Distributed Multi-robot Circumnavigation with Dynamic Spacing and Time Delay

Abstract

Circumnavigation is the process whereby a single agent or multiple agents rotate around a target while preserving a circular formation, which has promising potential in real-world applications such as entrapping a malicious target or escorting an important member. For the multi-robot circumnavigation problem, spacing (i.e., the angle differences) among robots plays an important role in forming a desirable circular formation. The spacing is usually assumed to be a unified constant in most of the studies. However, when robots have different or even time-varying kinematic capabilities, a fixed and equal spacing is probably not effective for accomplishing such task as preventing an enclosed target from fleeing, and thus dynamic spacing is naturally proposed and preferred. The variations of spacing are caused by the “weights” (termed utilities) of robots. This paper relaxes the condition of piecewise constant utilities and provides the ultimate bound and the input-to-state (ISS) stability conditions for the spacing error and its dynamics respectively. In addition, since time delay is ubiquitous in practical engineering systems while seldom considered in the current studies on circumnavigation, the maximum allowable time delay within which the circumnavigation remains stable is derived using both the frequency domain method and the Lambert-W function. Finally, the theoretical results are validated by a practical simulation system.