Global formation control of nonholonomic unicycle vehicles with guaranteed rate of convergence

Abstract

This paper studies the full‐state formation control problem of multiple nonholonomic unicycle vehicles. Firstly, the formation error model is transformed into standard nonholonomic chained form, including orientation and position error subsystems. For orientation subsystem, an angular velocity control law is designed to be a cooperative term plus an exponential decay function of time, ensuring orientations reach an agreement on a common value. For position error subsystem, a time‐varying output‐like variable is carefully constructed to ensure a stable zero dynamics, that is, the consensus of these output variables guarantees position formation, overcoming the intrinsic underactuated control difficulty. Then, a linear velocity control law is derived to realize consensus of outputs. It is proved that the proposed distributed time‐varying controller is capable of steering the vehicles to globally exponentially make into desired geometric position shape with the same orientations and vanishing velocities, provided that the communication topology is directed and having a spanning tree. The calculated convergence rates are shown dependent on controller coefficients; thus, the controller is modified to additionally reach a prescribed rate of convergence by redesigning conditions of controller parameters. Finally, two numerical simulations are implemented for five unicycle vehicles, demonstrating the effectiveness of the proposed control scheme.