# Traffic-Rule-Compliant Trajectory Repair via Satisfiability Modulo Theories and Reachability Analysis

arXiv: https://arxiv.org/abs/2412.15837 · HTML: https://mlsanity.com/paper/2412.15837/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 123 references that are in the map.
- First posted on arXiv 20 Dec 2024.

## Builds on (most cited first, 30 of 35)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [CARLA: An Open Urban Driving Simulator](https://mlsanity.com/paper/1711.03938/) (2017)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [The highD Dataset: A Drone Dataset of Naturalistic Vehicle Trajectories on German Highways for Validation of Highly Automated Driving Systems](https://mlsanity.com/paper/1810.05642/) (2018)
- [A Survey of Motion Planning and Control Techniques for Self-driving Urban Vehicles](https://mlsanity.com/paper/1604.07446/) (2016)
- [Robot Operating System 2: Design, Architecture, and Uses In The Wild](https://mlsanity.com/paper/2211.07752/) (2022)
- [Guided Conditional Diffusion for Controllable Traffic Simulation](https://mlsanity.com/paper/2210.17366/) (2022)
- [The inD Dataset: A Drone Dataset of Naturalistic Road User Trajectories at German Intersections](https://mlsanity.com/paper/1911.07602/) (2019)
- [Backpropagation through Signal Temporal Logic Specifications: Infusing Logical Structure into Gradient-Based Methods](https://mlsanity.com/paper/2008.00097/) (2020)
- [Reachability-based Trajectory Safeguard (RTS): A Safe and Fast Reinforcement Learning Safety Layer for Continuous Control](https://mlsanity.com/paper/2011.08421/) (2020)
- [EPSILON: An Efficient Planning System for Automated Vehicles in Highly Interactive Environments](https://mlsanity.com/paper/2108.07993/) (2021)
- [Robust Temporal Logic Model Predictive Control](https://mlsanity.com/paper/1511.00347/) (2015)
- [Rule-based Optimal Control for Autonomous Driving](https://mlsanity.com/paper/2101.05709/) (2021)
- [Interactive multi-modal motion planning with Branch Model Predictive Control](https://mlsanity.com/paper/2109.05128/) (2021)
- [Recurrent Neural Network Controllers for Signal Temporal Logic Specifications Subject to Safety Constraints](https://mlsanity.com/paper/2009.11468/) (2020)
- [Mixed-Integer Programming for Signal Temporal Logic with Fewer Binary Variables](https://mlsanity.com/paper/2204.06367/) (2022)
- [Formalizing Traffic Rules for Machine Interpretability](https://mlsanity.com/paper/2007.00330/) (2020)
- [Contingency Games for Multi-Agent Interaction](https://mlsanity.com/paper/2304.05483/) (2023)
- [EDGAR: An Autonomous Driving Research Platform -- From Feature Development to Real-World Application](https://mlsanity.com/paper/2309.15492/) (2023)
- [Incremental Sampling-based Algorithm for Minimum-violation Motion Planning](https://mlsanity.com/paper/1305.1102/) (2013)
- [MARC: Multipolicy and Risk-aware Contingency Planning for Autonomous Driving](https://mlsanity.com/paper/2308.12021/) (2023)
- [Real-Time Trajectory Replanning for MAVs using Uniform B-splines and a 3D Circular Buffer](https://mlsanity.com/paper/1703.01416/) (2017)
- [Receding Horizon Planning with Rule Hierarchies for Autonomous Vehicles](https://mlsanity.com/paper/2212.03323/) (2022)
- [Physically-Feasible Repair of Reactive, Linear Temporal Logic-based, High-Level Tasks](https://mlsanity.com/paper/2207.02834/) (2022)
- [Online monitoring for safe pedestrian-vehicle interactions](https://mlsanity.com/paper/1910.05599/) (2019)
- [Real-Time Capable Decision Making for Autonomous Driving Using Reachable Sets](https://mlsanity.com/paper/2309.12289/) (2023)
- [Modularized Control Synthesis for Complex Signal Temporal Logic Specifications](https://mlsanity.com/paper/2303.17086/) (2023)
- [DrPlanner: Diagnosis and Repair of Motion Planners for Automated Vehicles Using Large Language Models](https://mlsanity.com/paper/2403.07470/) (2024)
- [Trajectory Replanning for Quadrotors Using Kinodynamic Search and Elastic Optimization](https://mlsanity.com/paper/1903.01139/) (2019)
- [Road Traffic Law Adaptive Decision-making for Self-Driving Vehicles](https://mlsanity.com/paper/2204.11411/) (2022)

## Built on by (most cited first, 3 of 3)

- [Real-Time Out-of-Distribution Failure Prevention via Multi-Modal Reasoning](https://mlsanity.com/paper/2505.10547/) (2025)
- [CARVE: Certified Affordable Repair of Vetoed Maneuvers via Envelopes for Interactive Driving](https://mlsanity.com/paper/2606.02641/) (2026)
- [Real-Time Rulebook-Aware Nonlinear MPC for Autonomous Driving with Priority-Biased Tiered Slacks](https://mlsanity.com/paper/2607.10975/) (2026)

## Abstract (arXiv)

Complying with traffic rules is challenging for automated vehicles, as numerous rules need to be considered simultaneously. If a planned trajectory violates traffic rules, it is common to replan a new trajectory from scratch. We instead propose a trajectory repair technique to save computation time. By coupling satisfiability modulo theories with set-based reachability analysis, we determine if and in what manner the initial trajectory can be repaired. Experiments in high-fidelity simulators and in the real world demonstrate the benefits of our proposed approach in various scenarios. Even in complex environments with intricate rules, we efficiently and reliably repair rule-violating trajectories, enabling automated vehicles to swiftly resume legally safe operation in real time.