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

2025-07-15

AI Summary

Tethered robots face dual constraints—limited cable length and entanglement risk—in disaster response and subterranean exploration, hindering globally optimal path planning. To address this, we propose the CDT-TCS algorithmic framework, which introduces Convex Decomposition-based Topological Encoding (CDT Encoding) as a homotopy-invariant representation for compactly encoding the topological state of tethered paths—a first in the literature. Building upon this encoding, we develop four complementary algorithms: CDT-TCS (for global optimal configuration computation), CDT-TPP (topology-preserving planning), CDT-TMV (topology-manipulation verification), and CDT-UTPP (unified topology-aware path planning). All support one-shot global optimization and multi-task extension in 2D environments. Extensive simulations demonstrate significant performance gains over state-of-the-art methods. Real-robot experiments further validate the framework’s reliability and engineering practicality.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

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.

Problem

• Optimize tethered robot path planning under tether constraints
• Develop algorithm for all optimal homotopic configurations in 2D
• Extend applications to multi-goal visiting and untethered robots

Innovation

• CDT-TCS algorithm for optimal tethered robot configurations
• Integrates algebraic topology with geometric optimization
• Extends to three application-specific algorithms