https://alexandreamice.github.io/tags/graph-of-convex-sets/Graph of Convex SetsHugoBlox Kit (https://hugoblox.com)en-usSun, 26 Apr 2026 00:00:00 +0000https://alexandreamice.github.io/media/icon_hu_12f30033bf7ec525.pnghttps://alexandreamice.github.io/tags/graph-of-convex-sets/https://alexandreamice.github.io/project/vega-gcs/Sun, 26 Apr 2026 00:00:00 +0000https://alexandreamice.github.io/project/vega-gcs/<h1 id="motivation">Motivation</h1> <p>Graph of Convex Sets (GCS) is a powerful modeling framework for planning problems that combine discrete choices with continuous decisions. A path through the graph selects a sequence of convex regions or modes, while the optimization variables choose continuous states inside those regions.</p> <p>This makes GCS a natural fit for robotics problems such as motion planning through convex regions, manipulation with contact modes, and mixed discrete-continuous task planning. The challenge is scale. A centralized relaxation can become very large, and the graph structure that made the model natural is no longer fully exploited by a generic conic solve.</p> <h1 id="contribution">Contribution</h1> <p>VEGA is a decomposition solver for GCS programs written in C++. Instead of solving the full conic relaxation as one monolithic program, the method splits the problem into the pieces already present in the model: a local program at each vertex, a local program at each edge, and a global graph optimization update.</p> <p>At each iteration, these subproblems can be solved in parallel and then driven toward consensus. This creates a solver architecture that matches the original modeling structure and can scale to very large problems.</p> <p>In addition to VEGA, we provide a benchmark of GCS instances from the literature and distribute these instances as <code>GcsBench</code>. We provide new C++ and Python based infrastructure in <code>GcsCpp</code> for modelling, serializing, and deserializing instances so that other researchers can contribute their own instances to the benchmark. We also provide bridges to transform <code>Drake's</code> GraphOfConvexSets objects and <code>gcsopt</code> models to the standardized <code>GcsCpp</code> instances.</p> <p>The benchmark set includes maze navigation, helicopter flight, shelf planning, bimanual manipulation, semidefinite pushing, and contact-graph instances. These programs take anywhere from less than a second to tens of minutes to solve with general-purpose convex solvers. The contact-graph instances are too large to be solved in a reasonable time by general-purpose methods.</p> <h1 id="results">Results</h1> <p>VEGA is designed to solve GCS instances where the convex relaxation is too large to solve using a general-purpose, centralized solver.</p> <p>It is the only solver in the benchmark capable of solving any of the contact-graph instances. On problems where centralized solvers do succeed, VEGA is typically slower as the additional overhead of coordinating the local solvers outweighs any benefits from using the decomposition-based method.</p>