String Stability and a Delay-Based Spacing Policy for Vehicle Platoons Subject to Disturbances

Besselink, Bart; Johansson, Karl H. · 2017 · OpenAlex-citations

DOI: 10.1109/tac.2017.2682421

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Summary

This paper addresses the challenge of controlling vehicle platoons subject to external disturbances and spatially varying reference velocity profiles, such as heavy-duty vehicles traversing hilly terrain. Traditional spacing policies, including constant spacing and constant headway, are shown to be incompatible with tracking spatially varying velocity profiles because they enforce velocity changes in the time domain rather than the spatial domain. This mismatch can lead to infeasible control demands, such as requiring follower vehicles to accelerate beyond their engine power limits when climbing hills. To resolve this, the authors introduce a novel delay-based spacing policy and a corresponding stability notion called disturbance string stability. The proposed delay-based spacing policy specifies the desired intervehicular distance such that each vehicle tracks a time-delayed version of the preceding vehicle’s trajectory. This ensures that all vehicles in the platoon follow the same velocity profile relative to their position on the road (spatial domain), rather than relative to time. The authors define disturbance string stability as a uniform input-to-state stability property for interconnected systems, explicitly accounting for external disturbances acting on every vehicle in the platoon, not just the leader. This definition guarantees that perturbations do not grow unbounded as they propagate through the string of vehicles, regardless of the platoon’s length. The study presents a control design approach performed in the spatial domain to achieve tracking of the delay-based spacing policy while guaranteeing disturbance string stability. The authors derive theoretical conditions for stability, showing that if individual vehicles are input-to-state stable and the gain of the interconnection between vehicles is sufficiently small (specifically, bounded by a factor less than one), the entire platoon is disturbance string stable. The analysis extends to systems interconnected through outputs, providing less conservative stability conditions. The results are illustrated through simulations comparing the delay-based policy against constant spacing and constant headway policies. The simulations demonstrate that the delay-based policy successfully maintains uniform velocity profiles across the platoon in the spatial domain, whereas the traditional policies result in divergent velocity profiles and potential instability when tracking varying references. The significance of this work lies in providing a rigorous framework for platoon control that is robust to disturbances and compatible with spatially varying driving conditions. By shifting the control design to the spatial domain and introducing disturbance string stability, the paper offers a solution to the limitations of existing spacing policies. This approach ensures safe and efficient operation of vehicle platoons, particularly for heavy-duty vehicles where fuel efficiency and adherence to terrain-dependent velocity profiles are critical. The findings contribute to the broader field of automated transportation by establishing scalable stability guarantees for interconnected systems subject to pervasive disturbances.

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