# Safe and Nonconservative Contingency Planning for Autonomous Vehicles via Online Learning-Based Reachable Set Barriers arXiv: https://arxiv.org/abs/2509.07464 ยท HTML: https://mlsanity.com/paper/2509.07464/ ## Key facts - No citing papers in the map yet (data through 14 Oct 2026). - Placed in Reinforcement learning for driving, one of 9 directions in End-to-end autonomous driving. - Builds on 36 of its 71 references that are in the map. - First posted on arXiv 9 Sep 2025. ## Placed in - End-to-end autonomous driving / [Reinforcement learning for driving](https://mlsanity.com/driving/reinforcement-learning-for-driving/) ## Builds on (most cited first, 30 of 36) - [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021) - [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017) - [Milestones in Autonomous Driving and Intelligent Vehicles: Survey of Surveys](https://mlsanity.com/paper/2303.17220/) (2023) - [Training Neural Networks Without Gradients: A Scalable ADMM Approach](https://mlsanity.com/paper/1605.02026/) (2016) - [Robust Control Barrier-Value Functions for Safety-Critical Control](https://mlsanity.com/paper/2104.02808/) (2021) - [Safety-Critical Model Predictive Control with Discrete-Time Control Barrier Function](https://mlsanity.com/paper/2007.11718/) (2020) - [Interactive multi-modal motion planning with Branch Model Predictive Control](https://mlsanity.com/paper/2109.05128/) (2021) - [Optimal parameter selection for the alternating direction method of multipliers (ADMM): quadratic problems](https://mlsanity.com/paper/1306.2454/) (2013) - [Data-Driven Reachable Set Computation using Adaptive Gaussian Process Classification and Monte Carlo Methods](https://mlsanity.com/paper/1910.02500/) (2019) - [Stochastic Model Predictive Control with a Safety Guarantee for Automated Driving: Extended Version](https://mlsanity.com/paper/2009.09381/) (2020) - [Interactive Joint Planning for Autonomous Vehicles](https://mlsanity.com/paper/2310.18301/) (2023) - [Alternating Direction Method of Multipliers for Constrained Iterative LQR in Autonomous Driving](https://mlsanity.com/paper/2011.00462/) (2020) - [RACP: Risk-Aware Contingency Planning with Multi-Modal Predictions](https://mlsanity.com/paper/2402.17387/) (2024) - [Multi-Modal Model Predictive Control through Batch Non-Holonomic Trajectory Optimization: Application to Highway Driving](https://mlsanity.com/paper/2109.10392/) (2021) - [Scenario-Based Motion Planning with Bounded Probability of Collision](https://mlsanity.com/paper/2307.01070/) (2023) - [A Hamilton-Jacobi Reachability-Based Framework for Predicting and Analyzing Human Motion for Safe Planning](https://mlsanity.com/paper/1910.13369/) (2019) - [Scenario-Based Trajectory Optimization in Uncertain Dynamic Environments](https://mlsanity.com/paper/2103.12517/) (2021) - [Reachability-Based Confidence-Aware Probabilistic Collision Detection in Highway Driving](https://mlsanity.com/paper/2302.07109/) (2023) - [Fast, Smooth, and Safe: Implicit Control Barrier Functions through Reach-Avoid Differential Dynamic Programming](https://mlsanity.com/paper/2307.00193/) (2023) - [Spatiotemporal Receding Horizon Control with Proactive Interaction Towards Autonomous Driving in Dense Traffic](https://mlsanity.com/paper/2308.05929/) (2023) - [Predictive Control for Autonomous Driving with Uncertain, Multi-modal Predictions](https://mlsanity.com/paper/2310.20561/) (2023) - [Automated Lane Merging via Game Theory and Branch Model Predictive Control](https://mlsanity.com/paper/2311.14916/) (2023) - [Barrier-Enhanced Parallel Homotopic Trajectory Optimization for Safety-Critical Autonomous Driving](https://mlsanity.com/paper/2402.10441/) (2024) - [Experimental Validation of Safe MPC for Autonomous Driving in Uncertain Environments](https://mlsanity.com/paper/2305.03312/) (2023) - [Interaction-aware Traffic Prediction and Scenario-based Model Predictive Control for Autonomous Vehicles on Highways](https://mlsanity.com/paper/2310.07526/) (2023) - [Proactive Emergency Collision Avoidance for Automated Driving in Highway Scenarios](https://mlsanity.com/paper/2310.17381/) (2023) - [Safe and Real-Time Consistent Planning for Autonomous Vehicles in Partially Observed Environments via Parallel Consensus Optimization](https://mlsanity.com/paper/2409.10310/) (2024) - [Safety-Critical Coordination of Legged Robots via Layered Controllers and Forward Reachable Set based Control Barrier Functions](https://mlsanity.com/paper/2312.08689/) (2023) - [Robust Predictive Motion Planning by Learning Obstacle Uncertainty](https://mlsanity.com/paper/2403.06222/) (2024) - [Occlusion-Aware Contingency Safety-Critical Planning for Autonomous Driving](https://mlsanity.com/paper/2502.06359/) (2025) ## Abstract (arXiv) Autonomous vehicles must navigate dynamically uncertain environments while balancing safety and efficiency. This challenge is exacerbated by unpredictable human-driven vehicle (HV) behaviors and perception inaccuracies, necessitating planners that adapt to evolving uncertainties while maintaining safe trajectories. Overly conservative planning degrades driving efficiency, while deterministic methods risk failure in unexpected scenarios. To address these issues, we propose a real-time contingency trajectory optimization framework. Our method employs event-triggered online learning of HV control-intent sets to dynamically quantify multimodal HV uncertainties and incrementally refine their forward reachable sets (FRSs). Crucially, we enforce invariant safety through FRS-based barrier constraints that ensure safety without reliance on accurate trajectory prediction. These constraints are seamlessly embedded in contingency trajectory optimization and solved efficiently through consensus alternating direction method of multipliers (ADMM). The system continuously adapts to HV behavioral uncertainties, preserving feasibility and safety without excessive conservatism. High-fidelity simulations on highway and urban scenarios, along with a series of real-world experiments, demonstrate significant improvements in driving efficiency and passenger comfort while maintaining safety under uncertainty. The project page is available at https://pathetiue.github.io/frscp.github.io/.