  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.
