Influence of Prediction Horizon on Trajectory Optimization for Autonomous Vehicle Maneuvers

The advent of autonomous vehicles (AVs) marks a revolutionizing transformation in transportation, with the potential to significantly enhance safety and efficiency through advanced trajectory planning and optimization capabilities. A crucial component in realizing these benefits is the use of optimization-based control strategies for real-time path planning. Among these, model predictive path integral (MPPI) control algorithms stand out as a sampling-based stochastic control method, offering precise control in dynamic environments through random sampling. While the MPPI control has shown promising results, there has been limited investigation into the effects of different prediction horizon times on control performance of these algorithms. This paper seeks to address this gap by proposing a multi-input MPPI control method for AVs using a single-track vehicle dynamic model. Our research focuses on the influence of various prediction horizon times on trajectory optimization during lane-changing and lane-keeping maneuvers. Through comprehensive simulations, our findings demonstrate that the developed MPPI control algorithm effectively manages AV control in both driving behaviors, as its ability to optimize critical parameters such as steering and yaw angles. Moreover, the simulation results show that the trajectory optimization with a 0.7s prediction horizon is more effective, yielding a seamless transition between lane-changing and lane-keeping. In contrast, 2.5s prediction horizon introduces significant variations across various vehicle parameters, such as acceleration and yaw rate. Specifically, simulations indicate that the 0.7s horizon results in a 98.32% reduction in total average cost and a 72.47% decrease in calculation time compared to the 2.5s horizon. These findings provide valuable insights into the optimization of MPPI control algorithms for AVs, highlighting the importance of prediction horizon time in achieving efficient and safe trajectory planning.