  Recently it has been reported that range-measurement inconsistency, or
equivalently mismatches in prescribed inter-agent distances, may prevent the
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 ill
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 no distortion in the formation shape occurs.
Such motion control results are then applied to (a) the alignment of formations
orientations and (b) 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.
