On Enhancing Structural Resilience of Multirobot Coverage Control with Bearing Rigidity

TL;DR

This work addresses resilient multi-robot coverage in the presence of faults or losses by integrating centralized Voronoi-based partitioning with decentralized nonlinear tracking MPC augmented by a bearing-maintenance term. By enforcing bearing rigidity, the network preserves a minimally rigid structure that enables rapid reconfiguration via rigidity recovery when robots depart or fail, maintaining coverage performance. The authors establish recursive feasibility and convergence to centroidal Voronoi configurations, and provide a terminal-ingredients design via LQR for stability. Numerical simulations illustrate convergence to desired coverage patterns and demonstrate proactive rigidity recovery under agent loss, highlighting practical self-healing capabilities for MRS deployments.

Abstract

The problem of multi-robot coverage control has been widely studied to efficiently coordinate a team of robots to cover a desired area of interest. However, this problem faces significant challenges when some robots are lost or deviate from their desired formation during the mission due to faults or cyberattacks. Since a majority of multi-robot systems (MRSs) rely on communication and relative sensing for their efficient operation, a failure in one robot could result in a cascade of failures in the entire system. In this work, we propose a hierarchical framework for area coverage, combining centralized coordination by leveraging Voronoi partitioning with decentralized reference tracking model predictive control (MPC) for control design. In addition to reference tracking, the decentralized MPC also performs bearing maintenance to enforce a rigid MRS network, thereby enhancing the structural resilience, i.e., the ability to detect and mitigate the effects of localization errors and robot loss during the mission. Furthermore, we show that the resulting control architecture guarantees the recovery of the MRS network in the event of robot loss while maintaining a minimally rigid structure. The effectiveness of the proposed algorithm is validated through numerical simulations.

Figures (6)

• Figure 1: Illustration of multi-robot coverage control for environmental monitoring during wildfire. Our proposed distributed approach ensures the coordination of the network of robots even when some robots become unhealthy while executing the mission.
• Figure 2: Illustration of Henneberg construction to construct minimally rigid graphs utilizing two operations: (a) vertex-addition and (b) edge-splitting.
• Figure 3: Edge contraction operation for Rigidity recovery.
• Figure 4: Robot positions and Voronoi partitions along with bearing formation at time $k=0$, $50$, $140$.
• Figure 5: Coverage cost evolution with time, for three different values of $\mu$: (a) without bearing maintenance $(\mu = 1)$ and (b) with bearing maintenance $(\mu = 0.7)$ and $(\mu = 0.1)$.

Theorems & Definitions (17)

• Lemma 1: Bearing Rigidity Criterionzhao2015bearing
• Definition 1: Infinitesimal Bearing Rigidity zhao2015bearing
• Definition 2: Generically Bearing Rigid Graph trinh2019minimal
• Definition 3: Minimal Bearing Rigid Graph trinh2019minimal
• Definition 4: Laman Graph zhao2017laman
• Definition 5: Henneberg Construction zhao2017laman
• Remark 1
• Remark 2
• Definition 6: Invariant Set for Centroid Tracking
• Theorem 1