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This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE/ASME TRANSACTIONS ON MECHATRONICS 1 Designing Steering Feel for Steer-by-Wire Vehicles Using Objective Measures Avinash Balachandran and J. Christian Gerdes Abstract—Drivers use torque feedback at the handwheel of a production vehicles in 2013, artificially creating this feel be- vehicle, or steering feel, to obtain information about the road and comes increasingly important [4]. tire dynamics. This aids them in driving tasks like curve negotia- One way of creating steering feel on steer-by-wire vehicles tion. Steer-by-wire vehicles, due to the mechanical decoupling of the front tires and handwheel, do not have any inherent steering is to feedback the steering motor torque directly to the driver. feedback and require an artificial steering feel. One way to imple- Shengbing et al. demonstrated using hardware-in-the-loop sim- ment an artificial steering feel is to synthesize steering feedback ulation that steering motor current can generate steering feed- with a model running on board the vehicle. Identifying the appro- back [5]. Similarly, Asai et al. used a test bench setup to show priate level of model fidelity required involves understanding what that steering motor current coupled with a torque map can gener- elements of steering feel are important. This paper proposes using objective steering feel measures used in industry as a means of ate steering feel [6]. Though this technique generates a realistic understanding which elements of steering feel are most important. steering feel, this feel is tied to the physical properties of the It also introduces a steering feel model of appropriate fidelity to vehicle and cannot be varied easily in software. capture these important elements of steering feel while remain- Another way of creating steering feel is to use a steering model ing intuitive to tune objectively with a small set of parameters. with some abstraction of the physical system. Low fidelity mod- Experimental data show that the desired performance measures obtained via dynamic vehicle simulation can be replicated on an els, typically involving a spring model based on steering angle, actual steer-by-wire vehicle, validating the design technique. have been used on simulators by Segawa et al. [7] and Oh et al. [8]. Williams implemented a speed-varying spring model for Index Terms—Force feedback (FFB), haptic, objective measures, steer-by-wire, steering feel. steering feel on heavy trucks [9]. Low fidelity models, though simple to implement, cannot capture all the important elements of steering feel like power assist and “heaviness” of steering. In I. INTRODUCTION order to capture more elements of steering feel than low fidelity models, higher fidelity models have been used in simulators by RIVERS make extensive use of the torque feedback at the Salaani et al. [10] and Mandhata et al. [11]. Though higher fi- handwheel of a conventional vehicle (known as steering D delity models can capture more elements of steering feel, the feel) to obtain useful information about the road and tire dynam- increase in the number of model parameters makes tuning chal- ics. Using a driving simulator, Liu and Chang demonstrated that lenging. As a result, validation procedures such as the repeated having steering torque feedback results in better curve negoti- subjective human evaluations used by Mandhata et al. [12] are ation and skid recovery by a driver [1]. Forsyth and MacLean required. used a driving simulator and observed that without steering feed- Currently, conventional vehicles have wide variation of steer- back, drivers became disoriented in tight turns [2]. Similar re- ing feel. Steer-by-wire vehicles should not be different. There- sults have been found for driver assistance systems, for instance, fore, higher fidelity steering feel models, which can create a wide Switkes et al. showed that steering feedback must be carefully variation of steering feel, are necessary. However, as model fi- designed to ensure the stability of a lane-keeping controller [3]. delity increases, the tuning of these models to obtain desired Clearly, designing a good steering feel is important for driver feel becomes more challenging. Therefore, finding the appro- comfort and safety. priate level of steering model fidelity is critical. The model Steer-by-wire systems replace the mechanical steering must be complex enough to capture all the elements of steer- linkages between the handwheel and front tires with electronic ing feel that modern drivers care about while remaining simple sensors and actuators. This severing of the mechanical connec- enough to be tuned intuitively. This paper analyzes objective tion disrupts the steering feel, removing a useful source of driv- steering feel performance measures used by industry as a means ing feedback. As steer-by-wire technology moves into the first of understanding what elements of steering feel modern drivers care about. This paper