Distributed two-dimension model predictive control for left-turn control of connected and automated vehicle platoons at signalized intersections

Longitudinal control methods for Connected and Automated Vehicle (CAV) platoons have been extensively studied. However, the effective, efficient, and real-time deployable method for left-turn control of the CAV platoon at the intersection area is much less studied because it involves simultaneously controlling both vehicles’ acceleration/deceleration and steering. To address this gap, we proposed a Distributed Model Predictive Control (DMPC) strategy structured into two stages, i.e., the trajectory planning stage and the trajectory tracking control stage. The trajectory planning stage is developed based on a continuous optimal control problem to determine the optimal left-turn trajectory based on the leading vehicle’s state. In contrast, the trajectory tracking control stage sequentially solves a discrete quadratic optimization problem to compute the optimal acceleration/deceleration and steering for each following vehicle in the platoon, with an aim to reduce the trajectory tracking error and enhance driver comfort. The discrete quadratic optimization problem is solved using a proposed Norm-Relaxed Feasible Direction (NRMFD) algorithm. The control strategy is distributed in the sense that the CAV platoon into a decoupled system, and only one vehicle’s control decisions are solved at each time. This can dramatically reduce the computation time. Thereby, the proposed DMPC can be deployed in real-time. The stability property of the DMPC method is also analyzed to enhance platoon mobility. Numerical experiments indicate that the proposed DMPC strategy can maneuver the left-turn CAV platoon past the intersection more safely and efficiently than human-driven vehicles. Thereby, it can be used to control the CAV platoon in real-time at an intersection area.