Detailed Description

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

⨁ Xₙ = {x₁ + x₂ + ... + xₙ | x₁ ∈ X₁, x₂ ∈ X₂, ..., xₙ ∈ Xₙ}

Special behavior for IsEmpty: The Minkowski sum of zero sets (i.e. when we have sets_.size() == 0) is treated as the singleton {0}, which is nonempty. This includes the zero-dimensional case.

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

Public Member Functions
	MinkowskiSum ()
	Constructs a default (zero-dimensional, nonempty) set. More...

	MinkowskiSum (const ConvexSets &sets)
	Constructs the sum from a vector of convex sets. More...

	MinkowskiSum (const ConvexSet &setA, const ConvexSet &setB)
	Constructs the sum from a pair of convex sets. More...

	MinkowskiSum (const QueryObject< double > &query_object, GeometryId geometry_id, std::optional< FrameId > reference_frame=std::nullopt)
	Constructs a MinkowskiSum from a SceneGraph geometry and pose in the `reference_frame` frame, obtained via the QueryObject. More...

	~MinkowskiSum () final

int	num_terms () const
	The number of terms (or sets) used in the sum. More...

const ConvexSet &	term (int index) const
	Returns a reference to the ConvexSet defining the `index` term in the sum. More...

bool	PointInSet (const Eigen::Ref< const Eigen::VectorXd > &x, double tol=0) const
	Returns true if the point is in the set. More...

Implements CopyConstructible, CopyAssignable, MoveConstructible, MoveAssignable
	MinkowskiSum (const MinkowskiSum &)=default

MinkowskiSum &	operator= (const MinkowskiSum &)=default

	MinkowskiSum (MinkowskiSum &&)=default

MinkowskiSum &	operator= (MinkowskiSum &&)=default

Public Member Functions inherited from ConvexSet
virtual	~ConvexSet ()

std::unique_ptr< ConvexSet >	Clone () const
	Creates a unique deep copy of this set. More...

int	ambient_dimension () const
	Returns the dimension of the vector space in which the elements of this set are evaluated. More...

bool	IntersectsWith (const ConvexSet &other) const
	Returns true iff the intersection between `this` and `other` is non-empty. More...

bool	IsBounded () const
	Returns true iff the set is bounded, e.g., there exists an element-wise finite lower and upper bound for the set. More...

bool	IsEmpty () const
	Returns true iff the set is empty. More...

std::optional< Eigen::VectorXd >	MaybeGetPoint () const
	If this set trivially contains exactly one point, returns the value of that point. More...

std::optional< Eigen::VectorXd >	MaybeGetFeasiblePoint () const
	Returns a feasible point within this convex set if it is nonempty, and nullopt otherwise. More...

bool	PointInSet (const Eigen::Ref< const Eigen::VectorXd > &x, double tol=0) const
	Returns true iff the point x is contained in the set. More...

std::pair< VectorX< symbolic::Variable >, std::vector< solvers::Binding< solvers::Constraint > > >	AddPointInSetConstraints (solvers::MathematicalProgram *prog, const Eigen::Ref< const solvers::VectorXDecisionVariable > &vars) const
	Adds a constraint to an existing MathematicalProgram enforcing that the point defined by vars is inside the set. More...

std::vector< solvers::Binding< solvers::Constraint > >	AddPointInNonnegativeScalingConstraints (solvers::MathematicalProgram *prog, const Eigen::Ref< const solvers::VectorXDecisionVariable > &x, const symbolic::Variable &t) const
	Let S be this convex set. More...

std::vector< solvers::Binding< solvers::Constraint > >	AddPointInNonnegativeScalingConstraints (solvers::MathematicalProgram *prog, const Eigen::Ref< const Eigen::MatrixXd > &A, const Eigen::Ref< const Eigen::VectorXd > &b, const Eigen::Ref< const Eigen::VectorXd > &c, double d, const Eigen::Ref< const solvers::VectorXDecisionVariable > &x, const Eigen::Ref< const solvers::VectorXDecisionVariable > &t) const
	Let S be this convex set. More...

std::pair< std::unique_ptr< Shape >, math::RigidTransformd >	ToShapeWithPose () const
	Constructs a Shape and a pose of the set in the world frame for use in the SceneGraph geometry ecosystem. More...

double	CalcVolume () const
	Computes the exact volume for the convex set. More...

SampledVolume	CalcVolumeViaSampling (RandomGenerator *generator, const double desired_rel_accuracy=1e-2, const int max_num_samples=1e4) const
	Calculates an estimate of the volume of the convex set using sampling and performing Monte Carlo integration. More...

std::optional< std::pair< std::vector< double >, Eigen::MatrixXd > >	Projection (const Eigen::Ref< const Eigen::MatrixXd > &points) const
	Computes in the L₂ norm the distance and the nearest point in this convex set to every column of `points`. More...

bool	has_exact_volume () const
	Returns true if the exact volume can be computed for this convex set instance. More...