then proposes using a steering feel model Manuscript received August 29, 2013; revised April 16, 2014; accepted May with the appropriate fidelity to capture these important elements 12, 2014. Recommended by Technical Editor B. Shirinzadeh. The work of while remaining intuitive to tune objectively with a small set of A. Balachandran was supported by the Herbert Kunzel Stanford Graduate Fel- parameters. lowship. The authors are with the Dynamic Design Laboratory, Department of This paper begins with a simple steering feel model which Mechanical Engineering, Stanford University, Stanford, CA 94305 USA captures the effect of tire torques, power assist and the modifica- (e-mail:[email protected]; [email protected]). tion of inherent inertia, and damping of a steer-by-wire steering Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. system. Objective steering feel performance measures used by Digital Object Identifier 10.1109/TMECH.2014.2324593 industry are then introduced as a means of understanding and 1083-4435 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications standards/publications/rights/index.html for more information. This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. 2 IEEE/ASME TRANSACTIONS ON MECHATRONICS Fig. 3. Typical suspension geometry on conventional vehicle. Fig. 1. Conventional steering system. conventional steering system. In conventional steering vehicles, there are three major torques that make up the steering feel. They are as follows: 1) tire moments; 2) torques due to inertia and damping; 3) torque due to power assist. The weighted sum of these torques result in the steering feel felt by the driver. 1) Tire Moments: Fig. 1 illustrates a conventional Fig. 2. FFB steering system. mechanical steering system with the right and left front lat- eral tire forces (Fyfr,Fyfl) and the right and left front normal tire forces (Fzfr,Fzfl) displayed. Fig. 3 illustrates a typical characterizing steering feel. These performance measures do suspension geometry of a conventional vehicle with the steer not depend only on the steering model but also on the vehi- axis, mechanical trail (tm ), pneumatic trail (tp ), caster angle cle dynamics. Using a simple dynamic vehicle simulation, a (θc ), kingpin angle (θk ), and scrub radius (d) indicated. The critical set of steering model parameters that tune these mea- moments generated by the lateral and normal tire forces about sures is identified and a desired feel is designed. Experimental the steer axis form a major component of steer feel. data then show that the desired performance measures obtained The moment about the steer axis generated by the lateral tire via dynamic vehicle simulation can be replicated on an actual forces is known as the aligning moment and is given by (see steer-by-wire vehicle. [13]) − 2 2 II. ARTIFICIAL STEERING FEEL τalignMoment = (Fyfl + Fyfr)(tm + tp ) cos θc + θk . In conventional steering systems, the handwheel is mechan- (2) ically connected to the roadwheels as illustrated in Fig. 1. In The aligning moment results in a strong self-centering torque at steer-by-wire vehicles, the handwheel is mechanically decou- higher speeds. pled from the roadwheels. The driver’s steering commands are The moment about the steer axis generated by the normal tire transferred electronically to motors that in turn actuate the road- forces is known as the jacking torque and is given by (see [13]) wheels. This mechanical decoupling removes much of the steer- τ = − (F + F ) dsin θ sin δ + ing feel that would normally be present in a conventional vehicle. jackingTorque zfl zfr k rw Steering feel can be artificially created in a steer-by-wire (Fzfl − Fzfr) dsin θc cos δrw (3) vehicle using a force feedback (FFB) steering system, illustrated where the δ is the roadwheel angle. The jacking torque in Fig. 2. For this system, the handwheel torque felt by a driver rw accounts for most of the self-centering effect of the steering (τ ) has the following dynamics: hw feel at low speed when the effect of the aligning moment is ¨ ˙ τhw = τmotor + Jsystemδhw + bsystemδhw (1) small. Transmission of the aligning moment and jacking torque via where the handwheel FFB motor torque (τ ) is commanded, motor the steering linkages to the handwheel results in these two tire the inherent system inertia (J ) and system damping system moments having a significant impact on the resultant steering (b ) are known from an identification of the mechanical system feel. system, and the handwheel angle (δ ) is a driver input. hw 2) Torques Due to Inertia and Damping: Fig. 1 illustrates that between the handwheel and the roadwheels, there exists a A. Conventional Steering Feel set of mechanical connections including the steering column, Developing an artificial steering feel for steer-by-wire ve- power assist unit, rack, and suspension, which results in the hicle involves having the FFB steering system feel like a steering system having some inherent damping and inertia.

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