Global Tensor Motion Planning

TL;DR

GTMP introduces a tensor-based, batched approach to motion planning by discretizing the configuration space into a fixed-layer random multipartite graph that supports efficient vectorized sampling, collision checking, and Bellman-based search. The framework, implemented in JAX with per-edge cost probing and batch-wide value iteration, achieves probabilistic completeness while delivering large-scale batch planning speedups on GPUs/TPUs. An Akima spline extension (GTMP-Akima) provides smooth trajectories without gradient-based optimization, broadening applicability to learning-driven robotics. Theoretical guarantees ensure completeness under appropriate sampling and layering, and experiments demonstrate substantial batch-efficiency gains with competitive path quality across challenging environments and datasets.

Abstract

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.

Figures (4)

• Figure 1: GTMP can plan with multiple goals or vmap over goals. For clarity, we present an example of performing JAX vmap on GTMP (M=2, N=3) over the batch of $B=3$ seeds. (1) The objective is to find a batch of feasible paths from the start (red) to the goals (green). (2, 3) In each seed, we sample a multipartite graph and form a tensor (Algorithm \ref{['alg:gtmp']}, Line 1). (4) A batch of collision checks is performed and stored into cost matrices (Algorithm \ref{['alg:gtmp']}, Line 2). (5) Then, per seed, we execute finite value iterations (Algorithm \ref{['alg:gtmp']}, Line 5-7) and trace the optimal path from the optimal value matrices (Algorithm \ref{['alg:gtmp']}, Line 8-13). (6) For execution, we can select the best path in terms of exemplary shortest path criteria. More information can be found on https://sites.google.com/view/gtmp.
• Figure 2: Aggregated statistics of comparison experiments on Planar Occupancy (top-row) and Panda MBM dataset (bottom-row). We note the log scale on the Planning Time axes. The batch planning time is the sum of instance time for sequential planners (last column). All plotted data points are based on successful path statistics.
• Figure 3: For each $M$ (y-axis), $N$ (x-axis), we set the number of probing $H=30$ and plan the batch of $B=200$ paths. The red star denotes the minimum number of layers $M_m$, corresponding to the minimum requirement of $N$ to discover some solutions experimentally.
• Figure : Global Tensor Motion Planning

Theorems & Definitions (18)

• Definition 1: Feasible Path
• Definition 2: Random Multipartite Graph Discretization
• Definition 3: Path In $G$
• Proposition 1
• proof
• Definition 4: Akima Spline
• Definition 5: Akima Spline Graph
• Remark 1
• Proposition 2: Feasibility Check
• proof