Dr.-Ing. Tim Brüdigam

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

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

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

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

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.