GCS*: Forward Heuristic Search on Implicit Graphs of Convex Sets

TL;DR:

Abstract

We consider large-scale, implicit-search-based solutions to the Shortest Path Problems on Graphs of Convex Sets (GCS). We propose GCS*, a forward heuristic search algorithm that generalizes A* search to the GCS setting, where a continuous-valued decision is made at each graph vertex, and constraints across graph edges couple these decisions, influencing costs and feasibility. Such mixed discrete-continuous planning is needed in many domains, including motion planning around obstacles and planning through contact. This setting provides a unique challenge for best-first search algorithms: the cost and feasibility of a path depend on continuous-valued points chosen along the entire path. We show that by pruning paths that are cost-dominated over their entire terminal vertex, GCS* can search efficiently while still guaranteeing cost optimality and completeness. To find satisficing solutions quickly, we also present a complete but suboptimal variation, pruning instead reachability-dominated paths. We implement these checks using polyhedral-containment or sampling-based methods. The sampling-based implementation is probabilistically complete and asymptotically cost optimal, and performs effectively even with minimal samples in practice. We demonstrate GCS* on planar pushing tasks where the combinatorial explosion of contact modes renders prior methods intractable and show it performs favorably compared to the state-of-the-art.

GCS* applied to simplified planar pushing

To focus on the combinatorial explosion of contact modes, we consider a simplified planar pushing formulation with:

1. polyhedral bodies;
2. no rotations;
3. and only sliding contact (no friction).

WAFR Talk

Comparison with other algorithms

(Applied to shortest path problems in graphs of convex sets.)

BibTeX citation

@inproceedings{chewchiaGCSForwardHeuristic2024,
  author = {Chew Chia, Shao Yuan and Jiang, Rebecca H. and Graesdal, Bernhard Paus and Kaelbling, Leslie Pack and Tedrake, Russ},
  title = {GCS*: Forward Heuristic Search on Implicit Graphs of Convex Sets},
  booktitle = {To appear in Proceedings of the 16th International Workshop on the Algorithmic Foundations of Robotics (WAFR)},
  year = {2024},
  eprint={2407.08848},
  archivePrefix={arXiv},
  primaryClass={cs.RO},
  url={https://arxiv.org/abs/2407.08848}
}

Acknowledgements

This work was supported by the Aker Scholarship, the AI Institute, Amazon.com, and the Charles Stark Draper Laboratory, Inc. where Rebecca H. Jiang is a Draper Scholar.