Additional Inherited Members
Protected Member Functions inherited from ConvexSet
	ConvexSet (int ambient_dimension, bool has_exact_volume)
	For use by derived classes to construct a ConvexSet. More...

template<typename Archive >
void	Serialize (Archive *a)
	Implements non-virtual base class serialization. More...

virtual std::vector< std::optional< double > >	DoProjectionShortcut (const Eigen::Ref< const Eigen::MatrixXd > &points, EigenPtr< Eigen::MatrixXd > projected_points) const
	Non-virtual interface implementation for DoProjectionShortcut(). More...

virtual std::optional< bool >	DoPointInSetShortcut (const Eigen::Ref< const Eigen::VectorXd > &x, double tol) const
	A non-virtual interface implementation for PointInSet() that should be used when the PointInSet() can be computed more efficiently than solving a convex program. More...

virtual double	DoCalcVolume () const
	Non-virtual interface implementation for CalcVolume(). More...

std::optional< symbolic::Variable >	HandleZeroAmbientDimensionConstraints (solvers::MathematicalProgram prog, const ConvexSet &set, std::vector< solvers::Binding< solvers::Constraint >> constraints) const
	Instances of subclasses such as CartesianProduct and MinkowskiSum can have constituent sets with zero ambient dimension, which much be handled in a special manner when calling methods such as DoAddPointInSetConstraints. More...

	ConvexSet (const ConvexSet &)=default

ConvexSet &	operator= (const ConvexSet &)=default

	ConvexSet (ConvexSet &&)=default

ConvexSet &	operator= (ConvexSet &&)=default

Constructor & Destructor Documentation

◆ MinkowskiSum() [1/6]

MinkowskiSum ( const MinkowskiSum & )

default

◆ MinkowskiSum() [2/6]

MinkowskiSum ( MinkowskiSum && )

default

◆ MinkowskiSum() [3/6]

MinkowskiSum ( )

Constructs a default (zero-dimensional, nonempty) set.

◆ MinkowskiSum() [4/6]

MinkowskiSum ( const ConvexSets & sets )

explicit

Constructs the sum from a vector of convex sets.

◆ MinkowskiSum() [5/6]

MinkowskiSum	(	const ConvexSet &	setA,
		const ConvexSet &	setB
	)

Constructs the sum from a pair of convex sets.

◆ MinkowskiSum() [6/6]

MinkowskiSum	(	const QueryObject< double > &	query_object,
		GeometryId	geometry_id,
		std::optional< FrameId >	reference_frame = `std::nullopt`
	)

Constructs a MinkowskiSum from a SceneGraph geometry and pose in the reference_frame frame, obtained via the QueryObject.

If reference_frame frame is std::nullopt, then it will be expressed in the world frame.

Although in principle a MinkowskiSum can represent any ConvexSet as the sum of a single set, here we only support Capsule geometry, which will be represented as the (non-trivial) Minkowski sum of a sphere with a line segment. Most SceneGraph geometry types are supported by at least one of the ConvexSet class constructors.

Exceptions

std::exception if geometry_id does not correspond to a Capsule.

◆ ~MinkowskiSum()

~MinkowskiSum ( )

final

Member Function Documentation

◆ num_terms()

int num_terms ( ) const

The number of terms (or sets) used in the sum.

◆ operator=() [1/2]

MinkowskiSum& operator= ( MinkowskiSum && )

default

◆ operator=() [2/2]

MinkowskiSum& operator= ( const MinkowskiSum & )

default

◆ PointInSet()

bool PointInSet

Returns true if the point is in the set.

Note: This requires the solution of a convex program; the tol parameter is currently ignored, and the solver tolerance is used instead.

See also: ConvexSet::set_solver

◆ term()

const ConvexSet& term ( int index ) const

Returns a reference to the ConvexSet defining the index term in the sum.

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

drake/geometry/optimization/minkowski_sum.h

Detailed Description

Public Member Functions

Additional Inherited Members

Constructor & Destructor Documentation

◆ MinkowskiSum() [1/6]

◆ MinkowskiSum() [2/6]

◆ MinkowskiSum() [3/6]

◆ MinkowskiSum() [4/6]

◆ MinkowskiSum() [5/6]

◆ MinkowskiSum() [6/6]

◆ ~MinkowskiSum()

Member Function Documentation

◆ num_terms()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ PointInSet()

◆ term()