Distributed Coverage Control on Poriferous Surface via Poly-Annulus Conformal Mapping

TL;DR

This paper introduces a novel distributed coverage control method for agents on complex poriferous surfaces by transforming them into a simpler domain, enabling effective workload distribution and obstacle avoidance.

Contribution

It proposes a distributed conformal mapping and a sectorial partition mechanism, along with a Riemannian metric-based control law, to achieve safe, balanced coverage on non-convex surfaces.

Findings

The method guarantees obstacle avoidance and workload balance.

The control system is proven to be stable and convergent.

Simulations demonstrate robustness and scalability.

Abstract

The inherent non-convexity of poriferous surfaces typically entraps agents in local minima and complicates workload distribution. To resolve this, we propose a distributed diffeomorphic coverage control framework for the multi-agent system (MAS) in such surfaces. First, we establish a distributed poly-annulus conformal mapping that transforms arbitrary poriferous surfaces into a multi-hole disk. Leveraging this topological equivalence, a collision-free sectorial partition mechanism is designed in the multi-hole disk, which rigorously induces strictly connected subregions and workload balance on the poriferous surfaces. This mechanism utilizes a buffer-based sequence mechanism to ensure strict topological safety when bypassing obstacles. Furthermore, a pull-back Riemannian metric is constructed to define the length metric that encodes safety constraints. Based on this metric, a distributed gradient-based control law is synthesized to drive agents toward optimal configurations, ensuring simultaneous obstacle avoidance and coverage optimization. Theoretical analyses guarantee the Input-to-State Stability (ISS) of the partition dynamics and the asymptotic convergence of the closed-loop system. Numerical simulations confirm the reachability and robustness of the proposed coverage algorithm, offering a scalable solution for distributed coverage in poriferous surfaces.