Classes
class	AffineBall
	Implements an ellipsoidal convex set represented as an affine scaling of the unit ball {Bu + center \| \|u\|₂ ≤ 1}. More...

class	AffineSubspace
	An affine subspace (also known as a "flat", a "linear variety", or a "linear manifold") is a vector subspace of some Euclidean space, potentially translated so as to not pass through the origin. More...

class	CartesianProduct
	The Cartesian product of convex sets is a convex set: S = X₁ × X₂ × ⋯ × Xₙ = {(x₁, x₂, ..., xₙ) \| x₁ ∈ X₁, x₂ ∈ X₂, ..., xₙ ∈ Xₙ}. More...

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

class	ConvexHull
	Implements the convex hull of a set of convex sets. More...

class	ConvexSet
	Abstract base class for defining a convex set. More...

class	CspaceFreeBox
	This class tries to find large axis-aligned bounding boxes in the configuration space, such that all configurations in the boxes are collision free. More...

class	CspaceFreePolytope
	This class tries to find large convex polytopes in the tangential-configuration space, such that all configurations in the convex polytopes is collision free. More...

class	CspaceFreePolytopeBase
	This virtual class is the base of CspaceFreePolytope and CspaceFreeBox. More...

struct	CSpaceSeparatingPlane
	Wraps the information that a pair of collision geometries are separated by a plane. More...

struct	FindSeparationCertificateOptions

struct	GcsGraphvizOptions

class	GraphOfConvexSets
	GraphOfConvexSets (GCS) implements the design pattern and optimization problems first introduced in the paper "Shortest Paths in Graphs of Convex Sets". More...

struct	GraphOfConvexSetsOptions

class	HPolyhedron
	Implements a polyhedral convex set using the half-space representation: `{x\| A x ≤ b}`. More...

class	Hyperellipsoid
	Implements an ellipsoidal convex set represented by the quadratic form `{x \| (x-center)ᵀAᵀA(x-center) ≤ 1}`. More...

class	Hyperrectangle
	Axis-aligned hyperrectangle in Rᵈ defined by its lower bounds and upper bounds as {x\| lb ≤ x ≤ ub}. More...

class	Intersection
	A convex set that represents the intersection of multiple sets: S = X₁ ∩ X₂ ∩ ... More...

struct	IrisOptions
	Configuration options for the IRIS algorithm. More...

class	MinkowskiSum
	A convex set that represents the Minkowski sum of multiple sets: S = X₁ ⨁ X₂ ⨁ ... More...

struct	PlaneSeparatesGeometries
	Contains the information to enforce a pair of geometries are separated by a plane. More...

class	Point
	A convex set that contains exactly one element. More...

struct	SampledVolume
	The result of a volume calculation from CalcVolumeViaSampling(). More...

struct	SeparationCertificateProgramBase

struct	SeparationCertificateResultBase
	We certify that a pair of geometries is collision free by finding the separating plane over a range of configuration. More...

class	Spectrahedron
	Implements a spectrahedron (the feasible set of a semidefinite program). More...

class	VPolytope
	A polytope described using the vertex representation. More...

Typedefs
typedef std::vector< copyable_unique_ptr< ConvexSet > >	ConvexSets
	Provides the recommended container for passing a collection of ConvexSet instances. More...

typedef std::map< std::string, HPolyhedron >	IrisRegions
	Defines a standardized representation for (named) IrisRegions, which can be serialized in both C++ and Python. More...

Enumerations
enum	CIrisGeometryType { kSphere, kPolytope, kCylinder, kCapsule }
	The supported type of geometries in C-IRIS. More...

enum	PlaneSide { kPositive, kNegative }

enum	SeparatingPlaneOrder { kAffine = 1 }
	The separating plane aᵀx + b ≥ δ, aᵀx + b ≤ −δ has parameters a and b. More...

Functions
double	DistanceToHalfspace (const CIrisCollisionGeometry &collision_geometry, const Eigen::Vector3d &a, double b, multibody::BodyIndex expressed_body, PlaneSide plane_side, const multibody::MultibodyPlant< double > &plant, const systems::Context< double > &plant_context)
	Computes the signed distance from `collision_geometry` to the half space ℋ, where ℋ = {x \| aᵀx+b >= 0} if plane_side=PlaneSide::kPositive, and ℋ = {x \| aᵀx+b <= 0} if plane_side=PlaneSide::kNegative. More...

template<typename... Args>
ConvexSets	MakeConvexSets (Args &&... args)
	Helper function that allows the ConvexSets to be initialized from arguments containing ConvexSet references, or unique_ptr<ConvexSet> instances, or any object that can be assigned to ConvexSets::value_type. More...

