Nonlinear spacing policies for vehicle platoons: A geometric approach to decentralized control

Wijnbergen, Paul; Jeeninga, Mark; Besselink, Bart · 2021 · Crossref

DOI: 10.1016/j.sysconle.2021.104954

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Summary

This paper addresses the decentralized control of vehicle platoons using general nonlinear spacing policies, motivated by the potential for such policies to enhance safety and traffic flow compared to traditional linear approaches. While linear spacing policies (e.g., constant headway) are common, they may require unsafe acceleration or deceleration during transient events like emergency stops. The authors propose a predecessor–follower control structure where each vehicle maintains a desired distance relative to its predecessor, independent of the predecessor’s control actions. This approach supports heterogeneous platoons with varying vehicle dynamics. The study utilizes nonlinear geometric control theory to characterize which spacing policies allow for decentralized controllers that guarantee asymptotic tracking and stabilization. The methodology focuses on a two-vehicle model to establish necessary and sufficient conditions for the existence of decentralized state feedback controllers. The vehicle dynamics include position, velocity, and acceleration, with engine dynamics modeled by a time constant. The spacing error is defined as the difference between the actual inter-vehicle distance and a reference spacing policy, which is a function of the states of both vehicles. The authors derive conditions under which a controller can decouple the spacing error from the predecessor’s input. Specifically, they show that the spacing policy must be independent of the predecessor’s acceleration. Furthermore, if the policy depends on the follower’s acceleration, it must also be independent of the predecessor’s velocity. Using these conditions, the paper explicitly constructs nonlinear controllers that achieve input-output linearization and asymptotic stability of the spacing error. Key findings include the characterization of all nonlinear spacing policies that admit decentralized controllers for asymptotic tracking. The authors demonstrate that string stability—the attenuation of disturbances propagating through the platoon—is a property of the spacing policy itself rather than the controller design, provided the tracking conditions are met. As a specific example, the paper analyzes a nonlinear headway spacing policy quadratic in the follower’s velocity. It shows that this policy can enforce a lower bound on the follower’s acceleration, thereby preventing collisions even with limited braking capacity, while maintaining the same nominal spacing as a linear policy. Simulations illustrate that this nonlinear policy ensures safe acceleration profiles during velocity changes, unlike linear policies which may violate acceleration bounds. The significance of this work lies in providing a rigorous theoretical framework for designing decentralized controllers for nonlinear spacing policies in heterogeneous platoons. By linking string stability to the choice of spacing policy, the paper offers guidelines for selecting policies that ensure robust platoon performance. The results enable the synthesis of explicit nonlinear controllers that guarantee safety and stability, advancing the state of the art in automated vehicle platooning beyond linear control strategies. This approach is particularly relevant for heavy-duty vehicles and mixed-traffic scenarios where vehicle dynamics vary significantly.

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