GraphOfConvexSets (GCS) 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
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 mixedinteger 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 nontrivial 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 () 
Vertex *  AddVertex (const ConvexSet &set, std::string name="") 
Adds a vertex to the graph. More...  
Edge *  AddEdge (Vertex *u, Vertex *v, std::string name="") 
Adds an edge to the graph from Vertex u to Vertex v . More...  
void  RemoveVertex (Vertex *vertex) 
Removes vertex vertex from the graph as well as any edges from or to the vertex. More...  
void  RemoveEdge (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 (const Vertex &source, const Vertex &target, const GraphOfConvexSetsOptions &options=GraphOfConvexSetsOptions()) const 
Formulates and solves the mixedinteger convex formulation of the shortest path problem on the graph, as discussed in detail in. More...  
std::vector< const Edge * >  GetSolutionPath (const Vertex &source, const Vertex &target, const solvers::MathematicalProgramResult &result, double tolerance=1e3) const 
Extracts a path from source to target described by the result returned by SolveShortestPath(), via depthfirst search following the largest values of the edge binary variables. More...  
solvers::MathematicalProgramResult  SolveConvexRestriction (const std::vector< const Edge * > &active_edges, const GraphOfConvexSetsOptions &options=GraphOfConvexSetsOptions()) const 
The nonconvexity in a GCS problem comes from the binary variables (phi) associated with the edges being active or inactive in the solution. More...  
Does not allow copy, move, or assignment  
GraphOfConvexSets (const GraphOfConvexSets &)=delete  
GraphOfConvexSets &  operator= (const GraphOfConvexSets &)=delete 
GraphOfConvexSets (GraphOfConvexSets &&)=delete  
GraphOfConvexSets &  operator= (GraphOfConvexSets &&)=delete 
Friends  
class  PreprocessShortestPathTest 
using EdgeId = Identifier<class EdgeTag> 
using VertexId = Identifier<class VertexTag> 

delete 

delete 

default 
Constructs an empty graph.

virtual 
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.
void ClearAllPhiConstraints  (  ) 
Removes all constraints added to any edge with AddPhiConstraint.
std::vector<Edge*> Edges  (  ) 
Returns mutable pointers to the edges stored in the graph.
std::vector<const Edge*> Edges  (  )  const 
Returns pointers to the edges stored in the graph.
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.
show_slacks  determines whether the values of the intermediate (slack) variables are also displayed in the graph. 
precision  sets the floating point precision (how many digits are generated) of the annotations. 
scientific  sets the floating point formatting to scientific (if true) or fixed (if false). 
std::vector<const Edge*> GetSolutionPath  (  const Vertex &  source, 
const Vertex &  target,  
const solvers::MathematicalProgramResult &  result,  
double  tolerance = 1e3 

)  const 
Extracts a path from source
to target
described by the result
returned by SolveShortestPath(), via depthfirst search following the largest values of the edge binary variables.
tolerance  defines the threshold for checking the integrality conditions of the binary variables for each edge. tolerance = 0 would demand that the binary variables are exactly 1 for the edges on the path. tolerance = 1 would allow the binary variables to be any value in [0, 1]. The default value is 1e3. 
std::exception  if !result.is_success() or no path from source to target can be found in the solution. 

delete 

delete 
void RemoveEdge  (  Edge *  edge  ) 
Removes edge edge
from the graph.
void RemoveVertex  (  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.
solvers::MathematicalProgramResult SolveConvexRestriction  (  const std::vector< const Edge * > &  active_edges, 
const GraphOfConvexSetsOptions &  options = GraphOfConvexSetsOptions() 

)  const 
The nonconvexity in a GCS problem comes from the binary variables (phi) associated with the edges being active or inactive in the solution.
If those binary variables are fixed, then the problem is convex – this is a socalled "convex restriction" of the original problem.
The convex restriction can often be solved much more efficiently than solving the full GCS problem with additional constraints to fix the binaries; it can be written using less decision variables, and needs only to include the vertices associated with at least one of the active edges. Decision variables for all other convex sets will be set to NaN.
std::exception  if the program cannot be written as a convex optimization consumable by one of the standard solvers. 
solvers::MathematicalProgramResult SolveShortestPath  (  const Vertex &  source, 
const Vertex &  target,  
const GraphOfConvexSetsOptions &  options = GraphOfConvexSetsOptions() 

)  const 
Formulates and solves the mixedinteger 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
source  specifies 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. 
target  specifies the target set. The solver will choose any point in that set. 
options  include all settings for solving the shortest path problem. See GraphOfConvexSetsOptions for further details. The following default options will be used if they are not provided in options :

std::exception  if any of the costs or constraints in the graph are incompatible with the shortest path formulation or otherwise unsupported. All costs must be nonnegative for all values of the continuous variables. 
std::vector<Vertex*> Vertices  (  ) 
Returns mutable pointers to the vertices stored in the graph.
std::vector<const Vertex*> Vertices  (  )  const 
Returns pointers to the vertices stored in the graph.

friend 