Safe coverage of compact domains for second order dynamical systems

Autonomous systems operating in close proximity with each other to cover a specified area has many potential applications, but coordination and safety are two fundamental challenges. For coordination, we propose a locally asymptotically stable distributed coverage controller for moving compact domains for two types of vehicles with second order dynamics (double integrator and fixed-wing aircraft) with bounded input forces. This control policy is based on artificial potentials and consensus forces designed to promote desired vehicle-domain and inter-vehicle separations and relative velocities. We prove that certain coverage configurations are locally asymptotically stable. For safety, we establish minimal energy conditions for collision free motion and we utilize Hamilton-Jacobi (HJ) reachability theory for pairwise collision avoidance. Rather than computing numerical solutions of the associated HJ partial differential equation, we derive an analytical solution for the double integrator vehicle. We demonstrate our approach in several numerical simulations involving convex and non-convex moving domains.