ISS-Based Robust Leader/Follower Trailing Control

Abstract

The leader/follower scheme is one of the most important building blocks for formation control of autonomous mobile agents. Recently, the concept of input-to-state stability (ISS) has been proposed as a tool to relate the influence of the motion of the leader to the overall formation error in a leader/follower configuration. The ISS approach allows great flexibility in the formation topology, and yields computable gains relating the formation error to external inputs and disturbances. However, its application in this specific context requires some attention, due to the peculiar characteristics of the vehicular formation dynamics. In this paper, the problem of letting followers to trail their leader at desired relative position in a planar formation is cast into a stabilization problem by resorting to an equivalent non-holonomic kinematic model. The proposed solution, based on a local version of ISS originally given by Teel, employs saturated controls to enforce ISS of the dynamics, without resorting to input/output linearization techniques, and thus avoiding the need to deal with critically stable or locally asymptotically stable zero-dynamics. The aforementioned techniques- saturated control and ISS with restrictions- are key to robust control design which addresses leader-follower formation implicitly. Furthermore, the analysis also shows that the proposed controller not only can deal with a class of small measurement errors but also can accommodate small control input delays. Simulation results on an illustrative example are presented and discussed.