Joint Signal Timing and Trajectory Control With Uncertainty in Connected Automated Vehicle Dynamics

Optimizing the trajectory of connected automated vehicles (CAVs) through cooperation with signal controllers can smoothen the traffic flow and reduce energy consumption. However, most existing research efforts in this domain do not consider the effect of stochastic disturbances generated by exogenous systems. Ignoring these stochasticities may cause a mismatch between the estimated and real vehicle dynamics, which may result in a deviation among implemented and optimized trajectories, inefficient operational performance, and even collisions in the worst-case condition. This paper introduces a two-stage optimization model for CAVs trajectory and signal timing control that considers and responds to uncertainty in vehicle dynamics. The signal controller receives the speed, acceleration, and position of incoming CAVs within the communication range and identifies incoming platoons based on vehicle headways. At the upper stage, a mixed-integer linear program within the signal controller optimizes the trajectories of the platoon leaders and signal timing parameters. At the lower stage, platoon leaders optimize the trajectories of all other vehicles within the platoon based on a chance-constrained concept to consider uncertainties involved in implementing optimized trajectories. We utilize a sample-based approximation of the collision probabilities to formulate constraints to control vehicle trajectory. The resulting formulation ensures that the probability of satisfying inter-vehicle safety distance is above a certain threshold and reduces the probability of longitudinal crashes between vehicles. The proposed framework shows a 48%-67% reduction in travel delays in comparison with optimized fixed-time signal timing plans in a simulated signalized intersection under different levels of uncertainty in vehicle dynamics.