A dynamic programming MPC approach for automatic driving along tracks and its realization with online steering controllers

The paper is concerned with the computation of trajectories along a given track for automatic cars using a dynamic programming approach in combination with a model predictive control strategy, which leads to a feedback control law providing a local reference trajectory. In addition, the setup of a testing environment using scale RC cars is described, which allows to verify and test control strategies in realtime. Results of experiments are presented that show the ability of the online controllers to track the reference paths at a good precision.

Structure Exploitation in an Interior-Point Method for Fully Discretized, State Constrained Optimal Control Problems

We discuss a direct discretization method for state-constrained optimal control problems and an interior-point method, which is used to solve the resulting large-scale and sparse nonlinear optimization problems. The main focus of the paper is on the investigation of an efficient method to solve the occurring linear equations with saddle-point structure. To this end, we exploit the particular structure that arises from the optimal control problem and the discretization scheme and use a tailored linear algebra solver alglin in combination with a re-ordering of the saddle-point matrices. Numerical experiments for a simple optimal control problem show a significant speed-up compared to state-of-the-art sparse LU decomposition methods like MA57 or MUMPS in combination with Ipopt.