Distributed Communication-Free Control of Multiple Robots for Circumnavigation of a Speedy Unpredictably Maneuvering Target

Multiple fully actuated mobile robots travel in a plane with upper-limited speeds and are driven by accelerations limited in magnitude. The robots should arrive at a pre-specified distance from an unpredictable speedy target, then maintain this distance and achieve an even self-distribution over the respective moving circle, along with a given angular velocity of rotation about the target. The robots do not communicate with anybody and are anonymous to one another; pre-assignment of different roles to various robots is impossible. Every robot measures only the relative position of the target and companion robots (within a finite range of "visibility" in the latter case) and has access to the angular velocity of its own pure rotation; access to its own linear velocity may also be needed in some cases. Necessary conditions for the solvability of the mission are disclosed and a distributed control strategy is proposed. Its global convergence and collision avoidance property are rigorously proved under slight and partly unavoidable enhancement of the just mentioned necessary conditions. The performance of the control law is illustrated by computer simulations.