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.

Traffic rule compliance for automated vehicles is challenging, 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.



Dataset Evaluation

Violations of Safe Distance Rule & Speed Limit Rule

HighD dataset with formalized German interstate traffic rules


Safe Distance Rule: The ego vehicle must maintain a safe distance from vehicles in the same lane, ensuring collision avoidance even in cases of sudden stops by one or more vehicles.

Speed Limit Rule: The ego vehicle must not exceed:

  1. The speed limit of the lanes it drives on.
  2. The speed necessary to ensure collision freedom with vehicles outside its field of view.
  3. The maximum velocity permitted for its vehicle type.
  4. The speed necessary for comfortably adhering to traffic regulations.

  • Initial trajectory Violations of Rules GIF
  • Repaired trajectory Repaired Trajectory GIF

Violations of Stop Line Rule

InD dataset with formalized German intersection traffic rules


Stop Line Rule: The ego vehicle has to stop with respect to a stop sign (sign 206) before it enters the intersection at least for a duration in front of the associated stop line.

  • Initial trajectory
    Violations of Rules GIF
  • Repaired trajectory
    Repaired Trajectory GIF

Violations of Priority Rule

InD dataset with formalized German intersection traffic rules


Priority Rule: The ego vehicle is not allowed to enter an intersection if there is another vehicle with the right of way that will be endangered by the ego vehicle.

  • Initial trajectory
    Violations of Rules GIF
  • Repaired trajectory
    Repaired Trajectory GIF

CARLA Simulation

We use the urban downtown environment with CARLA map ID Town 03 and configure the traffic manager in autopilot mode to simulate realistic urban traffic scenarios.






Real-World Experiments

We integrate our approach into the EDGAR research vehicle, a Volkswagen T7 Multivan equipped with the necessary sensors and hardware for fully autonomous test runs.








Our Team


Technical University of Munich

coming soon!

If you have any questions, please contact Yuanfei Lin.