Exponential Stability for Formation Control Systems with Generalized Controllers

Abstract

This chapter discusses generalized controllers for distance-based rigid formation shape stabilization and aims to provide a unified approach for the convergence analysis. We consider two types of formation control systems according to different characterizations of target formations: minimally rigid target formations and non-minimally rigid target formations. For the former case, we firstly prove the exponential stability for rigid formation systems when using a general form of shape controller with certain properties. From this viewpoint, different formation controllers proposed in the previous literature can be included in a unified framework. We then extend the result to the case that the target formation is non-minimally rigid, and show that exponential stability of the formation system is still guaranteed with generalized controllers.