Coordinated adaptive consensus tracking of multiple impacting oscillator robot systems via distributed interactions

Coordinated control of multi-agent systems has become a very active topic. However, the issue of coordinated control for multiple impacting oscillator robot systems is still an open problem. This is due to the fact that the system is a high dimensional discontinuous nonlinear system whose dynamics are very complex and different initial states give rise to different dynamical behaviors. This paper not only focuses on the dynamic behavior of multiple impacting oscillator robot systems, but more importantly, on the controller design for such systems. A new distributed controller is constructed based on the Lyapunov method. It reveals that the multiple impacting oscillator robot systems are able to realize consensus tracking with different initial values with the designed controller, whereas the multiple impacting oscillator robot systems will converge to different steady states under the same system parameters and different initial values in the absence of applied control. It is possible to make the multi-impacting oscillator robot systems are free to switch to the desired steady state independently of the initial states by applying the proposed controller according to the actual needs. Simulation results are given to validate the presented findings.