This paper presents a supervised machine learning state estimation scheme that is able to estimate the current side-slip angle of a vehicle. It consists of a recurrent neural network with gated recurrent units, an additional input projection and a regression head. This structure has been chosen to limit the computational complexity of the model while preserving the expressiveness of the overall system. It will also be shown how equations of a simplified vehicle model can be incorporated to make use of existing domain knowledge. The results show that the neural network is able to reach an excellent estimation quality while generalizing over different tires, surfaces and driving situations. Comparisons of different model variants on selected data subsets allow to draw conclusions on the adaptation to varying parameters and show a quality improvement through the physical model. Evaluations with the mean squared error are complemented by more expressive fit and error plots to give a better understanding of the model behavior. All data for this paper has been collected with a Porsche 911 Turbo (Type 991 II) with a series sensor setup and an additional reference sensor.

Physics-informed neural networks (PINN) can be used to predict flow fields with a minimum of simulated or measured training data. As most technical flows are turbulent, PINNs based on the Reynolds-averaged Navier–Stokes (RANS) equations incorporating a turbulence model are needed. Several studies demonstrated the capability of PINNs to solve the Naver–Stokes equations for laminar flows. However, little work has been published concerning the application of PINNs to solve the RANS equations for turbulent flows. This study applied a RANS-based PINN approach to a backward-facing step flow at a Reynolds number of 5100. The standard k-$\omega$ model, the mixing length model, an equation-free ${\nu }_t$ and an equation-free pseudo-Reynolds stress model were applied. The results compared favorably to DNS data when provided with three vertical lines of labeled training data. For five lines of training data, all models predicted the separated shear layer and the associated vortex more accurately.

Tendon-based parallel manipulators with n d.o.f. use at least m = n + 1 tendons to guide the end effector along a given trajectory. Since tendons can only transmit limited and tractive forces, it is essential to apply a valid tendon force distribution. Due to safety and precision requirements, a combined position and force control is needed where the force calculation delivers the desired tendon force distributions. The high dynamic potential of the robot demands for realtime capable algorithms. To avoid steps in the motor torques the calculated tension force distributions also have to be continuous along the trajectory. In this paper, a new algorithm for tendon force distribution calculations capable for usage on a realtime system is proposed and its continuity is proven.