Drake
Drake C++ Documentation

Detailed Description

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

"Shortest Paths in Graphs of Convex Sets" by Tobia Marcucci, Jack Umenberger, Pablo A. Parrilo, Russ Tedrake. https://arxiv.org/abs/2101.11565

Warning
This feature is considered to be experimental and may change or be removed at any time, without any deprecation notice ahead of time.

Each vertex in the graph is associated with a convex set over continuous variables, edges in the graph contain convex costs and constraints on these continuous variables. We can then formulate optimization problems over this graph, such as the shortest path problem where each visit to a vertex also corresponds to selecting an element from the convex set subject to the costs and constraints. Behind the scenes, we construct efficient mixed-integer convex transcriptions of the graph problem using MathematicalProgram.

Design note: This class avoids providing any direct access to the MathematicalProgram that it constructs nor to the decision variables / constraints. The users should be able to write constraints against "placeholder" decision variables on the vertices and edges, but these get translated in non-trivial ways to the underlying program.

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

Classes

class  Edge
 An edge in the graph connects between vertex u and vertex v. More...
 
class  Vertex
 Each vertex in the graph has a corresponding ConvexSet, and a std::string name. More...
 

Public Types

using VertexId = Identifier< class VertexTag >
 
using EdgeId = Identifier< class EdgeTag >
 

Public Member Functions

 GraphOfConvexSets ()=default
 Constructs an empty graph. More...
 
virtual ~GraphOfConvexSets ()
 
VertexAddVertex (const ConvexSet &set, std::string name="")
 Adds a vertex to the graph. More...
 
EdgeAddEdge (VertexId u_id, VertexId v_id, std::string name="")
 Adds an edge to the graph from VertexId u_id to VertexId v_id. More...
 
EdgeAddEdge (const Vertex &u, const Vertex &v, std::string name="")
 Adds an edge to the graph from Vertex u to Vertex v. More...
 
void RemoveVertex (VertexId vertex_id)
 Removes vertex vertex_id from the graph as well as any edges from or to the vertex. More...
 
void RemoveVertex (const Vertex &vertex)
 Removes vertex vertex from the graph as well as any edges from or to the vertex. More...
 
void RemoveEdge (EdgeId edge_id)
 Removes edge edge_id from the graph. More...
 
void RemoveEdge (const Edge &edge)
 Removes edge edge from the graph. More...
 
std::vector< Vertex * > Vertices ()
 Returns mutable pointers to the vertices stored in the graph. More...
 
std::vector< const Vertex * > Vertices () const
 Returns pointers to the vertices stored in the graph. More...
 
std::vector< Edge * > Edges ()
 Returns mutable pointers to the edges stored in the graph. More...
 
std::vector< const Edge * > Edges () const
 Returns pointers to the edges stored in the graph. More...
 
void ClearAllPhiConstraints ()
 Removes all constraints added to any edge with AddPhiConstraint. More...
 
std::string GetGraphvizString (const std::optional< solvers::MathematicalProgramResult > &result=std::nullopt, bool show_slacks=true, int precision=3, bool scientific=false) const
 Returns a Graphviz string describing the graph vertices and edges. More...
 
solvers::MathematicalProgramResult SolveShortestPath (VertexId source_id, VertexId target_id, const GraphOfConvexSetsOptions &options=GraphOfConvexSetsOptions()) const
 Formulates and solves the mixed-integer convex formulation of the shortest path problem on the graph, as discussed in detail in. More...
 
solvers::MathematicalProgramResult SolveShortestPath (const Vertex &source, const Vertex &target, const GraphOfConvexSetsOptions &options=GraphOfConvexSetsOptions()) const
 Convenience overload that takes const reference arguments for source and target. More...
 
Does not allow copy, move, or assignment
 GraphOfConvexSets (const GraphOfConvexSets &)=delete
 
GraphOfConvexSetsoperator= (const GraphOfConvexSets &)=delete
 
 GraphOfConvexSets (GraphOfConvexSets &&)=delete
 
GraphOfConvexSetsoperator= (GraphOfConvexSets &&)=delete
 

Friends

class PreprocessShortestPathTest
 

Member Typedef Documentation

◆ EdgeId

using EdgeId = Identifier<class EdgeTag>

◆ VertexId

using VertexId = Identifier<class VertexTag>

Constructor & Destructor Documentation

◆ GraphOfConvexSets() [1/3]

GraphOfConvexSets ( const GraphOfConvexSets )
delete

◆ GraphOfConvexSets() [2/3]

◆ GraphOfConvexSets() [3/3]

GraphOfConvexSets ( )
default

Constructs an empty graph.

