Fixed-Time Formation Control of Multirobot Systems: Design and Experiments

Time delays exist in network-connected systems. Especially for vision-based multirobot systems, time delays are diverse and complicated due to the communication network, camera latency, image processing, etc. At the same time, many tasks, such as searching and rescue, have timing requirement. This paper focuses on fixed-time formation control of multirobot systems subject to delay constraints. First, predictor-based state transformation is employed for each robot to deal with the input delay, and the uncertain terms remained in the transformed systems are carefully considered. Then, a couple of nonlinear fixed-time formation protocols are proposed for the multirobot systems with respectively undirected and directed topology, and the corresponding settling time is derived by using the Lyapunov functions. In particular, the upper-bound estimation of the formation settling time is explicitly given irrelevant to the initial conditions. Finally, the protocols are validated through a numerical simulation example and then implemented on an E-puck robots platform. Both simulation and experimental results demonstrate the effectiveness of the proposed formation protocols.