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

TL;DR

GCS* is a novel forward heuristic search algorithm designed for large-scale implicit graphs of convex sets, enabling efficient and optimal solutions for complex continuous-discrete planning problems such as motion planning and contact planning.

Contribution

It generalizes A* search to the GCS setting, introducing pruning techniques for cost and reachability, and offers both optimal and suboptimal variants with practical implementations.

Findings

GCS* efficiently solves large-scale motion planning problems.

The method guarantees cost-optimality and completeness in the GCS setting.

It outperforms prior methods on planar pushing tasks with contact mode explosion.

Abstract

We consider large-scale, implicit-search-based solutions to 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 former implementation is complete and cost-optimal, while the latter 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. Project website: https://shaoyuan.cc/research/gcs-star/