# Accelerating Motion Planning via Optimal Transport

arXiv: https://arxiv.org/abs/2309.15970 · HTML: https://mlsanity.com/paper/2309.15970/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Sep 2023.

## Built on by (most cited first, 12 of 12)

- [Motion Planning Diffusion: Learning and Adapting Robot Motion Planning with Diffusion Models](https://mlsanity.com/paper/2412.19948/) (2024)
- [Dude: Dual Distribution-Aware Context Prompt Learning For Large Vision-Language Model](https://mlsanity.com/paper/2407.04489/) (2024)
- [Simulation-Free Differential Dynamics through Neural Conservation Laws](https://mlsanity.com/paper/2506.18604/) (2025)
- [Global Tensor Motion Planning](https://mlsanity.com/paper/2411.19393/) (2024)
- [Grasp2Grasp: Vision-Based Dexterous Grasp Translation via Schr"odinger Bridges](https://mlsanity.com/paper/2506.02489/) (2025)
- [Safe and Efficient Path Planning under Uncertainty via Deep Collision Probability Fields](https://mlsanity.com/paper/2409.04306/) (2024)
- [Toward Generalist Neural Motion Planners for Robotic Manipulators: Challenges and Opportunities](https://mlsanity.com/paper/2603.24318/) (2026)
- [Manifold Sampling via Entropy Maximization](https://mlsanity.com/paper/2605.12338/) (2026)
- [A Taxonomy of Self-Handover](https://mlsanity.com/paper/2504.04939/) (2025)
- [Model Tensor Planning](https://mlsanity.com/paper/2505.01059/) (2025)
- [Multi-robot Path Planning and Scheduling via Model Predictive Optimal Transport (MPC-OT)](https://mlsanity.com/paper/2508.21205/) (2025)
- [PolyStepOR: Learning to Decide Without Optimal Decisions](https://mlsanity.com/paper/2609.32465/) (2026)

## Abstract (arXiv)

Motion planning is still an open problem for many disciplines, e.g., robotics, autonomous driving, due to their need for high computational resources that hinder real-time, efficient decision-making. A class of methods striving to provide smooth solutions is gradient-based trajectory optimization. However, those methods usually suffer from bad local minima, while for many settings, they may be inapplicable due to the absence of easy-to-access gradients of the optimization objectives. In response to these issues, we introduce Motion Planning via Optimal Transport (MPOT) -- a textitgradient-free method that optimizes a batch of smooth trajectories over highly nonlinear costs, even for high-dimensional tasks, while imposing smoothness through a Gaussian Process dynamics prior via the planning-as-inference perspective. To facilitate batch trajectory optimization, we introduce an original zero-order and highly-parallelizable update rule: the Sinkhorn Step, which uses the regular polytope family for its search directions. Each regular polytope, centered on trajectory waypoints, serves as a local cost-probing neighborhood, acting as a textittrust region where the Sinkhorn Step "transports" local waypoints toward low-cost regions. We theoretically show that Sinkhorn Step guides the optimizing parameters toward local minima regions of non-convex objective functions. We then show the efficiency of MPOT in a range of problems from low-dimensional point-mass navigation to high-dimensional whole-body robot motion planning, evincing its superiority compared to popular motion planners, paving the way for new applications of optimal transport in motion planning.