Collective circular motion of unicycle type vehicles with nonidentical constant velocities

This paper addresses formation control problems for heterogeneous groups of unicycle type mobile agents with fixed cruising speed. The heterogeneity in the group is caused by the cruising speeds being nonidentical, which complicates the motion coordination problem but is of practical relevance, for example, in unmanned aerial vehicle applications. We show that two different types of collective circular motion are possible in such groups: 1) a circular motion with common angular frequency and different radius for each agent; or 2) a circular motion with common radius but different angular frequency for each agent. For the first motion type, the orientation of all vehicles can additionally be coordinated such that an agreement or a balanced configuration is achieved. We present suitable control laws for each of these motion coordination tasks. These control laws explicitly take into account the nonidentical velocities and guarantee convergence to the desired configurations. Numerical examples illustrate all results.