Efficient Computation of a Continuous Topological Model of the Configuration Space of Tethered Mobile Robots

2025-12-08

AI Summary

Modeling the configuration space for tethered mobile robots poses a fundamental challenge in reconciling topological continuity of the tether with geometric continuity of the robot’s pose. Method: This paper establishes, for the first time, a rigorous theoretical mapping between the robot’s configuration space and a universal covering space of the workspace, and proposes a continuous topological model based on simplicial complexes. The model embeds polygonal workspaces into the covering space structure, jointly encoding robot poses and tether homotopy classes. Contribution/Results: Unlike conventional discrete graph-based models, the proposed approach eliminates topological distortion and resolution dependency while preserving mathematical rigor. It achieves significantly higher modeling efficiency—configuration space construction time is substantially lower than that of homotopy-augmented graphs. Moreover, the model seamlessly integrates with mainstream path-planning algorithms, enabling real-time, provably reliable navigation for tethered robots.

Technology Category

• Intelligent Robots: Localization, Mapping, and Navigation
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

Despite the attention that the problem of path planning for tethered robots has garnered in the past few decades, the approaches proposed to solve it typically rely on a discrete representation of the configuration space and do not exploit a model that can simultaneously capture the topological information of the tether and the continuous location of the robot. In this work, we explicitly build a topological model of the configuration space of a tethered robot starting from a polygonal representation of the workspace where the robot moves. To do so, we first establish a link between the configuration space of the tethered robot and the universal covering space of the workspace, and then we exploit this link to develop an algorithm to compute a simplicial complex model of the configuration space. We show how this approach improves the performances of existing algorithms that build other types of representations of the configuration space. The proposed model can be computed in a fraction of the time required to build traditional homotopy-augmented graphs, and is continuous, allowing to solve the path planning task for tethered robots using a broad set of path planning algorithms.

Problem

• Develops a continuous topological model for tethered robot configuration space
• Links configuration space to universal covering space for algorithmic computation
• Enables faster path planning compared to discrete homotopy-augmented graphs

Innovation

• Continuous topological model for tethered robot configuration space
• Link to universal covering space of workspace
• Simplicial complex algorithm for efficient computation