# Non-Euclidean Motion Planning with Graphs of Geodesically-Convex Sets

arXiv: https://arxiv.org/abs/2305.06341 · HTML: https://mlsanity.com/paper/2305.06341/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 May 2023.

## Built on by (most cited first, 7 of 7)

- [Constant-time Motion Planning with Anytime Refinement for Manipulation](https://mlsanity.com/paper/2311.00837/) (2023)
- [Space-Time Graphs of Convex Sets for Multi-Robot Motion Planning](https://mlsanity.com/paper/2503.00583/) (2025)
- [GHOST: Solving the Traveling Salesman Problem on Graphs of Convex Sets](https://mlsanity.com/paper/2511.06471/) (2025)
- [Toward Generalist Neural Motion Planners for Robotic Manipulators: Challenges and Opportunities](https://mlsanity.com/paper/2603.24318/) (2026)
- [Flow Motion Policy: Manipulator Motion Planning with Flow Matching Models](https://mlsanity.com/paper/2604.07084/) (2026)
- [Search-Based Spatiotemporal and Multi-Robot Motion Planning on Graphs of Space-Time Convex Sets](https://mlsanity.com/paper/2607.00444/) (2026)
- [Approximately Optimal Global Planning for Contact-Rich SE(2) Manipulation on a Graph of Reachable Sets](https://mlsanity.com/paper/2601.10827/) (2026)

## Abstract (arXiv)

Computing optimal, collision-free trajectories for high-dimensional systems is a challenging problem. Sampling-based planners struggle with the dimensionality, whereas trajectory optimizers may get stuck in local minima due to inherent nonconvexities in the optimization landscape. The use of mixed-integer programming to encapsulate these nonconvexities and find globally optimal trajectories has recently shown great promise, thanks in part to tight convex relaxations and efficient approximation strategies that greatly reduce runtimes. These approaches were previously limited to Euclidean configuration spaces, precluding their use with mobile bases or continuous revolute joints. In this paper, we handle such scenarios by modeling configuration spaces as Riemannian manifolds, and we describe a reduction procedure for the zero-curvature case to a mixed-integer convex optimization problem. We demonstrate our results on various robot platforms, including producing efficient collision-free trajectories for a PR2 bimanual mobile manipulator.