Coordinated Car-following Using Distributed MPC

TL;DR

This work tackles the problem of stop-and-go waves and suboptimal throughput in high-density traffic by formulating coordinated car-following as a Markov-game with distributed model predictive control (DMPC). The authors develop iterated best-response algorithms with both implicit and explicit coordination, leveraging input re-parameterization and softmax grid search to achieve real-time performance on fleets of vehicles; offline mechanism design tunes the ideal speed $v^*$ to optimize flow under smoothness constraints. Key findings show that explicit coordination can roughly double fleet speed at high density and suppress oscillations, approaching Nash-equilibrium or centralized-optimal outcomes while remaining robust and computationally tractable on commodity hardware. The study also reveals that linear stability analysis alone does not fully capture traffic stability, highlighting the importance of fast transients attenuation and neighborhood-level coordination. Overall, the approach provides a scalable, incentive-compatible framework for traffic stabilization that relies on short-range communication and avoids rigid platooning, with promising extensions to broader traffic scenarios.

Abstract

Within the modeling framework of Markov games, we propose a series of algorithms for coordinated car-following using distributed model predictive control (DMPC). Instead of tracking prescribed feasible trajectories, driving policies are solved directly as outcomes of the DMPC optimization given the driver's perceivable states. The coordinated solutions are derived using the best response dynamics via iterated self-play, and are facilitated by direct negotiation using inter-agent or agent-infrastructure communication. These solutions closely approximate either Nash equilibrium or centralized optimization. By re-parameterizing the action sequence in DMPC as a curve along the planning horizon, we are able to systematically reduce the original DMPC to very efficient grid searches such that the optimal solution to the original DMPC can be well executed in real-time. Within our modeling framework, it is natural to cast traffic control problems as mechanism design problems, in which all agents are endogenized on an equal footing with full incentive compatibility. We show how traffic efficiency can be dramatically improved while keeping stop-and-go phantom waves tamed at high vehicle densities. Our approach can be viewed as an alternative way to formulate coordinated adaptive cruise control (CACC) without an explicit platooning (or with all vehicles in the traffic system treated as a single extended platoon). We also address the issue of linear stability of the associated discrete-time traffic dynamics and demonstrate why it does not always tell the full story about the traffic stability.

Figures (13)

• Figure 1: Description of the four solution concepts under the rubric of the DMPC modeling framework. By "No central authority" we only mean that drivers' decision-making is not centralized. Central authority may still be needed for facilitating the coordination technically, such as providing communication channels among agents.
• Figure 2: Two possible limit solutions of the traffic dynamics when all agents are modeled as human drivers (using adaptiveSeek) with the same set of preference parameters. Left: free-flow fixed-point. Right: stop-and-go wave. The headway is defined as $d_{i,t}\equiv x_{i+1,t}-x_{i,t}\mod C$.
• Figure 3: Brief description of the proposed algorithms. In the "Computation & Communication" column,"D" stands for decentralized, i.e. computation done by the onboard computer of each vehicle, and "C" stands for centralized, i.e. computation done by the centralized server.
• Figure 4: Traffic efficiency improvement: average fleet velocity vs. vehicle density. Orange: non-intervened human driving which suffers from stop-and-go waves. Blue: human driving with a density-dependent variable speed advisory. Green: game theory coordinated solution with V2X communication. Gray: centralized optimization solution. Stop-and-go waves are suppressed in the last three cases.
• Figure 5: The onset of stop-and-go waves is substantially delayed till much higher vehicle density if the grid search is upgraded from 1D to 2D in the MPC. Top row: Average velocities when the initial traffic condition is closer to the free-flow fixed point. Bottom row: Average Velocities when the initial traffic condition is closer to the stop-and-go wave.