SeparatingPlaneOrder	ToPlaneOrder (int plane_degree)
	Convert an integer degree to the SeparatingPlaneOrder. More...

int	ToPlaneDegree (SeparatingPlaneOrder plane_order)
	Convert SeparatingPlaneOrder to an integer degree. More...

template<typename D , typename S , typename V >
void	CalcPlane (const VectorX< D > &decision_variables, const VectorX< S > &s_for_plane, int plane_degree, Vector3< V > a_val, V b_val)
	Computes the parameters a, b in the plane { x \| aᵀx+b=0 }. More...

bool	CheckIfSatisfiesConvexityRadius (const geometry::optimization::ConvexSet &convex_set, const std::vector< int > &continuous_revolute_joints)
	Given a convex set, and a list of indices corresponding to continuous revolute joints, checks whether or not the set satisfies the convexity radius. More...

geometry::optimization::ConvexSets	PartitionConvexSet (const geometry::optimization::ConvexSet &convex_set, const std::vector< int > &continuous_revolute_joints, const double epsilon=1e-5)
	Partitions a convex set into (smaller) convex sets whose union is the original set and that each respect the convexity radius as in CheckIfSatisfiesConvexityRadius. More...

geometry::optimization::ConvexSets	PartitionConvexSet (const geometry::optimization::ConvexSets &convex_sets, const std::vector< int > &continuous_revolute_joints, const double epsilon=1e-5)
	Function overload to take in a list of convex sets, and partition all so as to respect the convexity radius. More...

std::pair< std::vector< std::pair< int, int > >, std::vector< Eigen::VectorXd > >	ComputePairwiseIntersections (const ConvexSets &convex_sets_A, const ConvexSets &convex_sets_B, const std::vector< int > &continuous_revolute_joints, bool preprocess_bbox=true)
	Computes the pairwise intersections between two lists of convex sets, returning a list of edges, and a list of their corresponding offsets. More...

std::vector< std::tuple< int, int, Eigen::VectorXd > >	CalcPairwiseIntersections (const ConvexSets &convex_sets_A, const ConvexSets &convex_sets_B, const std::vector< int > &continuous_revolute_joints, bool preprocess_bbox=true)
	Computes the pairwise intersections between two lists of convex sets, returning a list of edges. More...

std::pair< std::vector< std::pair< int, int > >, std::vector< Eigen::VectorXd > >	ComputePairwiseIntersections (const ConvexSets &convex_sets_A, const ConvexSets &convex_sets_B, const std::vector< int > &continuous_revolute_joints, const std::vector< geometry::optimization::Hyperrectangle > &bboxes_A, const std::vector< geometry::optimization::Hyperrectangle > &bboxes_B)
	Overload of `ComputePairwiseIntersections` allowing the user to supply axis- aligned bounding boxes if they're known a priori, to save on computation time. More...

std::vector< std::tuple< int, int, Eigen::VectorXd > >	CalcPairwiseIntersections (const ConvexSets &convex_sets_A, const ConvexSets &convex_sets_B, const std::vector< int > &continuous_revolute_joints, const std::vector< geometry::optimization::Hyperrectangle > &bboxes_A, const std::vector< geometry::optimization::Hyperrectangle > &bboxes_B)
	Overload of `CalcPairwiseIntersections` allowing the user to supply axis- aligned bounding boxes if they're known a priori, to save on computation time. More...

std::pair< std::vector< std::pair< int, int > >, std::vector< Eigen::VectorXd > >	ComputePairwiseIntersections (const ConvexSets &convex_sets, const std::vector< int > &continuous_revolute_joints, bool preprocess_bbox=true)
	Convenience overload to compute pairwise intersections within a list of convex sets. More...

std::vector< std::tuple< int, int, Eigen::VectorXd > >	CalcPairwiseIntersections (const ConvexSets &convex_sets, const std::vector< int > &continuous_revolute_joints, bool preprocess_bbox=true)
	Convenience overload to compute pairwise intersections within a list of convex sets. More...

std::pair< std::vector< std::pair< int, int > >, std::vector< Eigen::VectorXd > >	ComputePairwiseIntersections (const ConvexSets &convex_sets, const std::vector< int > &continuous_revolute_joints, const std::vector< geometry::optimization::Hyperrectangle > &bboxes)
	Overload of `ComputePairwiseIntersections` allowing the user to supply axis- aligned bounding boxes if they're known a priori, to save on computation time. More...

std::vector< std::tuple< int, int, Eigen::VectorXd > >	CalcPairwiseIntersections (const ConvexSets &convex_sets, const std::vector< int > &continuous_revolute_joints, const std::vector< geometry::optimization::Hyperrectangle > &bboxes)
	Overload of `CalcPairwiseIntersections` allowing the user to supply axis- aligned bounding boxes if they're known a priori, to save on computation time. More...

HPolyhedron	Iris (const ConvexSets &obstacles, const Eigen::Ref< const Eigen::VectorXd > &sample, const HPolyhedron &domain, const IrisOptions &options=IrisOptions())
	The IRIS (Iterative Region Inflation by Semidefinite programming) algorithm, as described in. More...

ConvexSets	MakeIrisObstacles (const QueryObject< double > &query_object, std::optional< FrameId > reference_frame=std::nullopt)
	Constructs ConvexSet representations of obstacles for IRIS in 3D using the geometry from a SceneGraph QueryObject. More...

