Finite-time settling real-time control for multi-robot formation

A recent algorithm proposed for real-time computation of individual agent reference trajectories for formation tracking under realistic dynamic and actuator constraints shows remarkable formation keeping and formation reconfiguration capability. A key assumption for its successful execution however is that the accurate system state should be available at the beginning of each computation segment. The success in utilizing that algorithm in real-time practical implementation therefore calls for any tracking errors due to system uncertainties to be zero prior to the commencement of the following computation segment. In this paper addressed is this important issue. By considering a class of nonlinear systems with favorable finite-time convergence characteristics, sufficient conditions for exponential finite-time stability are presented and then applied to distributed formation tracking controls. This manifests in the settling time of the controlled system being finite and no longer than the predefined reference trajectory segment computing time interval, thus making tracking errors go to zero by the end of the time interval. This leads to a guarantee of desired multi-robot motion evolution in spite of the system uncertainties. Simulations of multi-robot formation keeping and formation reconfiguration verify the effectiveness of the proposed control strategies.