Adaptive event-triggered set-membership formation of heterogeneous multi-agent systems with application to omnidirectional robots

This article focuses on the leader-following formation control for heterogeneous multi-agent systems against actuator saturation and switching topologies. To save limited agent resources, a novel adaptive event-triggered strategy is evolved to regulate the update frequency of controller, such that some unnecessary data processing can be avoided. Different from the conventional adaptive strategy where the tracking error is simply regarded as the triggering benchmark, a transformation law is introduced in this work to develop an adaptive triggering benchmark, which provides greater potential for the triggering condition to save computational resources to a greater extent. Then, the formation control protocols are proposed by introducing the set-membership concept. Subsequently, considering the saturation constraints, optimization problems of the set-membership formation control are established to ensure that the tracking errors are always restrained to the desired ellipsoids. For achieving the leader-following formation, an online recursive algorithm based on the optimization problems is consequently provided such that the set-membership controllers meeting the ellipsoidal state sets can be continuously obtained. Finally, the superiority and applicability of the proposed method were validated through numerical simulations and its implementation on an omnidirectional robot platform.