A Hybrid Approach to Side-Slip Angle Estimation With Recurrent Neural Networks and Kinematic Vehicle Models

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 us 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 have been collected with a Porsche 911 Turbo (Type 991 II) with a series sensor setup and an additional reference sensor.

[1]  Mujahid Abdulrahim.  On the Dynamics of Automobile Drifting , 2006 .

[2]  Matt C. Best,et al.  An Extended Adaptive Kalman Filter for Real-time State Estimation of Vehicle Handling Dynamics , 2000 .

[3]  Andrew W. Senior,et al.  Long Short-Term Memory Based Recurrent Neural Network Architectures for Large Vocabulary Speech Recognition , 2014, ArXiv.

[4]  Yoshua Bengio,et al.  Learning long-term dependencies with gradient descent is difficult , 1994, IEEE Trans. Neural Networks.

[5]  Edoardo Sabbioni,et al.  On the vehicle sideslip angle estimation through neural networks: Numerical and experimental results , 2011 .

[6]  M. Struijk,et al.  Central Differential Control of an Active Four Wheel Drive Vehicle , 2015 .

[7]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[8]  Jürgen Schmidhuber,et al.  Learning to forget: continual prediction with LSTM , 1999 .

[9]  Harutoshi Ogai,et al.  Control of Yaw Angle and Sideslip Angle Based on Kalman Filter Estimation for Autonomous EV from GPS , 2017, IMECS 2017.

[10]  Tobias Ortmaier,et al.  State estimation of vehicle's lateral dynamics using unscented Kalman filter , 2014, 53rd IEEE Conference on Decision and Control.

[11]  Aldo Sorniotti,et al.  Enhancing vehicle cornering limit through sideslip and yaw rate control , 2016 .

[12]  Hiroyuki Yamaguchi,et al.  Development of Vehicle Stability Control System Based on Vehicle Sideslip Angle Estimation , 2001 .

[13]  Jürgen Schmidhuber,et al.  Long Short-Term Memory , 1997, Neural Computation.

[14]  Zachary Chase Lipton.  A Critical Review of Recurrent Neural Networks for Sequence Learning , 2015, ArXiv.

[15]  Jürgen Schmidhuber,et al.  Deep learning in neural networks: An overview , 2014, Neural Networks.

[16]  Yoshua Bengio,et al.  Learning Phrase Representations using RNN Encoder–Decoder for Statistical Machine Translation , 2014, EMNLP.

[17]  Sepp Hochreiter,et al.  Untersuchungen zu dynamischen neuronalen Netzen , 1991 .

[18]  Hans-Georg Zimmermann,et al.  Recurrent Neural Networks are Universal approximators , 2007, Int. J. Neural Syst..

[19]  Jürgen Schmidhuber,et al.  Learning Precise Timing with LSTM Recurrent Networks , 2003, J. Mach. Learn. Res..

[20]  Andreas Kugi,et al.  Unscented Kalman filter for vehicle state estimation , 2011 .

[21]  Hideaki Sasaki,et al.  A Side-Slip Angle Estimation Using Neural Network for a Wheeled Vehicle , 2000 .

[22]  J. Christian Gerdes,et al.  Autonomous Vehicle Control at the Limits of Handling , 2012 .

[23]  Yoshua Bengio,et al.  Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling , 2014, ArXiv.

[24]  Hans B. Pacejka,et al.  Tyre Modelling for Use in Vehicle Dynamics Studies , 1987 .

[25]  Dirk Langer,et al.  Up to the limits: Autonomous Audi TTS , 2012, 2012 IEEE Intelligent Vehicles Symposium.

[26]  Christopher M. Bishop,et al.  Pattern Recognition and Machine Learning (Information Science and Statistics) , 2006 .