Efficient Virtual Design and Testing of Autonomous Vehicles - Peitz, Sebastian; Dellnitz, Michael; Bannenberg, Sebastian (German Success Stories in Industrial Mathematics)
With the ever increasing capabilities of sensors and controllers, autonomous driving is quickly becoming a reality. This disruptive change in the automotive industry poses major challenges for manufacturers as well as suppliers as entirely new design and testing strategies have to be developed to remain competitive. Most importantly, the complexity of autonomously driving vehicles in a complex, uncertain, and safety-critical environment requires new testing procedures to cover the almost infinite range of potential scenarios.

Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control - Dellnitz, Michael; Eckstein, Julian; Flaßkamp, Kathrin; Friedel, Patrick; Horenkamp, Christian; Köhler, Ulrich; Ober-Blöbaum, Sina; Peitz, Sebastian; Tiemeyer, Sebastian (Progress in Industrial Mathematics at ECMI 2014)
During the last years, alternative drive technologies, for example electrically powered vehicles (EV), have gained more and more attention, mainly caused by an increasing awareness of the impact of CO2 emissions on climate change and by the limitation of fossil fuels. However, these technologies currently come with new challenges due to limited lithium ion battery storage density and high battery costs which lead to a considerably reduced range in comparison to conventional internal combustion engine powered vehicles. For this reason, it is desirable to increase the vehicle range without enlarging the battery. When the route and the road slope are known in advance, it is possible to vary the vehicles velocity within certain limits in order to reduce the overall drivetrain energy consumption. This may either result in an increased range or, alternatively, in larger energy reserves for comfort functions such as air conditioning. In this presentation, we formulate the challenge of range extension as a multiobjective optimal control problem. We then apply different numerical methods to calculate the so-called Pareto set of optimal compromises for the drivetrain power profile with respect to the two concurrent objectives battery state of charge and mean velocity. In order to numerically solve the optimal control problem by means of a direct method, a time discretization of the drivetrain power profile is necessary. In combination with a vehicle dynamics simulation model, the optimal control problem is transformed into a high dimensional nonlinear optimization problem. For the approximation of the Pareto set, two different optimization algorithms implemented in the software package GAIO are used. The first one yields a global optimal solution by applying a set-oriented subdivision technique to parameter space. By construction, this technique is limited to coarse discretizations of the drivetrain power profile. In contrast, the second technique, which is based on an image space continuation method, is more suitable when the number of parameters is large while the number of objectives is less than five. We compare the solutions of the two algorithms and study the influence of different discretizations on the quality of the solutions. A MATLAB/Simulink model is used to describe the dynamics of an EV. It is based on a drivetrain efficiency map and considers vehicle properties such as rolling friction and air drag, as well as environmental conditions like slope and ambient temperature. The vehicle model takes into account the traction battery too, enabling an exact prediction of the batterys response to power requests of drivetrain and auxiliary loads, including state of charge.

Multiobjective Optimal Control Methods for the Development of an Intelligent Cruise Control - Dellnitz, Michael; Eckstein, Julian; Flaßkamp, Kathrin; Friedel, Patrick; Horenkamp, Christian; Köhler, Ulrich; Ober-Blöbaum, Sina; Peitz, Sebastian; Tiemeyer, Sebastian (Mathematics in Industry)

Modelling and Analysis of the Nonlinear Dynamics of the Transrapid and Its Guideway - Dellnitz, Michael; Dignath, Florian; Flaßkamp, Kathrin; Molo, Mirko Hessel-von; Krüger, Martin; Timmermann, Robert; Zheng, Qinghua (Mathematics in Industry)

Modelling and Analysis of the Nonlinear Dynamics of the Transrapid and Its Guideway - Dellnitz, Michael; Dignath, Florian; Flaßkamp, Kathrin; Molo, Mirko Hessel-von; Krüger, Martin; Timmermann, Robert; Zheng, Qinghua (Mathematics in Industry)