# Barrier-Enhanced Parallel Homotopic Trajectory Optimization for Safety-Critical Autonomous Driving

arXiv: https://arxiv.org/abs/2402.10441 · HTML: https://mlsanity.com/paper/2402.10441/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Feb 2024.

## Built on by (most cited first, 4 of 4)

- [LD-Scene: LLM-Guided Diffusion for Controllable Generation of Adversarial Safety-Critical Driving Scenarios](https://mlsanity.com/paper/2505.11247/) (2025)
- [CounterScene: Counterfactual Causal Reasoning in Generative World Models for Safety-Critical Closed-Loop Evaluation](https://mlsanity.com/paper/2603.21104/) (2026)
- [DualShield: Safe Model Predictive Diffusion via Reachability Analysis for Interactive Autonomous Driving](https://mlsanity.com/paper/2601.15729/) (2026)
- [Safe and Nonconservative Contingency Planning for Autonomous Vehicles via Online Learning-Based Reachable Set Barriers](https://mlsanity.com/paper/2509.07464/) (2025)

## Abstract (arXiv)

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 parallel homotopic trajectory optimization (BPHTO) approach with the 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 BPHTO as a bi-convex optimization problem. Then constraint transcription and the 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.