Bearing-based Circumnavigation with Collision Avoidance in Time-varying Graphs under Limited Target Information

Abstract

In this paper, we study distributed circumnavigation of a stationary target by a heterogeneous team of agents. Each agent is modelled as a disk rather than a point mass to account for its physical dimensions. The target location is assumed to be accessible only to a small subset of agents, called leaders. The rest, called followers, therefore use only local information available from their designated out-neighbour in the interaction graph characterised by the selection of nearest neighbours. By controlling only angular speeds, we develop a distributed guidance law to circumnavigate a stationary target. The proposed guidance law works for both static and time-varying interaction graphs. Inter-agent collision avoidance is enforced through a logarithmic Barrier Lyapunov (BLF) Function, which guarantees forward invariance of the collision-free set. We show that every follower converges to circumnavigation about the same target as the leader at the end of its directed path in the interaction graph, provided the initial conditions are admissible. Numerical simulations illustrate the effectiveness of the proposed method for both static and time-varying topologies.