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Title: Safe game-theoretic planning for autonomous vehicles

Background: Game-theoretic frameworks combined with machine learning techniques (e.g., inverse reinforcement learning [1]) has been shown to successfully yield interaction-aware models for autonomous vehicles from relatively small amounts of data and with high generalisability ability [2,3,4]. Despite these models' generalisability, the autonomous vehicles might still encounter novel situations where either the collected data or the assumptions in the game-theoretic model reduce the performance, potentially making the autonomous vehicle unsafe. The objective of this project is to integrate a safety-aware feature in the game-theoretic frameworks, which prevents the autonomous vehicle from entering unsafe modes of driving. Adding this feature will allow an autonomous vehicle to operate in a safe interaction-aware manner, with only slight adjustments when unsafe modes of driving are close.

Description: Towards the objective above, the first step is to consider the safety-aware framework in [5] based on reachability analysis, which checks if an unsafe state can be reached in the near future. This safety-aware framework will be integrated with game-theoretic models from [2,3,4], which predicts future nominal behaviour between drivers on the road by explicitly modelling the drivers’ interaction. In this integration, the safety-aware framework will intervene whenever the predicted future nominal behaviour from the game-theoretic model results in an unsafe state. Evaluations will be carried out in a driving simulator, where the examples from [2,3,4] may serve as a start.

Work plan:

1. Read relevant background knowledge and conduct a literature review.

2. Combine the safety-aware framework from [5] with the game-theoretic models from [2,3,4].

3. Implement the formalism in Python.

4. Validate the approach via simulations.

The start date of the project will be individually discussed.


1. Elementary knowledge in applied mathematics, including mathematical control theory (e.g., SF2832 or SF2852 or similar) and numerical analysis (e.g., SF1544 or similar). Recommended is also a course related to machine learning (e.g., EL2805 or SF2957 or similar).

2. Elementary knowledge in programming, including Python.

Supervisors: Elis Stefansson ( and Yulong Gao  (
Examiner : Karl H. Johansson - (


[1] Ziebart, Brian D., et al. "Maximum entropy inverse reinforcement learning." Aaai. Vol. 8. 2008.

[2] Sadigh, Dorsa, et al. "Planning for autonomous cars that leverage effects on human actions." Robotics: Science and Systems. Vol. 2. 2016.

[3] Fisac, Jaime F., et al. "Hierarchical game-theoretic planning for autonomous vehicles." 2019 International Conference on Robotics and Automation (ICRA). IEEE, 2019.

[4] Stefansson, Elis, et al. "Human-robot interaction for truck platooning using hierarchical dynamic games." 2019 18th European Control Conference (ECC). IEEE, 2019.

[5] Leung, Karen, et al. "On infusing reachability-based safety assurance within planning frameworks for human–robot vehicle interactions." The International Journal of Robotics Research 39.10-11 (2020): 1326-1345.


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