Adaptive Prescribed-Time Formation Control for Nonholonomic Vehicles Subject to Uncertain Disturbances

This paper proposes an adaptive prescribed-time formation control protocol based on time scaling state mapping for nonholonomic vehicles. First, the nonholonomic vehicle is divided into position and attitude subsystems through coordinate transformation. Then, adaptive prescribed-time controllers are designed for the two subsystems, and the corollary of Barbalat's lemma proves the stability. It guarantees that nonholonomic vehicles can track the desired trajectory within a prescribed time in a desired formation. Moreover, the convergence rate of the system can be tuned via a regulated parameter, and adaptive laws are employed to deal with the uncertain disturbances. Finally, numerical simulations are introduced to demonstrate the feasibility of the proposed protocol and the influence of the regulated parameter in the controllers and initial states of the vehicles.