Fixed-Time Rotating Consensus for Multiple Second-Order Underactuated Mobile Vehicles

This paper introduces a bias point transformation to deal with the nonholonomic constraints of multiple second-order underactuated mobile vehicles, and transforms such systems into equivalent holonomic systems. In complex environments, follower vehicles cannot directly acquire the leader’s position and velocity due to limited sensing ranges or communication constraints. To this end, a distributed fixed-time observer is developed, which can accurately estimate the leader’s state for all followers within a fixed settling time using only local neighboring information. Based on the estimated states, a distributed fixed-time controller is further proposed and it enables the system to achieve fixed-time rotating consensus without requiring velocity measurements. The fixed-time stability of the closed-loop system is rigorously analyzed via bilateral homogeneity theory and Lyapunov stability theory. Theoretical results confirm that the developed observer and controller ensure that all underactuated mobile vehicles achieve rotating consensus within a fixed time. Finally, numerical simulation results demonstrate the effectiveness of the presented control protocol.