Enhancing Safety-Critical Autonomous Driving: Integrated Decision-Making and Planning With Barrier-Enhanced Homotopic Parallel Trajectory Optimization
Lei Zheng, Rui Yang, Michael Yu Wang, and Jun Ma
Abstract
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.
What does Barrier-Enhanced Homotopic Parallel Trajectory Optimization (BPHTO) do?
The primary objective of the BPHTO is to seamlessly integrate discrete decision-making maneuvers with continuous trajectory variables for safety-critical autonomous driving. The algorithm operates in real-time, optimizing trajectories of autonomous vehicles to ensure safety, stability, and proactive interaction with uncertain human-driven vehicles across various driving tasks, utilizing over-relaxed ADMM iterations. We provide a comprehensive theoretical analysis of safety robustness, demonstrating the asymptotic convergence of the EV from an unsafe state to a safe state in the sense of Lyapunov stability.
The solid line with an arrow represents the intended trajectory of the EV, while other solid lines denote alternative free-end homotopic candidate trajectories of the EV. Each trajectory shares the same initial state and corresponds to a specific driving maneuver denoted as ξ, with values of {0,1,−1}, representing lane-keeping, left-lane-change, and right-lane-change behaviors, respectively
Results
We demonstrate our method in different scenarios (see below)
Implementation: Developed in C++ and Robot Operating System 2, running on an Ubuntu 22.04 system with an AMD Ryzen 5 5600G CPU.
Safe Navigation in Cluttered Static Environments
Navigating the EV safely while maintaining a desired speed in static conditions with dense obstacles. The number of driving lanes is set to 5 with a width of 3.75 m. The target cruise velocity is 15 m/s.
Adaptive Cruise in Dynamic Traffic
This task requires the EV to safely cruise at an average speed of 15 m/s to navigate through dense traffic, where HVs exhibit multi-modal behaviors.
IDM Dataset
NGSIM Dataset
Constrained High-speed Racing Scenario
The EV is tasked with accelerating to a high speed and demonstrating rapid decision-making and adaptability under dynamic traffic scenarios. The key objective is to evaluate the EV's capabilities concerning driving stability and efficiency within a limited time frame. The desired motion is confined to the bottom three driving lanes. The initial and target racing speeds are 15 m/s and 22 m/s, respectively..
Adaptive Cruise Control under Road Construction
The goal is to assess the performance of the BPHTO algorithm in managing variations in road conditions under varying traffic density and road construction, particularly when confronted with the constraint of a limited sensing range.
Reacting to Abrupt Cut-ins During Lane Merging
A Lane-change conflict scenario
The EV (in red) in Lane 3 is executing a lane change to the upper Lane 2. Meanwhile, an imperceptible blue HV2 in Lane 1 is initiating a lane change to Lane 2 from a different direction, potentially leading to a hazardous situation.
Real-time Performance Tests
Statistical results of computing time with varying numbers of homotopic trajectories using an optimization horizon of 50 steps
Statistical results of computing time for five homotopic trajectories with different numbers of nearest considered HVs, using an optimization horizon of 50 steps.
Authors
Lei Zheng Rui Yang Michael Yu Wang Jun Ma
Lei Zheng, Rui Yang, and Jun Ma are with The Hong Kong University of Science and Technology, China.
Michael Yu Wang is with the School of Engineering, Great Bay University, Dongguan, China.