Approximating the Region of Multi-Task Coordination via the Optimal Lyapunov-Like Barrier Function

TL;DR

This paper introduces a systematic approach to approximate the safe region for multi-task coordination in multi-agent systems by optimizing Lyapunov-like barrier functions, ensuring safety, connectivity, and convergence.

Contribution

It proposes a novel method to find optimal Lyapunov-like barrier functions that maximize the estimated safe coordination region for multi-agent systems.

Findings

The method effectively estimates the safety guaranteed region of multi-task coordination.

Numerical examples demonstrate the approach's ability to maximize the under-estimate of the safe region.

The approach outperforms fixed barrier functions in approximating the safe set.

Abstract

We consider the multi-task coordination problem for multi-agent systems under the following objectives: 1. collision avoidance; 2. connectivity maintenance; 3. convergence to desired destinations. The paper focuses on the safety guaranteed region of multi-task coordination (SG-RMTC), i.e., the set of initial states from which all trajectories converge to the desired configuration, while at the same time achieve the multi-task coordination and avoid unsafe sets. In contrast to estimating the domain of attraction via Lyapunov functions, the main underlying idea is to employ the sublevel sets of Lyapunov-like barrier functions to approximate the SG-RMTC. Rather than using fixed Lyapunov-like barrier functions, a systematic way is proposed to search an optimal Lyapunov-like barrier function such that the under-estimate of SG-RMTC is maximized. Numerical examples illustrate the effectiveness of the proposed method.