIrisCollisionGeometry object.
body_index	The index of the body to which this geometry is fixed.
id	The ID of this geometry.
X_BG	The pose of the geometry (G) in the attached body frame (B).

Member Function Documentation

body_index()

multibody::BodyIndex body_index

(

)

const

geometry()

const Shape& geometry

(

)

const

id()

GeometryId id

(

)

const

num_rationals()

int num_rationals

(

)

const

Returns the number of rationals in the condition "this geometry is on one side of the plane.

"

OnPlaneSide()

void OnPlaneSide	(	const Vector3< symbolic::Polynomial > &	a,
		const symbolic::Polynomial &	b,
		const multibody::RationalForwardKinematics::Pose< symbolic::Polynomial > &	X_AB_multilinear,
		const multibody::RationalForwardKinematics &	rational_forward_kin,
		PlaneSide	plane_side,
		const VectorX< symbolic::Variable > &	y_slack,
		std::vector< symbolic::RationalFunction > *	rationals
	)		const

Impose the constraint that the geometry is on a given side of the plane {x | aᵀx+b=0}.

For example, to impose the constraint that a polytope is on the positive side of the plane, we consider the following constraints aᵀp_AVᵢ + b ≥ 1 (1) where Vᵢ is the i'th vertex of the polytope. (1) says rational functions are non-negative.

To impose the constraint that a sphere is on positive side of the plane, we consider the following constraints aᵀp_AS + b ≥ r*|a| (2a) aᵀp_AS + b ≥ 1 (2b) where S is the sphere center, r is the sphere radius.

We can reformulate (2a) as the following constraint ⌈aᵀp_AS + b aᵀ⌉ is psd. (3) ⌊ a (aᵀp_AS + b)/r²*I₃⌋ (3) is equivalent to the rational ⌈1⌉ᵀ*⌈aᵀp_AS + b aᵀ⌉*⌈1⌉ ⌊y⌋ ⌊ a (aᵀp_AS+ b)/r²*I₃⌋ ⌊y⌋ is positive.

Parameters

a	The normal vector in the separating plane. a is expressed in frame A. Note that a doesn't need to have a unit length.
b	The constant term in the separating plane.
X_AB_multilinear	The pose of the collision geometry body (B) in the expressed frame A, written as a multilinear polynomial. This quantity is generated from RationalForwardKinematics::CalcBodyPoseAsMultilinearPolynomial.
rational_forward_kin	This object is constructed with the MultibodyPlant containing this collision geometry.
plane_side	Whether the geometry is on the positive or negative side of the plane.
y_slack	The slack variable y in the documentation above, used for non-polytopic geometries. For spheres and capsules, y_slack has size 3. For cylinders, y_slack has size 2.
[in/out]	rationals We append new rational functions to rationals. If these new rational functions are positive, then the geometry is on a given side of the plane.

Precondition

rationals != nullptr

operator=() [1/2]

CIrisCollisionGeometry& operator= ( CIrisCollisionGeometry &&  )

default

operator=() [2/2]

CIrisCollisionGeometry& operator= ( const CIrisCollisionGeometry &  )

default

type()

CIrisGeometryType type

(

)

const

X_BG()

const math::RigidTransformd& X_BG

(

)

const

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

• drake/geometry/optimization/c_iris_collision_geometry.h