J Electr Eng Technol.2017; 12(2): 937-943 https://doi.org/10.5370/JEET.2017.12.2.937 937 Copyright ⓒ The Korean Institute of Electrical Engineers This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/ licenses/by-nc/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. Empirical Modeling of Steering System for Autonomous Vehicles Ju-Young Kim*, Kyungdeuk Min** and Young Chol Kim † Abstract – To design an automatic steering controller with high performance for autonomous vehicle, it is necessary to have a precise model of the lateral dynamics with respect to the steering command input. This paper presents an empirical modeling of the steering system for an autonomous vehicle. The steering system here is represented by three individual transfer function models: a steering wheel actuator model from the steering command input to the steering angle of the shaft, a dynamic model between the steering angle and the yaw rate of the vehicle, and a dynamic model between the steering command and the lateral deviation of vehicle. These models are identified using frequency response data. Experiments were performed using a real vehicle. It is shown that the resulting identified models have been well fitted to the experimental data. Keywords: Autonomous vehicle, Steering system, Automatic steering Control, Identification, Frequency response based modeling 1. Introduction Automatic steering control of vehicles has been investigated for both autonomous vehicles (AV) [1-3] and driver steering assistance [4, 5]. Driver steering assistance systems under development include collision avoidance systems, adaptive cruise control, and lane departure avoidance systems. The design of an automatic steering system requires a mathematical model that describes the lateral dynamic motion of the vehicle relative to the steering angle input. A variety of lateral dynamic models have been presented [1, 6-8]. These models are theoretically derived and are described in the form of nonlinear state equations that include a number of physical parameters. Additionally, linear approximate models are often used for the design of steering controllers. These models generally establish inputs as the steering angle of the wheels and the road curvature and output as the lateral deviation to the lane centerline at a look-ahead distance. The main difficulty with this approach is the precise identification of some of the physical parameters, such as, the location of the center of gravity, cornering stiffness, and moment of inertia. Moreover, these values are dependent upon tire model and susceptible to changes in payload. In this paper, we deal with empirical modeling of the steering system for an AV. We consider that the steering system of an AV consists of a steering handle actuator driven by a DC servo-motor, electric power assisted steering (EPAS), a column, gear, wheels, etc. We suppose that the dynamics of the steering system is linear at a fixed operating condition, which is the vehicle speed. This steering system is represented by three transfer function models; a steering actuator model ( ܩ ௔ ) from the steering command input to the steering angle of the steering shaft, a dynamic model ( ܩ ௬ ) between the steering angle and the yaw rate of the vehicle body, and an overall steering model (ܩ) from the steering command input to the lateral deviation of vehicle. These models are identified using frequency response data. Frequency responses were obtained through experimental tests on a real vehicle, which is an SUV adapted as an AV [7]. To obtain the pertinent response data, we first present a simple scheme that estimates the location and orientation of the vehicle individually from the measurement data using GPS, a gyroscope, and acceleration sensors. It is shown that the resulting identified models fits the measured data well. 2. Experimental Set-Up for Steering System Modeling The test vehicle is an SUV (Tucson ix, 2010, Hyundai Motor Co.) as shown in Fig. 1. It has been adapted as an autonomous vehicle by using various actuators and sensors including GPS, LIDAR, cameras, laptop computers etc. [7]. It is possible for us to examine this vehicle under the following operating conditions: (i) the vehicle can keep a predetermined constant speed; and (ii) steering commands of sinusoidal form with various frequencies can be applied to the steering wheel. The experimental set-up for the frequency response test is shown in Fig. 2. A software tool with LabVIEW (National Instruments Corp.) was developed so that one can set sinusoidal inputs † Corresponding Author: School of Electronic Eng., Chungbuk National University, Korea. (yckim @cbu.ac.kr) * Chungbuk Engineering Team, LG Uplus Corp., Korea. (procit@lguplus.co.kr) ** ADAS Engineering Design Team, Research & Development Division, Hyundai Motor Group, Korea. (kdmin@hyundai.com) Received: February 2, 2016; Accepted: December 26, 2016 ISSN(Print) 1975-0102 ISSN(Online) 2093-7423