  Autonomous coverage of a specified area by robots operating in close
proximity with each other has many potential applications such as real-time
monitoring of rapidly changing environments, and search and rescue; however,
coordination and safety are two fundamental challenges. For coordination, we
propose a distributed controller for covering 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 alignment 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 energy conditions for collision free motion and utilize
Hamilton-Jacobi (HJ) reachability theory for last-resort pairwise collision
avoidance. We derive an analytical solution to the associated HJ partial
differential equation corresponding to the collision avoidance problem between
two double integrator vehicles. We demonstrate our approach in several
numerical simulations involving the two types of vehicles covering convex and
non-convex moving domains.
