A semidefinite programming framework for controlling multi-robot systems in dynamic environments

In this paper, a discrete-time, semidefinite programming (SDP) framework is synthesized for controlling mobile robot teams operating in dynamic environments. Given an initially feasible configuration, the proffered framework embeds formation shape control and guarantees inter-agent and agent-obstacle collision avoidance and network interconnectivity across the formation given a sufficiently small Δt - provided that a feasible solution exists. Additionally, it affords goal-directed behaviors, which are explored, most notably, in terms of its application to directional coverage control, where the objective is to ensure that a set of mobile targets are being observed by at least a single member of the team at any given time. Central to our formulation is melding the recent application of shape theoretic constructs to globally optimal shape planning with state-dependent graphs whose enforced connectivity (gauged via their Fiedler value) implies satisfaction of the aforementioned constraints. Simulation results are presented to highlight the utility of our approach.