Motion Planning for a Pair of Tethered Robots

TL;DR

This paper develops a motion planning framework for two tethered robots in polygonal environments, extending visibility graph methods to account for cable constraints and coordination, with proven theoretical guarantees and practical algorithms.

Contribution

It introduces a formalization that reduces the tethered two-robot planning problem to graph search, incorporating cable length constraints and coordination considerations.

Findings

Effective discretization using reduced visibility graph.

Theoretical proof enabling path-based planning instead of trajectory planning.

Implementation of A* search with experimental validation.

Abstract

Considering an environment containing polygonal obstacles, we address the problem of planning motions for a pair of planar robots connected to one another via a cable of limited length. Much like prior problems with a single robot connected via a cable to a fixed base, straight line-of-sight visibility plays an important role. The present paper shows how the reduced visibility graph provides a natural discretization and captures the essential topological considerations very effectively for the two robot case as well. Unlike the single robot case, however, the bounded cable length introduces considerations around coordination (or equivalently, when viewed from the point of view of a centralized planner, relative timing) that complicates the matter. Indeed, the paper has to introduce a rather more involved formalization than prior single-robot work in order to establish the core theoretical result -- a theorem permitting the problem to be cast as one of finding paths rather than trajectories. Once affirmed, the planning problem reduces to a straightforward graph search with an elegant representation of the connecting cable, demanding only a few extra ancillary checks that ensure sufficiency of cable to guarantee feasibility of the solution. We describe our implementation of A${}^\star$ search, and report experimental results. Lastly, we prescribe an optimal execution for the solutions provided by the algorithm.