Soft Subdivision Motion Planning for Complex Planar Robots

TL;DR

This paper introduces a scalable, resolution-exact motion planning method for complex planar polygonal robots using soft predicates, enabling efficient, real-time collision detection and planning.

Contribution

It presents a novel decomposition technique for soft collision predicates that scales linearly with robot complexity, advancing sound and complete planning for planar robots.

Findings

The method scales linearly with the number of robot vertices.

Algorithms perform in real time on complex environments.

Outperforms many sampling-based planning methods.

Abstract

The design and implementation of theoretically-sound robot motion planning algorithms is challenging. Within the framework of resolution-exact algorithms, it is possible to exploit soft predicates for collision detection. The design of soft predicates is a balancing act between easily implementable predicates and their accuracy/effectivity. In this paper, we focus on the class of planar polygonal rigid robots with arbitrarily complex geometry. We exploit the remarkable decomposability property of soft collision-detection predicates of such robots. We introduce a general technique to produce such a decomposition. If the robot is an m-gon, the complexity of this approach scales linearly in m. This contrasts with the O(m^3) complexity known for exact planners. It follows that we can now routinely produce soft predicates for any rigid polygonal robot. This results in resolution-exact planners for such robots within the general Soft Subdivision Search (SSS) framework. This is a significant advancement in the theory of sound and complete planners for planar robots. We implemented such decomposed predicates in our open-source Core Library. The experiments show that our algorithms are effective, perform in real time on non-trivial environments, and can outperform many sampling-based methods.