Longitude Trajectory Optimization for Autonomous Vehicles: An Approach Based on Simplified Car-Following Model

In this paper, the authors present an approach to optimize longitude vehicle trajectories for autonomous vehicles based on the simplified (linear) car following model to minimize vehicles’ total travel cost and guarantee the minimal safety spacing between vehicles. Based on Newell’s linear car-following model, they formulate the multi-vehicle simultaneous trajectory optimization problem as a linear programming (LP) problem solvable with the commercial solvers, such as GAMS, at a small scale. In addition, they also formulate the same problem using the dynamic programming technique and develop efficient DP algorithms to guarantee the minimal safety distance between vehicles by a shifted state representation during searching the optimal trajectories. In the end, several numerical experiments are performed to illustrate how to use the approach proposed in this paper to optimize vehicle trajectories under different scenarios.