Distributed Receding Horizon Control of Vehicle Platoons: Stability and String Stability

This paper considers the problem of distributed control of a platoon of vehicles with nonlinear dynamics. We present distributed receding horizon control algorithms and derive sufficient conditions that guarantee asymptotic stability, leader-follower string stability, and predecessor-follower string stability, following a step speed change in the platoon. Vehicles compute their own control in parallel, and receive communicated position and velocity error trajectories from their immediate predecessor. Leader-follower string stability requires additional communication from the lead car at each update, in the form of a position error trajectory. Predecessor-follower string stability, as we define it, implies leader-follower string stability. Predecessor-follower string stability requires stricter constraints in the local optimal control problems than the leader-follower formulation, but communication from the lead car is required only once at initialization. Provided an initially feasible solution can be found, subsequent feasibility of the algorithms are guaranteed at every update. The theory is generalized for nonlinear decoupled dynamics, and is thus applicable to fleets of planes, robots, or boats, in addition to cars. A simple seven-car simulation examines parametric tradeoffs that affect stability and string stability. Analysis on platoon formation, heterogeneity and size (length) is also considered, resulting in intuitive tradeoffs between lead car and following car control flexibility.