Distributed Formation Control of Multi-agent Systems with Exogenous Disturbances

Abstract

Recent advances in sensor, control, and communication technologies have enabled real-time processing of inter-agent local information such as relative distance, relative bearing, and relative displacement. In this aspect, the distributed formation control theory of multi-agent systems, which aims to control a group of agents to achieve a specific formation shape using local information, has attracted a significant amount of research interest due to their great potential in various applications. However, even though uncertainties and disturbances are ubiquitous in reality, most of the previous literature has been studied under ideal circumstances. This dissertation presents the distributed formation control problems of multi-agent systems with exogenous disturbances. We conduct a robust stability analysis on distance-based and bearing-based formation systems, which are being actively studied recently since those control methods require less sensing capability compared to the others. The following distance-based robust formation control problems are solved first. 1. A linear matrix inequality (LMI) problem for prescribed upper-bound of formation errors: A linear matrix inequality (LMI) condition is derived via Lyapunov stability analysis, which ensures prescribed upper-bound of formation errors. Also, we find a specific system that satisfies the LMI condition through a feasibility test. 2. Design of a robust adaptive gradient control law: Motivated by the issues to be supplemented in the LMI problem, a robust adaptive gradient control law is newly proposed. Based on the proposed control law, we derive an explicit upper-boundary set of the formation errors and analyze system parameters – i – for reducing the formation errors. Afterward, the following bearing-based robust formation control problems are solved. 1. Stability analysis for leaderless formation systems: Based on a bearing-based control law, we derive an upper-boundary set of the formation errors and analyze system parameters for reducing the formation errors. 2. Stability analysis for leader-fixed follower formation systems: Only limited information is obtained in the leaderless formation systems. Therefore, stationary leader agents are introduced, and the remaining agents are considered as follower agents. As the upper-boundary set becomes computable in leader-fixed follower formation systems, we could obtain beneficial information to anticipate and reduce the formation errors. Lastly, simulation examples are provided to validate the theoretical results. The developed robust stability analysis could be widely utilized in practical applications, such as an autonomous driving technology, multiple satellites control, and an outdoor drone performance show, to anticipate and reduce the formation errors in harsh environments.