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Recently it has been reported that range-measurement inconsistency, orequivalently mismatches in prescribed inter-agent distances, may prevent thepopular gradient controllers from guiding rigid formations of mobile agents toconverge to their desired shape, and even worse from standing still at anylocation. In this paper, instead of treating mismatches as the source of illperformance, we take them as design parameters and show that by introducingsuch a pair of parameters per distance constraint, distributed controllerachieving simultaneously both formation and motion control can be designed thatnot only encompasses the popular gradient control, but more importantly allowsus to achieve constant collective translation, rotation or their combinationwhile guaranteeing asymptotically no distortion in the formation shape occurs.Such motion control results are then applied to (a) the alignment of formationsorientations and (b) enclosing and tracking a moving target. Besides rigorousmathematical proof, experiments using mobile robots are demonstrated to showthe satisfying performances of the proposed formation-motion distributedcontroller.

Distributed rotational and translational maneuvering of rigid formations and their applications