Simulation-based Analysis Of Highway Trajectory Planning Using High-Order Polynomial For Highly Automated Driving Function

TL;DR

This work tackles safe highway Lane Change for Highly Automated Driving Function by coupling a Behavior Planning Module with a high-order polynomial trajectory generator. It demonstrates that elevating the longitudinal polynomial order (up to 6th) and using a 5th-order lateral path can yield collision-free, smooth trajectories, with a 7th-order lateral path explored for further robustness. The approach is evaluated in MATLAB/Simulink, showing improved safety and stability through closed-form trajectory expressions and boundary-condition-driven coefficients. The study highlights computational efficiency and practical relevance for real-time planning while noting avenues for richer dynamics modeling and joint optimization to extend to more complex driving environments.

Abstract

One of the fundamental tasks of autonomous driving is safe trajectory planning, the task of deciding where the vehicle needs to drive, while avoiding obstacles, obeying safety rules, and respecting the fundamental limits of road. Real-world application of such a method involves consideration of surrounding environment conditions and movements such as Lane Change, collision avoidance, and lane merge. The focus of the paper is to develop and implement safe collision free highway Lane Change trajectory using high order polynomial for Highly Automated Driving Function (HADF). Planning is often considered as a higher-level process than control. Behavior Planning Module (BPM) is designed that plans the high-level driving actions like Lane Change maneuver to safely achieve the functionality of transverse guidance ensuring safety of the vehicle using motion planning in a scenario including environmental situation. Based on the recommendation received from the (BPM), the function will generate a desire corresponding trajectory. The proposed planning system is situation specific with polynomial based algorithm for same direction two lane highway scenario. To support the trajectory system polynomial curve can be used to reduces overall complexity and thereby allows rapid computation. The proposed Lane Change scenario is modeled, and results has been analyzed (verified and validate) through the MATLAB simulation environment. The method proposed in this paper has achieved a significant improvement in safety and stability of Lane Changing maneuver.

Figures (9)

• Figure 1: Highway Lane Change scenariob3
• Figure 2: Behaviour Planner for Lane Change maneuver decisions
• Figure 3: Longitudinal and Lateral Acceleration of the trajectory 5$^{th}$order
• Figure 4: Longitudinal and Lateral acceleration of the trajectory 6$^{th}$order
• Figure 5: Lane Change trajectory of 5$^{th}$order