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：在避免过度保守行为的同时确保安全性，对于自动驾驶汽车实现高任务性能至关重要。本文提出一种基于过度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，用于实时集成式决策与规划。为促进自车（EV）与周围车辆的安全交互，基于势垒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，采用差异化势垒系数以应对周围人类驾驶车辆（HVs）的运动不确定性，并缓解保守行为。此外，利用驾驶操纵的离散特性，基于可达性分析初始化以标称行为为导向的末端自由同伦轨迹族，每条轨迹局部约束为特定驾驶操纵，同时共享相同任务目标。通过结合安全模块的双凸性与自车运动学特性，我们将BHPTO建模为双凸优化问题。随后采用约束转录与过度松弛ADMM简化优化过程，从而在保证可行性的前提下实时生成多条轨迹。通过一系列实验，基于合成与真实交通数据集，所提方法在多种交通场景中展现出更高的任务精度、稳定性与一致性。