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### M.Sc.TimBrüdigam

Technical University of Munich

Chair of Automatic Control Engineering (Prof. Buss)

Postal:
Theresienstr. 90
80333 München

### Short Biography

 05/2021 - 10/2021 Research Stay University of California, Berkeley, USA Since 05/2017 Research Associate Chair of Automatic Control Engineering Technical University Munich, Germany (TUM) 04/2016 - 01/2017 Master Thesis: Influence of Flexible Wings on Flight Performance California Institute of Technology, USA 2014 - 2017 Master of Science, Electrical Engineering and Information Technology Focus: Control Theory and Automation Technology, Robotics Technical University Munich, Germany (TUM) 04/2014 - 08/2014 Bachelor Thesis: L1 Adaptive Control for Quadrocopters University of South Carolina, USA 2011 - 2014 Bachelor of Science, Electrical Engineering and Information Technology Focus: Control Theory, Electrical Machines Technical University Munich, Germany (TUM)

### Research Interests

My research focuses on Model Predictive Control (MPC) and specifically Stochastic MPC with application to automated driving.

Short example videos for different projects are available here.

#### Stochastic MPC Introduction

If you are interested in Stochastic MPC, check out this simple Matlab example:

SMPC example

A brief introduction to the theory of Stochastic MPC is available here:

SMPC introduction

#### Stochastic Model Predictive Control (for autonomous driving)

Model Predictive Control (MPC) has proved to be effective for trajectory planning. Regarding the example of autonomous driving, an optimization problem is solved to generate a vehicle trajectory for the near future. After the optimized input is applied to only the next time step, the optimization problem is solved again – but now the horizon is shifted by one step. In Stochastic MPC probabilistic constraints are formulated to efficiently account for system uncertainty.

We are currently working on improving efficiency and safety for Stochastic MPC, as well as providing guarantees for stability and recursive feasibility.

As driving takes place in environments that are not deterministic, it is necessary to account for these uncertainties, e.g. due to multiple possible maneuvers by other vehicles. For this purpose we are working on Stochastic MPC for autonomous driving in cooperation with BMW.

Details

#### Minimizing Constraint Violation Probability in MPC

System uncertainty can be handled in different ways within MPC. Robust MPC, as the name indicates, robustly accounts for the uncertainty, often resulting in conservative solutions. While Stochastic MPC yields efficient solutions, a small probability of constraint violation is permitted, based on a predefined risk parameter.

In contrast to Robust MPC and Stochastic MPC, we propose an MPC method (CVPM-MPC), which minimizes the probability that a constraint is violated while also optimizing other control objectives. The proposed method is capable of dealing with changing uncertainty and does not require to choose a risk parameter. CVPM-MPC can be reagarded as a link between Robust and Stochastic MPC.

Details

### Extending the MPC Prediction Horizon

A long prediction horizon in MPC is often beneficial. However, a long prediction horizon with a detailed prediction model quickly becomes computationally challenging. We provide different adaptations to MPC in order to take advantage of long prediction horizons while keeping the computational effort manageable. In addition, these adaptations are combined with methods from Robust MPC and Stochastic MPC to account for potential model uncertainty and disturbances.

Details

#### Legible Model Predictive Control for autonomous driving

Autonomous vehicles can assist other traffic participants in correctly predicting the autonomous vehicle’s future maneuvers. This cooperative behavior has a positive effect on traffic flow, while not increasing risk. For this reason, we developed and investigate Legible MPC to generate readable vehicle trajectories.

### Student Theses

I am always looking for motivated students that are interested in my research. Feel free to contact me if you are interested in a thesis, even if no topics are currently listed below.

Please let me know when you plan to start, include your transcript of records, and if available your resume, so that I can find a topic that fits your background.

(From May to October 2021, I will join the University of California, Berkeley for a research stay. I will therefore only be able to supervise a small number of student theses.)

### 2021

• Brüdigam, T.; Gaßmann, V.; Wollherr, D.; Leibold, M.: Minimization of constraint violation probability in model predictive control. Int J Robust Nonlinear Control, 2021, 1-33 more… Full text ( DOI ) Full text (mediaTUM)
• Brüdigam, T.; Olbrich, M.; Wollherr, D.; Leibold, M.: Stochastic Model Predictive Control with a Safety Guarantee for Automated Driving. IEEE Transactions on Intelligent Vehicles, 2021, 1-1 more… Full text ( DOI ) Full text (mediaTUM)
• Brüdigam, T.; Prader, D.; Wollherr, D.; Leibold, M.: Model Predictive Control with Models of Different Granularity and a Non-uniformly Spaced Prediction Horizon. American Control Conference (ACC), 2021 more…
• Brüdigam, T.; Zhan, J.; Wollherr, D.; Leibold, M.: Collision Avoidance with Stochastic Model Predictive Control for Systems with a Twofold Uncertainty Structure. Accepted to the 24rd IEEE International Conference on Intelligent Transportation Systems, 2021 more… Full text (mediaTUM)

### 2020

• Brüdigam, T.; Teutsch, J.; Wollherr, D.; Leibold, M.: Combined Robust and Stochastic Model Predictive Control for Models of Different Granularity. 21st IFAC World Congress, 2020 more… Full text ( DOI ) Full text (mediaTUM)
• Brüdigam, T.; di Luzio, F.; Pallottino, L.; Wollherr, D.; Leibold, M.: Grid-Based Stochastic Model Predictive Control for Trajectory Planning in Uncertain Environments. 2020 23rd IEEE International Conference on Intelligent Transportation Systems, 2020 more… Full text ( DOI ) Full text (mediaTUM)
• Causevic, V.; Fanger, Y.; Brüdigam, T.; Hirche, S.: Information-constrained Model-Predictive Control with Application to Vehicle Platooning. 21st IFAC World Congress, 2020 more… Full text (mediaTUM)

### 2018

• Brüdigam, T.; Ahmic, K.; Leibold, M.; Wollherr, D.: Legible Model Predictive Control for Autonomous Driving on Highways. IFAC-PapersOnLine 51 (20), 2018, 215-221 more… Full text ( DOI ) Full text (mediaTUM)
• Brüdigam, T.; Olbrich, M.; Leibold, M.; Wollherr, D.: Combining Stochastic and Scenario Model Predictive Control to Handle Target Vehicle Uncertainty in an Autonomous Driving Highway Scenario. 2018 21st International Conference on Intelligent Transportation Systems (ITSC), 2018, 1317-1324 more… Full text ( DOI ) Full text (mediaTUM)