◆ ~GraphOfConvexSets()

virtual ~GraphOfConvexSets ( )
virtual

Member Function Documentation

◆ AddEdge() [1/2]

Edge* AddEdge ( VertexId  u_id,
VertexId  v_id,
std::string  name = "" 
)

Adds an edge to the graph from VertexId u_id to VertexId v_id.

The ids must refer to valid vertices in this graph. If name is empty then a default name will be provided.

◆ AddEdge() [2/2]

Edge* AddEdge ( const Vertex u,
const Vertex v,
std::string  name = "" 
)

Adds an edge to the graph from Vertex u to Vertex v.

The vertex references must refer to valid vertices in this graph. If name is empty then a default name will be provided.

◆ AddVertex()

Vertex* AddVertex ( const ConvexSet set,
std::string  name = "" 
)

Adds a vertex to the graph.

A copy of set is cloned and stored inside the graph. If name is empty then a default name will be provided.

◆ ClearAllPhiConstraints()

void ClearAllPhiConstraints ( )

Removes all constraints added to any edge with AddPhiConstraint.

◆ Edges() [1/2]

std::vector<Edge*> Edges ( )

Returns mutable pointers to the edges stored in the graph.

◆ Edges() [2/2]

std::vector<const Edge*> Edges ( ) const

Returns pointers to the edges stored in the graph.

◆ GetGraphvizString()

std::string GetGraphvizString ( const std::optional< solvers::MathematicalProgramResult > &  result = std::nullopt,
bool  show_slacks = true,
int  precision = 3,
bool  scientific = false 
) const

Returns a Graphviz string describing the graph vertices and edges.

If results is supplied, then the graph will be annotated with the solution values.

Parameters
show_slacksdetermines whether the values of the intermediate (slack) variables are also displayed in the graph.
precisionsets the floating point precision (how many digits are generated) of the annotations.
scientificsets the floating point formatting to scientific (if true) or fixed (if false).

◆ operator=() [1/2]

GraphOfConvexSets& operator= ( GraphOfConvexSets &&  )
delete

◆ operator=() [2/2]

GraphOfConvexSets& operator= ( const GraphOfConvexSets )
delete

◆ RemoveEdge() [1/2]

void RemoveEdge ( EdgeId  edge_id)

Removes edge edge_id from the graph.

Precondition
The edge must be part of the graph.

◆ RemoveEdge() [2/2]

void RemoveEdge ( const Edge edge)

Removes edge edge from the graph.

Precondition
The edge must be part of the graph.

◆ RemoveVertex() [1/2]

void RemoveVertex ( VertexId  vertex_id)

Removes vertex vertex_id from the graph as well as any edges from or to the vertex.

Runtime is O(nₑ) where nₑ is the number of edges in the graph.

Precondition
The vertex must be part of the graph.

◆ RemoveVertex() [2/2]

void RemoveVertex ( const Vertex vertex)

Removes vertex vertex from the graph as well as any edges from or to the vertex.

Runtime is O(nₑ) where nₑ is the number of edges in the graph.

Precondition
The vertex must be part of the graph.

◆ SolveShortestPath() [1/2]

solvers::MathematicalProgramResult SolveShortestPath ( VertexId  source_id,
VertexId  target_id,
const GraphOfConvexSetsOptions options = GraphOfConvexSetsOptions() 
) const

Formulates and solves the mixed-integer convex formulation of the shortest path problem on the graph, as discussed in detail in.

"Shortest Paths in Graphs of Convex Sets" by Tobia Marcucci, Jack Umenberger, Pablo A. Parrilo, Russ Tedrake. https://arxiv.org/abs/2101.11565

Parameters
sourcespecifies the source set. The solver will choose any point in that set; to start at a particular continuous state consider adding a Point set to the graph and using that as the source.
targetspecifies the target set. The solver will choose any point in that set.
optionsinclude all settings for solving the shortest path problem. See GraphOfConvexSetsOptions for further details.
Exceptions
std::exceptionif any of the costs or constraints in the graph are incompatible with the shortest path formulation or otherwise unsupported. All costs must be non-negative for all values of the continuous variables.

◆ SolveShortestPath() [2/2]

solvers::MathematicalProgramResult SolveShortestPath ( const Vertex source,
const Vertex target,
const GraphOfConvexSetsOptions options = GraphOfConvexSetsOptions() 
) const

Convenience overload that takes const reference arguments for source and target.

◆ Vertices() [1/2]

std::vector<Vertex*> Vertices ( )

Returns mutable pointers to the vertices stored in the graph.

◆ Vertices() [2/2]

std::vector<const Vertex*> Vertices ( ) const

Returns pointers to the vertices stored in the graph.

Friends And Related Function Documentation

◆ PreprocessShortestPathTest

friend class PreprocessShortestPathTest
friend

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