# Global Tensor Motion Planning

arXiv: https://arxiv.org/abs/2411.19393 · HTML: https://mlsanity.com/paper/2411.19393/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Robot learning from demonstration, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 19 of its 46 references that are in the map.
- First posted on arXiv 28 Nov 2024.

## Placed in

- Offline RL and imitation learning from data / [Robot learning from demonstration](https://mlsanity.com/offlinerl/robot-learning-from-demonstration/)

## Builds on (most cited first, 19 of 19)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Goal-Conditioned Imitation Learning using Score-based Diffusion Policies](https://mlsanity.com/paper/2304.02532/) (2023)
- [Motion Planning Diffusion: Learning and Planning of Robot Motions with Diffusion Models](https://mlsanity.com/paper/2308.01557/) (2023)
- [Learning Sampling Distributions for Robot Motion Planning](https://mlsanity.com/paper/1709.05448/) (2017)
- [Motion Policy Networks](https://mlsanity.com/paper/2210.12209/) (2022)
- [Continuous-Time Gaussian Process Motion Planning via Probabilistic Inference](https://mlsanity.com/paper/1707.07383/) (2017)
- [STORM: An Integrated Framework for Fast Joint-Space Model-Predictive Control for Reactive Manipulation](https://mlsanity.com/paper/2104.13542/) (2021)
- [Stein Variational Model Predictive Control](https://mlsanity.com/paper/2011.07641/) (2020)
- [Fast Marching Tree: a Fast Marching Sampling-Based Method for Optimal Motion Planning in Many Dimensions](https://mlsanity.com/paper/1306.3532/) (2013)
- [Batch Informed Trees (BIT*): Informed Asymptotically Optimal Anytime Search](https://mlsanity.com/paper/1707.01888/) (2017)
- [Adaptively Informed Trees (AIT*): Fast Asymptotically Optimal Path Planning through Adaptive Heuristics](https://mlsanity.com/paper/2002.06599/) (2020)
- [Sampling-Based Motion Planning: A Comparative Review](https://mlsanity.com/paper/2309.13119/) (2023)
- [Learning Implicit Priors for Motion Optimization](https://mlsanity.com/paper/2204.05369/) (2022)
- [Reducing Collision Checking for Sampling-Based Motion Planning Using Graph Neural Networks](https://mlsanity.com/paper/2210.08864/) (2022)
- [Motions in Microseconds via Vectorized Sampling-Based Planning](https://mlsanity.com/paper/2309.14545/) (2023)
- [MotionBenchMaker: A Tool to Generate and Benchmark Motion Planning Datasets](https://mlsanity.com/paper/2112.06402/) (2021)
- [Multimodal Trajectory Optimization for Motion Planning](https://mlsanity.com/paper/2003.07054/) (2020)
- [Accelerating Motion Planning via Optimal Transport](https://mlsanity.com/paper/2309.15970/) (2023)
- [Multi-Modal Model Predictive Control through Batch Non-Holonomic Trajectory Optimization: Application to Highway Driving](https://mlsanity.com/paper/2109.10392/) (2021)

## Built on by (most cited first, 2 of 2)

- [A Taxonomy of Self-Handover](https://mlsanity.com/paper/2504.04939/) (2025)
- [Model Tensor Planning](https://mlsanity.com/paper/2505.01059/) (2025)

## Abstract (arXiv)

Batch planning is increasingly necessary to quickly produce diverse and quality motion plans for downstream learning applications, such as distillation and imitation learning. This paper presents Global Tensor Motion Planning (GTMP) -- a sampling-based motion planning algorithm comprising only tensor operations. We introduce a novel discretization structure represented as a random multipartite graph, enabling efficient vectorized sampling, collision checking, and search. We provide a theoretical investigation showing that GTMP exhibits probabilistic completeness while supporting modern GPU/TPU. Additionally, by incorporating smooth structures into the multipartite graph, GTMP directly plans smooth splines without requiring gradient-based optimization. Experiments on lidar-scanned occupancy maps and the MotionBenchMarker dataset demonstrate GTMP's computation efficiency in batch planning compared to baselines, underscoring GTMP's potential as a robust, scalable planner for diverse applications and large-scale robot learning tasks.