Drake
Drake C++ Documentation

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 ConvexSetterm (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
 
MinkowskiSumoperator= (const MinkowskiSum &)=default
 
 MinkowskiSum (MinkowskiSum &&)=default
 
MinkowskiSumoperator= (MinkowskiSum &&)=default
 
- Public Member Functions inherited from ConvexSet
virtual ~ConvexSet ()
 
std::unique_ptr< ConvexSetClone () 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...
 
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 double DoCalcVolume () const
 Non-virtual interface implementation for CalcVolume(). More...
 
std::optional< symbolic::VariableHandleZeroAmbientDimensionConstraints (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
 
ConvexSetoperator= (const ConvexSet &)=default
 
 ConvexSet (ConvexSet &&)=default
 
ConvexSetoperator= (ConvexSet &&)=default
 

Constructor & Destructor Documentation

◆ MinkowskiSum() [1/6]

MinkowskiSum ( const MinkowskiSum )
default

◆ MinkowskiSum() [2/6]

MinkowskiSum ( MinkowskiSum &&  )
default

◆ MinkowskiSum() [3/6]

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::exceptionif 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: