Distributed Rotational and Translational Maneuvering of Rigid Formations and Their Applications

Recently, it has been reported that inconsistent range-measurement or, equivalently, mismatches in prescribed interagent distances, may prevent popular gradient controllers from guiding rigid formations of mobile agents to converge to their desired shape and, even worse, from standing still at any location. In this paper, instead of treating mismatches as the source of poor performance, we take them as design parameters and show that by introducing such a pair of parameters per distance constraint, distributed controller achieving simultaneously both formation and motion control can be designed that not only encompasses the popular gradient control, but more importantly allows us to achieve constant collective translation, rotation, or their combination, while guaranteeing asymptotically that no distortion in the formation shape occurs. Such motion control results are then applied to 1) the alignment of formations' orientations and 2) enclosing and tracking a moving target. Besides rigorous mathematical proof, experiments using mobile robots are demonstrated to show the satisfying performances of the proposed formation-motion distributed controller.