Optimization-based trajectory planning for autonomous vehicles in scenarios with multiple reference lines

Enabling autonomous vehicles to adhere to the reference line as much as possible is a regulatory consensus that ensures predictability in vehicle's behavior within mixed traffic flow, thereby reducing the risk of accidents. State-of-the-art Cartesian-based trajectory planning methods overcome limitations inherent in traditional Frenet-based approaches, particularly regarding constraint violations in high-curvature scenarios. However, these methods encounter theoretical challenges in handling reference line constraints, hindering their direct application in road scenarios. In this paper, an optimization-based trajectory planning method in Cartesian Frame is proposed to address road scenarios with multiple reference lines. The main work can be summarized into three parts. In the first part, The on-road trajectory planning task is reframed as an Optimal Control Problem (OCP) with multiple-reference lines constraints (MRLC), where the nominal OCP ensures safety and feasibility. The incorporation of nominal MRLC ensures that the generated trajectory closely follows the reference lines while maintaining the trajectory's longitudinal deformation capability. However, nominal MRLC, which involves a minimum optimization problem when describing the distance between the trajectory and reference lines, cannot be directly embedded into an OCP. To address this issue, in the second part, an approximate calculation method is proposed to explicitly describe MRLC. The MRLC constructed in this way not only preserves the trajectory's good deformability but also handles the generation of continuous lane-changing trajectories. In the third part, an improved dynamic programming approach tailored for multi-reference line scenarios is proposed, providing high-quality initial guesses for OCP-MRLC to enhance its convergence speed. Finally, comprehensive benchmarking against state-of-the-art methods is presented, showcasing the significance of the proposed OCP-MRLC in meeting reference line constraints and ensuring trajectory quality. Experiments conducted with real-world datasets validate the practicality of the algorithm.