msc-thesis-proposals
List of Master's thesis projects:
Project 1: Solving high-dimensional control problems using tensor decompositions
Project 2: Safe game-theoretic planning for autonomous vehicles
For details, see below.
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Project 1: Solving high-dimensional control problems using tensor decompositions
Background:
Typical control problems in real life, such as controlling an autonomous vehicle on the road or steering a quadcopter in the air, live in large (i.e., high-dimensional) state spaces given by all the different configurations the control system may be in. As an example, the state of just one quadcopter is 12-dimensional given by the position, velocity and the different angles. This high-dimensional feature prohibits methods from obtaining optimal controllers naively, and an important open problem is therefore to obtain good approximate solutions (i.e., efficient controllers of high dimensional systems with a low computational cost). Obtaining such approximate solutions would have a huge impact on today’s society due to the increased usage of complex robotic and automated systems in everyday life and industrial applications.
Description:
This project will solve high-dimensional control problems using optimal control theory and tensor decomposition. Optimal control theory is used to recast the problem of finding the optimal controller for a generic control theory problem (such as steering an autonomous vehicle or a quadcopter) to solving a certain partial differential equation known as the Hamilton-Jacobi-Bellman (HJB) equation [1]. An inherent feature of this recasting is that a high-dimensional control problem results in a high-dimensional HJB equation. This high-dimensional feature will be addressed with tensor decompositions [2,3], which intuitively splits up the high-dimensional problem into lower-dimensional entities, thereby enabling approximate solutions of the HJB equation to be obtained. Recent work has demonstrated the promise of this approach [4,5]. This project will extend the setup in [5] to more general control-theoretic problems (e.g., following the setup in [4]), and validate the extension via simulations (e.g., steering a quadcopter).
Work plan:
1. Read relevant background knowledge and conduct a literature review.
2. Extend the setup in [5] to more general control-theoretic problems.
3. Implement the extended formalism in MATLAB.
4. Validate the approach via simulations.
The start date of the project will be individually discussed.
Prerequisites:
1. Elementary knowledge in applied mathematics, including mathematical control theory (e.g., SF2832 or similar), numerical analysis (e.g., SF1544 or similar), and probability theory (e.g., SF2940 or similar). It is also recommended (but not required) that the student has taken a course in optimal control theory (e.g., SF2852 or similar).
2. Elementary knowledge in programming, including MATLAB.
Supervisors:
Elis Stefansson - Supervisor (elisst@kth.se)
Apostolos Rikos - Co-supervisor (rikos@kth.se)
Karl H. Johansson - Examiner (kallej@kth.se)
References:
[1] Fleming, Wendell H., and Halil Mete Soner. Controlled Markov processes and viscosity solutions. Vol. 25. Springer Science & Business Media, 2006.
[2] Kolda, Tamara G., and Brett W. Bader. "Tensor decompositions and applications." SIAM review 51.3 (2009): 455-500.
[3] Oseledets, Ivan V. "Tensor-train decomposition." SIAM Journal on Scientific Computing 33.5 (2011): 2295-2317.
[4] Stefansson, Elis, and Yoke Peng Leong. "Sequential alternating least squares for solving high dimensional linear hamilton-jacobi-bellman equation." 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). IEEE, 2016.
[5] Dolgov, Sergey, Dante Kalise, and Karl Kunisch. "Tensor decomposition methods for high-dimensional Hamilton-Jacobi-Bellman equations." SIAM Journal on Scientific Computing (2021).
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Project 2: 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.
Prerequisites:
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:
Supervisors: Elis Stefansson (elisst@kth.se) and Yulong Gao (yulongg@kth.se)
Examiner: Karl H. Johansson (kallej@kth.se)
References:
[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.
