A Fast Method for Planning All Optimal Homotopic Configurations for Tethered Robots and Its Extended Applications

TL;DR

This paper introduces CDT-TCS, a novel algorithm combining algebraic topology and geometric optimization to efficiently compute all optimal tethered robot configurations in 2D environments, with broad applications and validated through simulations and real-world tests.

Contribution

The paper presents CDT-TCS, a new method that computes all optimal tethered robot configurations using homotopy invariants, advancing path planning in constrained environments.

Findings

Significantly outperforms existing methods in simulations

Successfully validated on real robotic platforms

Provides comprehensive solutions for multiple tethered robot planning problems

Abstract

Tethered robots play a pivotal role in specialized environments such as disaster response and underground exploration, where their stable power supply and reliable communication offer unparalleled advantages. However, their motion planning is severely constrained by tether length limitations and entanglement risks, posing significant challenges to achieving optimal path planning. To address these challenges, this study introduces CDT-TCS (Convex Dissection Topology-based Tethered Configuration Search), a novel algorithm that leverages CDT Encoding as a homotopy invariant to represent topological states of paths. By integrating algebraic topology with geometric optimization, CDT-TCS efficiently computes the complete set of optimal feasible configurations for tethered robots at all positions in 2D environments through a single computation. Building on this foundation, we further propose three application-specific algorithms: i) CDT-TPP for optimal tethered path planning, ii) CDT-TMV for multi-goal visiting with tether constraints, iii) CDT-UTPP for distance-optimal path planning of untethered robots. All theoretical results and propositions underlying these algorithms are rigorously proven and thoroughly discussed in this paper. Extensive simulations demonstrate that the proposed algorithms significantly outperform state-of-the-art methods in their respective problem domains. Furthermore, real-world experiments on robotic platforms validate the practicality and engineering value of the proposed framework.