Trajectory planner based on fifth-order polynomials applied for lane changing in autonomous driving

Abstract

This paper focuses on the motion control of autonomous cars, particularly for executing safe lane change maneuvers. The proposed solution integrates Model Predictive Control (MPC) with a fifth-order polynomial trajectory planner to handle lane changes and avoid collisions in dynamic driving environments. The primary advantage of this approach is its minimal computational resource requirements, making it suitable for real-time deployment while maintaining high performance in complex traffic conditions. The paper starts by developing a nonlinear dynamic model of the car, emphasizing lateral dynamics, which is crucial for planning and controlling the car’s movement during lane changes. The model accounts for important parameters like yaw rate, lateral forces, and steering angles. The trajectory planner is designed to calculate an optimal, collision-free path for the car to follow when changing lanes or overtaking other cars, ensuring that the car stays within safety constraints, such as maintaining an appropriate distance from preceding cars. A novel aspect of the proposed solution is the integration of decision-making with trajectory planning. The system calculates the safe distance from the preceding car using time-to-collision and inter-vehicular time metrics. These metrics enable the car to decide whether to stay in its lane or initiate a lane change, based on the safety of the maneuver. Once a decision is made, the trajectory planner generates a new reference path, ensuring a safe and smooth lane change, even in the presence of obstacles. The effectiveness of the proposed system is demonstrated through extensive simulations in a variety of driving scenarios. These simulations show that the car can successfully perform lane changes and overtakes without colliding with other cars, while maintaining comfort and minimizing control errors. The simulation results validate that the MPC-based control system, combined with the polynomial trajectory planner, offers a reliable and efficient solution for real-time trajectory planning and control in autonomous driving.