# Rule-based Optimal Control for Autonomous Driving

arXiv: https://arxiv.org/abs/2101.05709 · HTML: https://mlsanity.com/paper/2101.05709/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jan 2021.

## Built on by (most cited first, 21 of 21)

- [Towards learning-based planning:The nuPlan benchmark for real-world autonomous driving](https://mlsanity.com/paper/2403.04133/) (2024)
- [Driving Everywhere with Large Language Model Policy Adaptation](https://mlsanity.com/paper/2402.05932/) (2024)
- [WALL-E: World Alignment by Rule Learning Improves World Model-based LLM Agents](https://mlsanity.com/paper/2410.07484/) (2024)
- [A Review of Reward Functions for Reinforcement Learning in the context of Autonomous Driving](https://mlsanity.com/paper/2405.01440/) (2024)
- [The Reasonable Crowd: Towards evidence-based and interpretable models of driving behavior](https://mlsanity.com/paper/2107.13507/) (2021)
- [Receding Horizon Planning with Rule Hierarchies for Autonomous Vehicles](https://mlsanity.com/paper/2212.03323/) (2022)
- [A Rule-Based Behaviour Planner for Autonomous Driving](https://mlsanity.com/paper/2407.00460/) (2024)
- [TorchDriveEnv: A Reinforcement Learning Benchmark for Autonomous Driving with Reactive, Realistic, and Diverse Non-Playable Characters](https://mlsanity.com/paper/2405.04491/) (2024)
- [Learning Performance-Oriented Control Barrier Functions Under Complex Safety Constraints and Limited Actuation](https://mlsanity.com/paper/2401.05629/) (2024)
- [Model Predictive Robustness of Signal Temporal Logic Predicates](https://mlsanity.com/paper/2209.07881/) (2022)
- [Multi-Predictor Fusion: Combining Learning-based and Rule-based Trajectory Predictors](https://mlsanity.com/paper/2307.01408/) (2023)
- [Traffic-Rule-Compliant Trajectory Repair via Satisfiability Modulo Theories and Reachability Analysis](https://mlsanity.com/paper/2412.15837/) (2024)
- [Towards Defensive Autonomous Driving: Collecting and Probing Driving Demonstrations of Mixed Qualities](https://mlsanity.com/paper/2109.07995/) (2021)
- [Semi-Supervised Imitation Learning with Mixed Qualities of Demonstrations for Autonomous Driving](https://mlsanity.com/paper/2109.11280/) (2021)
- [EnergyShield: Provably-Safe Offloading of Neural Network Controllers for Energy Efficiency](https://mlsanity.com/paper/2302.06572/) (2023)
- [Safe CoR: A Dual-Expert Approach to Integrating Imitation Learning and Safe Reinforcement Learning Using Constraint Rewards](https://mlsanity.com/paper/2407.02245/) (2024)
- [A Framework for Learning Scoring Rules in Autonomous Driving Planning Systems](https://mlsanity.com/paper/2502.11352/) (2025)
- [Drive As You Like: Multi-Head Diffusion with Reinforcement Learning for Personalized Driving](https://mlsanity.com/paper/2508.16947/) (2025)
- [Control Analysis and Design for Autonomous Vehicles Subject to Imperfect AI-Based Perception](https://mlsanity.com/paper/2509.12137/) (2025)
- [Integrating Legal and Logical Specifications in Perception, Prediction, and Planning for Automated Driving: A Survey of Methods](https://mlsanity.com/paper/2510.25386/) (2025)
- [Real-Time Rulebook-Aware Nonlinear MPC for Autonomous Driving with Priority-Biased Tiered Slacks](https://mlsanity.com/paper/2607.10975/) (2026)

## Abstract (arXiv)

We develop optimal control strategies for Autonomous Vehicles (AVs) that are required to meet complex specifications imposed by traffic laws and cultural expectations of reasonable driving behavior. We formulate these specifications as rules, and specify their priorities by constructing a priority structure. We propose a recursive framework, in which the satisfaction of the rules in the priority structure are iteratively relaxed based on their priorities. Central to this framework is an optimal control problem, where convergence to desired states is achieved using Control Lyapunov Functions (CLFs), and safety is enforced through Control Barrier Functions (CBFs). We also show how the proposed framework can be used for after-the-fact, pass / fail evaluation of trajectories - a given trajectory is rejected if we can find a controller producing a trajectory that leads to less violation of the rule priority structure. We present case studies with multiple driving scenarios to demonstrate the effectiveness of the proposed framework.