Theoretical foundations for rendezvous of glowworm-inspired agent swarms at multiple locations

We present theoretical foundations for a variation of the multi-agent rendezvous problem involving design of local control strategies that enable agent swarms, with hard-limited sensing ranges, to split into disjoint subgroups, exhibit simultaneous taxis behavior toward, and eventually rendezvous at, multiple unknown locations of interest. The algorithm used to solve the above problem is based on a glowworm swarm optimization (GSO) technique, developed earlier, that finds multiple optima of multi-modal objective functions. We characterize the various phases of the algorithm that help us to develop a theoretical framework required for analysis. In particular, we show through simulations that the implementation of the GSO algorithm at the individual agent level gives rise to two major phases at the group level–splitting of the agent-swarm into subgroups and local convergence of agents in each subgroup to the peak locations. We provide local convergence results under certain restricted set of assumptions, leading to a simplified model of the algorithm, making it amenable to analysis, while still reflecting most of the features of the original algorithm. In particular, we find an upper bound on the time taken by the agents to converge to an isolated leader and on the time taken by the agents to converge to one of the leaders with non-isolated and non-overlapping neighborhoods. Finally, we show that agents under the influence of multiple leaders with overlapping neighborhoods asymptotically converge to one of the leaders. We present some illustrative simulations to support the theoretical findings of the paper.