Generalized controllers for rigid formation stabilization with application to event-based controller design

Abstract

This paper discusses generalized controllers for rigid formation shape stabilization. We provide unified analysis to show convergence using different controllers reported in the literature, and further prove an exponential stability of the formation system when using the general form of shape controllers. We also show that different agents can use different controllers for controlling different distances to achieve a desired rigid formation, which enables the implementation of heterogeneous agents in practice for formation shape control. We further propose an event-triggered rigid formation control scheme based on the generalized controllers. The triggering condition, event function and convergence analysis are discussed.

Cooperative Event-Based Rigid Formation Control

“…This section focuses on the design of feasible event-based formation controllers, by assuming that a centralized processor is available for collecting the global information and broadcasting the triggering signal to all the agents such that their control inputs can be updated. The results in this section extend the event-based formation control reported in [31] by proposing an alternative approach for the event function design, which also simplifies the event-based controllers proposed in [32], [33]. Furthermore, the novel idea used for designing a simpler event function in this section will be useful for designing a feasible distributed version of an event-based formation control system, which will be reported in the next section.…”

“…Some preliminary results have been presented in conference contributions [31] and [32]. Compared to [31] and [32], this paper proposes new control methodologies to design eventbased controllers as well as event-triggering functions.…”

“…Some preliminary results have been presented in conference contributions [31] and [32]. Compared to [31] and [32], this paper proposes new control methodologies to design eventbased controllers as well as event-triggering functions. The event controller presented in [31] is a preliminary one, which only updates parts of the control input and the control is not necessarily piecewise constant.…”

“…Also, the complicated controllers in [32] have been simplified. Moreover, and centrally to the novelty of the paper, we will focus on the design of distributed controllers based on novel event-triggering functions to achieve the cooperative formation task, while the event controllers in both [31] and [32] are centralized. We prove that Zeno behavior is excluded in the distributed eventbased formation control system by proving a positive lower bound of the inter-event triggering time.…”

“…To be specific, we will propose two feasible eventbased control schemes (a centralized triggering scheme and a distributed triggering scheme) that aim to stabilize a general rigid formation shape. In this paper, by a careful design of the triggering condition and event function, the aforementioned communication requirements and controller complexity in e.g., [31]- [33] are avoided. For all cases, the triggering condition, event function and triggering behavior are discussed in detail.…”