Distributed encirclement control with arbitrary spacing for multiple anonymous mobile robots

Encirclement control enables a multi-robot system to rotate around a target while they still preserve a circle formation, which is useful in real world applications such as entrapping a hostile target. In this paper, a distributed control law is proposed for any number of anonymous and oblivious robots in random three dimensional positions to form a specified circular formation with any desired inter-robot angular distances (i.e. spacing) and encircle around the target. Arbitrary spacing is useful for a system composed of heterogeneous robots which, for example, possess different kinematics capabilities, since the spacing can be designed manually for any specific purpose. The robots are modelled by single-integrator models, and they can only sense the angular positions of their two neighbouring robots, so the control law is distributed. Theoretical analysis and simulation results are provided to prove the stability and effectiveness of the proposed control strategy.