Robust fixed-time consensus tracking with application to formation control of unicycles

This study investigates the robust fixed-time consensus tracking problem of second-order multi-agent systems under fixed topology. A novel type of non-linear protocol and the corresponding sufficient conditions for achieving robust fixed-time consensus tracking are proposed with the aid of sliding mode technique and Lyapunov theory. Compared to finite-time consensus tracking, the convergence time of the tracking errors is globally bounded for any initial conditions of the agents, which is also the global information for each agent. Furthermore, the results obtained for second-order multi-agent systems are also extended to deal with the fixed-time formation tracking problem for unicycle-type robots. Extensive numerical experiments are performed to illustrate the effectiveness of the present theoretical results.