Safe and Non-Conservative Contingency Planning for Autonomous Vehicles via Online Learning-Based Reachable Set Barriers

Rui Yang1, Lei Zheng1, Shuzhi Sam Ge2, Jun Ma1
1Robotics and Autonomous Systems Thrust, HKUST(Guangzhou) 2Department of Electrical and Computer Engineering, National University of Singapore
Video

Abstract

Autonomous vehicles must navigate dynamically uncertain environments while balancing safety requirements and driving efficiency. This challenge is exacerbated by the unpredictable nature of surrounding human-driven vehicles (HVs) and perception inaccuracies, which require planners to adapt to evolving uncertainties while maintaining safe trajectories. Overly conservative planners degrade driving efficiency, while deterministic approaches may fail dangerously with infeasibility when encountering sudden, unexpected maneuvers. To address these issues, we propose a real-time contingency trajectory optimization framework. By employing event-triggered online learning of HV control-intent sets, our method dynamically quantifies multi-modal HV uncertainties and refines the forward reachable set (FRS) incrementally. Crucially, we enforce invariant safety through FRS-based barrier constraints that ensure safety without reliance on accurate trajectory prediction of HVs. %despite inaccurate HV prediction These constraints are embedded in contingency trajectory optimization and solved efficiently through consensus alternative direction method of multipliers (ADMM). The system continuously adapts to the uncertainties in HV behaviors, preserving feasibility and safety without resorting to excessive conservatism. High-fidelity simulations on highway and urban scenarios, and 1:10-scale hardware experiments demonstrate significant improvements in driving efficiency and passenger comfort while maintaining safety under uncertainty.

Simulation

Highway Scenario (NGSIM Dataset)

An HV in the leftmost lane initiates a rightward staged lane change, briefly pauses in the second leftmost lane, and then abruptly resumes its rightward maneuver just as the EV approaches. Meanwhile, other HVs maintain steady driving. The EV is required to dynamically capture the uncertain HV intentions and proactively responds to the potential cut-in of the HV.

Ablations

Our method: Online update the HV FRS for defensive driving via a contingency planning framework.

Deterministic-Barrier-Planner: Rely on deterministic prediction, resulting in collission with sudden cut-in HV.

Worst-Case-Barrier-Planner: Yield the HV conservatively with premature deceleration.

Comparisons

Our method: Smooth speed adjustment with moderate lateral avoidance.

ST-RHC [7]: Resort to last-minute aggressive avoidance.

Uncertainty-Aware Planner [44]: Keep safe with excessive deceleration and abrupt lateral maneuvers.

highway_p

Trajectory and speed profiles of the EV under different planning methods in the abrupt cut-in scenario.

highway_a

Evolution of longitudinal and lateral acceleration profiles of EV with different planning methods (bounds shown as dashed lines).

Performance Evaluation Across Key Metrics

Method Safety Comfort Efficiency Time (s)
Coll. (%) Min. (m) Jerkx (m/s3) Jerky (m/s3) Speed (m/s) Dist. (m)
Deter. Barr. Pl. 27.27 0.31 5.00 3.21 19.86 234.05 0.035
Wors. Barr. Pl. 0.00 6.53 6.17 7.08 15.75 186.07 0.033
Proposed 0.00 1.48 4.41 3.13 19.31 228.38 0.034
ST-RHC [7] 18.18 0.35 6.39 3.83 20.21 239.49 0.029
Uncert. Pl. [44] 0.00 5.61 9.67 10.23 14.28 168.16 0.038

Stress testing shows that the proposed method achieves superior safety (0% collision rate) while preserving comparable travel efficiency and comfort metrics.

[7] Zheng et al. (2024) | [44] Zhou et al. (2025)

Unsignalized Intersection Scenario

An oncoming southbound HV initially exhibits normal driving behavior before abruptly executing a right turn across the intended path of the EV. The EV is required to handle dense traffic and emergent conflicts with proactive defensive maneuvers for HV uncertainties.

Ablations

Our method: Safely navigate with anticipatory deceleration and controlled rightward avoidance maneuvers.

Deterministic-Barrier-Planner: Lack of defensive driving capability to handle uncertain HV behaviors.

Worst-Case-Barrier-Planner: Yield until intersection clearance with excessive early deceleration.

Comparisons

Our method: Preserve the feasibility of safe trajectories, supporting defensive driving in uncertain traffic conflicts.

ST-RHC [7]: Collide with HV and result in planner infeasibility due to rapidly shrinking feasible space between adjacent vehicles.

Uncertainty-Aware Planner [43]: Navigate conservatively with excessive speed reduction and the shortest travel distance.

intersection_p

Trajectory comparison in the intersection scenario demonstrates coordinated defensive deceleration and proactive lateral adjustments, achieving the longest navigation distance.

intersection_min_dist

The minimum EV-HV distances show that our method maintains appropriate safety margins.

Sensitivity Analysis

consensus_step

Impact of the consensus step parameter N_s on intersection navigation behaviors. Smaller values enable aggressive maneuvers while larger values enforce conservative strategies with preemptive deceleration.

prob

Effect of the weighting parameter p_s on intersection navigation behaviors. Higher values emphasize FRS-based safety constraints, resulting in more defensive behaviors.

Hardware Experiments

Validation on 1:10 scale Ackermann mobile robot platform in overtaking scenarios

Scenario I: The EV (black) overtakes an HV (white) executing aggressive, erratic lane intrusion.

Scenario II: The EV (black) overtakes an HV (white) with steady lane intrusion.

Experimental Setup

  • TianRacer robot with NVIDIA Jetson Xavier NX
  • 1:10 scale vehicle (380mm × 210mm)
  • OptiTrack motion capture system (180Hz)
  • Real-time planning at 10Hz
  • Scenarios with different HV behavior uncertainties

Real-World Navigation Snapshots

mild intersection

Scenario I: The EV (red dashed box) maintains both progress and safety with relatively large distance from the HV.

aggressive through

Scenario II: The EV (red dashed box) naturally generates overtaking trajectories with reduced conservatism.

Data Analysis

exp_p

Overtaking trajectory comparison under different uncertainty levels. Scenario I (Top) with erratic HV shows larger safety margins against intrusion risks; Scenario II (Bottom) with relatively steady HV demonstrates mild overtaking maneuvers with reduced conservatism.

triggering

The triggering condition prompts updates of control-intent set. Scenario I (left) shows a more rapid increase of set volume corresponding to aggressive behaviors than that in Scenario II (right).

Key Results

  • Maintain safe and non-conservative driving against possible lane intrusions
  • Dynamically update the HV FRS for real-time safety assurance
  • Achieve real-time performance under uncertain traffic conditions

BibTeX

@article{yang2025safe,
  title={Safe and Non-Conservative Contingency Planning for Autonomous Vehicles via Online Learning-Based Reachable Set Barriers},
  author={Rui Yang, Lei Zheng, and Jun Ma},
  journal={arXiv preprint arXiv:--},
  year={2025}
}