Despite the great success of using gradient-based controllers to stabilizerigid formations of autonomous agents in the past years, surprising yetintriguing undesirable collective motions have been reported recently wheninconsistent measurements are used in the agents' local controllers. To makethe existing gradient control robust against such measurement inconsistency, weexploit local estimators following the well known internal model principle forrobust output regulation control. The new estimator-based gradient control isstill distributed in nature and can be constructed systematically even when thenumber of agents in a rigid formation grows. We prove rigorously that theproposed control is able to guarantee exponential convergence and thendemonstrate through robotic experiments and computer simulations that thereported inconsistency-induced orbits of collective movements are effectivelyeliminated.
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