Mixed Discrete and Continuous Planning using Shortest Walks in Graphs of Convex Sets
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866908449778958336 |
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| author | Morozov, Savva Marcucci, Tobia Graesdal, Bernhard Paus Amice, Alexandre Parrilo, Pablo A. Tedrake, Russ |
| author_facet | Morozov, Savva Marcucci, Tobia Graesdal, Bernhard Paus Amice, Alexandre Parrilo, Pablo A. Tedrake, Russ |
| contents | We study the Shortest-Walk Problem (SWP) in a Graph of Convex Sets (GCS). A GCS is a graph where each vertex is paired with a convex program, and each edge couples adjacent programs via additional costs and constraints. A walk in a GCS is a sequence of vertices connected by edges, where vertices may be repeated. The length of a walk is given by the cumulative optimal value of the corresponding convex programs. To solve the SWP in GCS, we first synthesize a piecewise-quadratic lower bound on the problem's cost-to-go function using semidefinite programming. Then we use this lower bound to guide an incremental-search algorithm that yields an approximate shortest walk. We show that the SWP in GCS is a natural language for many mixed discrete-continuous planning problems in robotics, unifying problems that typically require specialized solutions while delivering high performance and computational efficiency. We demonstrate this through experiments in collision-free motion planning, skill chaining, and optimal control of hybrid systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10878 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mixed Discrete and Continuous Planning using Shortest Walks in Graphs of Convex Sets Morozov, Savva Marcucci, Tobia Graesdal, Bernhard Paus Amice, Alexandre Parrilo, Pablo A. Tedrake, Russ Robotics We study the Shortest-Walk Problem (SWP) in a Graph of Convex Sets (GCS). A GCS is a graph where each vertex is paired with a convex program, and each edge couples adjacent programs via additional costs and constraints. A walk in a GCS is a sequence of vertices connected by edges, where vertices may be repeated. The length of a walk is given by the cumulative optimal value of the corresponding convex programs. To solve the SWP in GCS, we first synthesize a piecewise-quadratic lower bound on the problem's cost-to-go function using semidefinite programming. Then we use this lower bound to guide an incremental-search algorithm that yields an approximate shortest walk. We show that the SWP in GCS is a natural language for many mixed discrete-continuous planning problems in robotics, unifying problems that typically require specialized solutions while delivering high performance and computational efficiency. We demonstrate this through experiments in collision-free motion planning, skill chaining, and optimal control of hybrid systems. |
| title | Mixed Discrete and Continuous Planning using Shortest Walks in Graphs of Convex Sets |
| topic | Robotics |
| url | https://arxiv.org/abs/2507.10878 |