HPolyhedron	IrisInConfigurationSpace (const multibody::MultibodyPlant< double > &plant, const systems::Context< double > &context, const IrisOptions &options=IrisOptions())
	A variation of the Iris (Iterative Region Inflation by Semidefinite programming) algorithm which finds collision-free regions in the configuration space of `plant`. More...

void	SetEdgeContainmentTerminationCondition (IrisOptions *iris_options, const Eigen::Ref< const Eigen::VectorXd > &x_1, const Eigen::Ref< const Eigen::VectorXd > &x_2, const double epsilon=1e-3, const double tol=1e-6)
	Modifies the `iris_options` to facilitate finding a region that contains the edge between x_1 and x_2. More...

Eigen::MatrixXd	GetVertices (const Convex &convex)
	Obtains all the vertices stored in the convex object. More...

Typedef Documentation

◆ ConvexSets

typedef std::vector<copyable_unique_ptr<ConvexSet> > ConvexSets

Provides the recommended container for passing a collection of ConvexSet instances.

◆ IrisRegions

typedef std::map<std::string, HPolyhedron> IrisRegions

Defines a standardized representation for (named) IrisRegions, which can be serialized in both C++ and Python.

Enumeration Type Documentation

◆ CIrisGeometryType

enum CIrisGeometryType

strong

The supported type of geometries in C-IRIS.

Enumerator
kSphere
kPolytope
kCylinder
kCapsule

◆ PlaneSide

enum PlaneSide

strong

Enumerator
kPositive
kNegative

◆ SeparatingPlaneOrder

enum SeparatingPlaneOrder

strong

The separating plane aᵀx + b ≥ δ, aᵀx + b ≤ −δ has parameters a and b.

These parameterize a polynomial function of s_for_plane with the specified order. s_for_plane is a sub set of the configuration-space variable s, please refer to the RationalForwardKinematics class or the paper above on the meaning of s.

Enumerator
kAffine	a and b are affine functions of s.

Function Documentation

◆ CalcPlane()

void drake::geometry::optimization::CalcPlane	(	const VectorX< D > &	decision_variables,
		const VectorX< S > &	s_for_plane,
		int	plane_degree,
		Vector3< V > *	a_val,
		V *	b_val
	)

Computes the parameters a, b in the plane { x | aᵀx+b=0 }.

a and b are both polynomials of vars_for_plane. The coefficients of these polynomials are in decision_variables in graded reverse lexicographic order.

Template Parameters

D,S,V

The valid combination of D, S, V are

D=symbolic::Variable, S=symbolic::Variable, V=symbolic::Polynomial.
D=double, S=symbolic::Variable, V=symbolic::Polynomial
D=double, S=double, V=double

◆ DistanceToHalfspace()

double drake::geometry::optimization::DistanceToHalfspace	(	const CIrisCollisionGeometry &	collision_geometry,
		const Eigen::Vector3d &	a,
		double	b,
		multibody::BodyIndex	expressed_body,
		PlaneSide	plane_side,
		const multibody::MultibodyPlant< double > &	plant,
		const systems::Context< double > &	plant_context
	)

Computes the signed distance from collision_geometry to the half space ℋ, where ℋ = {x | aᵀx+b >= 0} if plane_side=PlaneSide::kPositive, and ℋ = {x | aᵀx+b <= 0} if plane_side=PlaneSide::kNegative.

The half space is measured and expressed in the expressed_body's body frame. This works for both collision_geometry separated from the half space, and collision geometry in penetration with the halfspace.

Note: a does not need to be a unit length vector (but should be non-zero).

◆ GetVertices()

Eigen::MatrixXd drake::geometry::optimization::GetVertices ( const Convex & convex )

Obtains all the vertices stored in the convex object.

Return values

vertices. Each column of vertices is a vertex. We don't impose any specific order on the vertices. The vertices are expressed in the convex shape's own frame.

◆ MakeConvexSets()

ConvexSets drake::geometry::optimization::MakeConvexSets ( Args &&... args )

Helper function that allows the ConvexSets to be initialized from arguments containing ConvexSet references, or unique_ptr<ConvexSet> instances, or any object that can be assigned to ConvexSets::value_type.

◆ ToPlaneDegree()

int drake::geometry::optimization::ToPlaneDegree ( SeparatingPlaneOrder plane_order )

Convert SeparatingPlaneOrder to an integer degree.

◆ ToPlaneOrder()

SeparatingPlaneOrder drake::geometry::optimization::ToPlaneOrder ( int plane_degree )

Convert an integer degree to the SeparatingPlaneOrder.

Classes

Typedefs

Enumerations

Functions

Typedef Documentation

◆ ConvexSets

◆ IrisRegions

Enumeration Type Documentation

◆ CIrisGeometryType

◆ PlaneSide

◆ SeparatingPlaneOrder

Function Documentation

◆ CalcPlane()

◆ DistanceToHalfspace()

◆ GetVertices()

◆ MakeConvexSets()

◆ ToPlaneDegree()

◆ ToPlaneOrder()