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Master Thesis - Model predictive control approach to vehicle trajectory planning

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 The Model Predictive Control (MPC) approach to vehicle trajectory planning for Autonomous Driving is based on using Non-Linear Programming (NLP) to optimize the EGO-vehicle trajectory over a prediction horizon from the current EGO-vehicle position, heading and velocity. The optimization criterion and constraints are designed to enable comfortable and safe cruise and comfortable and safe lane changes.

The MPC approach to vehicle trajectory planning is widely used in the academia with a large number of available publications. However, since most of these publications do not consider the uncertainty and interaction with surrounding traffic, it is difficult to assess the tractability of the approach when used in the Autonomous Drive system. For example, in order to avoid overconfident planning and risk taking, the NLP-MPC vehicle trajectory planner must somehow consider the uncertainty in the trajectories of surrounding vehicles. A way to include this uncertainty, is to model surrounding vehicles with scenario trees that in the NLP results in constraints on the EGO-vehicle trajectory. The scenario trees are also affecting the optimization criterion which is typically composed of a comfort constraint based on the distance to surrounding vehicles and a comfort penalty on the lateral jerk and acceleration of the EGO-vehicle. A drawback with the scenario approach is that number of variables will increase exponentially with the number of scenarios thereby increasing the computational complexity.

Moreover, in order to be able to plan and execute lane changes and enter the highway from the on ramp in dense traffic, the constraints that model the motion of surrounding vehicles must be setup so that the EGO-vehicle is to some extent able to slow down the motion of vehicles coming from the rear.

With the available computational power in the next generation vehicles will the MPC-NLP approach be possible to extend to include the uncertainty and interaction with surrounding traffic or will the computational complexity still be too high?


Project Description 

In this master thesis project, you will evaluate the tractability of the Model predictive control approach to vehicle trajectory planning by studying

  • how to include comfort constraints and penalties to enforce smoothness of the trajectory,
  • how to model uncertainty in surrounding traffic (scenario trees, soft constraints, ...),
  • bench-marking commercial and open source solvers for the vehicle trajectory planning problem and evaluate the computational complexity when the problem is solved on the next generation core computing platforms.


    We are looking for candidates with a background in optimization, dynamic systems and modelling. Skills in C++ and or Python are meriting.


      Further information

      Final application date: 2022-11-30. Please send in individual applications with CV, motivational letter, and grade transcripts. If you wish to partner with someone, simply note that in your application.

      Planned start: 2022-01-15, with some flexibility.

      Duration: 30 ECTS

      For questions regarding the project, please contact:
      Lars Mårdh: lars.johannesson.mardh@zenseact.com
      Giuseppe Giordano: giuseppe.giordano@zenseact.com

      Gabriel Campos: gtabriel.campos@zenseact.com

      Additional information

      • Remote status

        Flexible remote

      Or, know someone who would be a perfect fit? Let them know!

      Gothenburg, Sweden

      Lindholmspiren 2
      417 56 Gothenburg, Sweden Directions View page


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