Enforcing safety while preventing overly conservative behaviors is essential for autonomous vehicles to achieve high task performance. In this paper, we propose a barrier-enhanced homotopic parallel trajectory optimization (BHPTO) approach with over-relaxed alternating direction method of multipliers (ADMM) for real-time integrated decision-making and planning. To facilitate safety interactions between the ego vehicle (EV) and surrounding vehicles, a spatiotemporal safety module exhibiting bi-convexity is developed on the basis of barrier function. Varying barrier coefficients are adopted for different time steps in a planning horizon to account for the motion uncertainties of surrounding HVs and mitigate conservative behaviors. Additionally, we exploit the discrete characteristics of driving maneuvers to initialize nominal behavior-oriented free-end homotopic trajectories based on reachability analysis, and each trajectory is locally constrained to a specific driving maneuver while sharing the same task objectives. By leveraging the bi-convexity of the safety module and the kinematics of the EV, we formulate the BHPTO as a bi-convex optimization problem. Then constraint transcription and over-relaxed ADMM are employed to streamline the optimization process, such that multiple trajectories are generated in real time with feasibility guarantees. Through a series of experiments, the proposed development demonstrates improved task accuracy, stability, and consistency in various traffic scenarios using synthetic and real-world traffic datasets.

翻译：在防止过度保守行为的同时保证安全，对于自动驾驶汽车实现高任务性能至关重要。本文提出一种基于超松弛交替方向乘子法（ADMM）的屏障增强同伦并行轨迹优化（BHPTO）方法，用于实时集成决策与规划。为促进自车（EV）与周围车辆的安全交互，基于屏障函数开发了具有双凸性的时空安全模块。针对规划时域内不同时间步采用可变屏障系数，以考虑周围人类驾驶车辆（HV）的运动不确定性并缓解保守行为。此外，我们利用驾驶操纵的离散特性，基于可达性分析初始化名义行为导向的自由末端同伦轨迹，每条轨迹在共享相同任务目标的同时被局部约束为特定驾驶操纵。通过利用安全模块的双凸性和自车运动学，将BHPTO表述为双凸优化问题。随后采用约束变换和超松弛ADMM简化优化过程，从而在保证可行性的情况下实时生成多条轨迹。通过一系列实验，该方法在合成和真实交通数据集的各种场景中展示了提升的任务准确性、稳定性和一致性。