Robust Formation Control of Bidirectional Vehicular Platoons with Prescribed Tracking Performance*

This paper investigates the longitudinal robust formation control problem of bidirectional vehicular platoons with prescribed tracking performance in the presence of time-varying parametric uncertainties. First, the collision avoidance and high traffic throughput requirements are explicitly expressed as pre-scribed tracking performance defined by bilateral inequality constraints bounded by decaying functions of time. Since the original Udwadia-Kalaba (UK) approach cannot handle inequality constraints, a mathematical transformation framework based on bijective functions is applied to transform the bounded state into an equivalent unbounded one. Then, combined with a series of equality constraints integrating the information of proximal (preceding and following) vehicles, we convert the platoon formation control problem into a servo constraint-following task. A novel adaptive robust controller based on the UK approach is designed to render the uniform boundedness (UB) and uniform ultimate boundedness (UUB) performance for the transformed state, in turn ensuring the platoon formation control objectives. Simulation results show the effectiveness of the control strategy.