A Rendezvous Strategy With $\mathbb{R}^{2}$ Reachability for Kinematic Agents
Souradip De, Soumya Ranjan Sahoo, Pankaj Wahi · IEEE Transactions on Automatic Control · 2020
In this article, we present a consensus strategy based on cyclic pursuit that ensures rendezvous at any desired point in 2-D space (ℝ2reachability) starting with any nonsingular initial configuration of the agents. Choice of a negative gain expands the reachable set beyond the convex hull of the initial configuration of agents. However, the entire ℝ2is not reachable in general. We first find the necessary and sufficient condition for the initial configuration of the agents, which ensures ℝ2reachability. We show that any desired point can be reached with finite controller gains under basic cyclic pursuit if the initial configuration of agents forms a nonconvex polygon. Next, we employ a control strategy using deviated cyclic pursuit to reach the special configuration mentioned above starting from an arbitrary initial configuration. With a switching between these two strategies we can achieve ℝ2reachability with finite gains. We also present an implementation algorithm to realize this strategy including computation of the finite gains.