Model-Based Current Limiting for Traction Control of an Electric Four-Wheel Drive Race Car Daniel Bohl, Nikolaos Kariotoglou, Andreas B. Hempel, Paul J. Goulart, and John Lygeros Abstract— This paper describes a novel traction control method and its application to an electric four-wheel driven race car. The proposed control method is based on a detailed model of tire dynamics and is designed for hardware with limited memory and computational power. We derive a linear parameter-varying model from first principles and validate it against a full nonlinear vehicle model. We then use the model to design a gain-scheduled LQRI controller, parametric on the measured vehicle velocity and lateral acceleration. We show that when incorporating additional information about the tire state, a gain scheduled LQRI controller is capable of minimizing excessive wheel spin by limiting the maximum torque available to the driver. This leads to a performance gain in acceleration while improving the handling characteristics of the race car. The proposed controller is thoroughly tested for its sensitivity to sensor noise and changes in system parameters in simulation and then implemented on a prototype race car competing in Formula Student. Experiments indicate satisfactory exper- imental performance from the initial control design without additional tuning of the controller parameters. This illustrates the simplicity of the design and ease of implementation. I. I NTRODUCTION In recent years, various driver-assist systems have been implemented in passenger cars. These systems primarily focus on influencing longitudinal [1] or lateral [2] dynamics. As indicated by [3] and [4], one of the most challenging parts of driver assistance is traction control. In the most general sense, a traction controller is used to improve the handling in different driving situations and under different environmental conditions like rain or mud on the road. Most systems either limit the torque command of the driver or the speed of the wheel, which in turn influences the wheel slip [1]. The ultimate goal is to prevent the driver from applying too much torque to the driven wheels and losing longitudinal traction. The goal of the approach presented in this paper is to assist the driver of an electrically powered four-wheel driven race car competing in the Formula Student competition [5]. We achieve this with a traction control system that lim- its wheel-slip, known to be the main component of the traction force [6]. In this way, we help the driver achieve good acceleration performance during high-speed races while increasing longitudinal stability. Note that lateral stability The authors are with the Automatic Control Laboratory, ETH Z¨ urich, Physikstrasse 3, 8092 Z¨ urich, Switzerland, e-mail contact ad- dresses: dbohl@student.ethz.ch, {karioto, hempel, pgoulart, lygeros}@control.ee.ethz.ch. The research leading to these results has received funding from the Swiss Secretariat for Education and Research under COST-Action IC0806 and the European Union Seventh Framework Programme under grant agreement number FP7-ICT-257462 (HYCON2). is not an explicit goal of our approach since a certain amount of lateral instability increases the agility of the car which is beneficial to the cornering behaviour. Overall, the controller is able to assist the driver under racing conditions, improving the performance of the race car on the track. Using the designed controller the Academic Motorsportsclub Zurich (AMZ) competed against over 120 teams in Formula Student [5] winning two and scoring second in the other two major events becoming the world champion for 2013. Similar traction control problems have been addressed by many researchers. In several publications the main chal- lenge arises in the relation between slip and transmitted force, which is very difficult to model and highly non- linear [6]. As a result most approaches employ an estimator for the transmittable force and design controllers that react to changes. Several different control strategies like sliding- mode [7], fuzzy logic [8], adaptive schemes [9], model predictive control [10], or hybrid system approaches [11] have been proposed in the literature. In these approaches, tire data is not usually available or it varies substantially between different driving situations. For high performance race cars, the problem is fundamen- tally different. Due to extensive testing and the availability of additional sensor equipment a detailed model of the tire forces can be identified from measured data. Moreover, a traction controller for a passenger car must detect and adapt to all possible changes in environmental conditions while in a race car the driver or design team can manually switch between specially designed controllers for different condi- tions. Using additional sensor information we alleviate the estimation problem and can implement slip ratio regulation. Another crucial difference between our design and general traction controllers is that the dynamics of a race car differ significantly from the dynamics of the average passenger car. As a result, some typical simplifications, valid for the devel- opment of a classical traction controller, become invalid [12], [13]. The most significant of these simplifications is that all wheels can be modelled and controlled individually [9]. Because of the faster dynamics relative to a passenger car, coupling between the four wheels has to be introduced into the system model. This is due to weight transfer, which describes the shift in tire normal load depending on the driving situation and has a direct influence on the transmit- table force [1], [6]. Finally, it is important to consider that most race cars exist in prototype form which is subject to changes, making test time extremely limited. Any proposed controller must be simple enough to work immediately upon implementation without much reconfiguration of parameters 2014 European Control Conference (ECC) June 24-27, 2014. Strasbourg, France 978-3-9524269-1-3 © EUCA 1981