Abstract
This article investigates circular formation control problems for a group of anonymous mobile robots in the plane, where all robots can converge asymptotically to a predefined circular orbit around a fixed target point without collision, and maintain any desired relative distances from their neighbors. Given the limited resources for communication and computation of robots, a distributed event-triggered method is firstly designed to reduce dependence on resources in multi-robot systems, where the controller's action is determined by whether the norm of the event-trigger function exceeds zero through continuous sampling. And then, to further minimize communications costs, a self-triggered strategy is proposed, which only uses discrete states sampled and sent by neighboring robots at their event instants. Furthermore, for the two proposed control laws, a Lyapunov functional is constructed, which allows sufficient stability conditions to be obtained on the circular formation for multi-robot systems. And at the same time, the controllers are proved to exclude Zeno behavior. At last, numerical simulation of controlling uniform and non-uniform circular formations by two control methods are conducted. Simulation results show that the designed controller can control all mobile robots to form either a uniform circular formation or a non-uniform circular formation while maintaining any desired relative distances between robots and guaranteeing that there is no collision during the whole evolution. One of the essential features of the proposed control methods is that they reduce the update rates of controllers and the communication frequency between robots. And also, the spatial order of robots is also preserved throughout the evaluation of the system without collision.
Highlights
In recent years, the control of multi-robot systems (MRSs) has gained increasing attention due to their wide applications, such as source localization [1], [2], pursuit and evasion [3] and surveillance [4]–[6], as well as theoretical challenges arising from the limitation in implementations
For the two proposed control laws, a Lyapunov functional is constructed, which allows sufficient stability conditions to be obtained on the circular formation for multi-robot systems
Simulation results show that the designed controller can control all mobile robots to form either a uniform circular formation or a non-uniform circular formation while maintaining any desired relative distances between robots and guaranteeing that there is no collision during the whole evolution
Summary
The control of multi-robot systems (MRSs) has gained increasing attention due to their wide applications, such as source localization [1], [2], pursuit and evasion [3] and surveillance [4]–[6], as well as theoretical challenges arising from the limitation in implementations. P. Xu et al.: Distributed Event-Triggered Circular Formation Control for Multiple Anonymous Mobile Robots desirable to design algorithms that can effectively utilize the communication medium’s throughput capacity and robots’ computing resources. A distributed event-triggered control method is designed to solve the circular formation control problems for MRSs. Secondly, a self-triggered strategy is proposed to further reduce the number of control actions and the amount of communication between neighbors without a significant performance reduction. The differences between this article and previous works lie in: (i) Different from previous works [19], [20], [29]–[31], the main goal of this article is to design distributed event-triggered control laws that can guide a group of anonymous mobile robots with restricted computation and communication ability to form any given circular formation.
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