String Stability Analysis for Heterogeneous Vehicle Strings

The spacing errors of a string stable, homogeneous vehicle string attenuate uniformly down the vehicle chain. This result is useful for implementing vehicle formation control because it provides a guideline for the proper intervehicle spacing. In the heterogeneous case, the differing dynamics of the vehicles means the spacing errors do not attenuate or amplify uniformly down the vehicle chain, regardless of whether the formation is string stable or not. Questions arise regarding how heterogeneous string stability should be defined, and what should the proper intervehicle spacing be in order to guarantee nominal safety. In this paper, heterogeneous vehicle strings under simple decentralized control laws with the constant spacing control policy are analyzed. A definition for heterogeneous string stability is proposed. The necessary and sufficient conditions for heterogeneous string stability are given for the constant spacing leader-predecessor following control strategy. The scalability of the control scheme is verified by analyzing the worst case disturbance to error gain. It is shown that string stability can be achieved for heterogeneous vehicle strings of arbitrary length and arbitrary vehicle type ordering.