Vehicle Testing with P1 at Moffett Field

Current Researchers

Yung-Hsiang (Judy) Hsu
Shad Laws
Professor Chris Gerdes

Sponsors

Nissan Motor Company
The National Science Foundation

Test Run Videos

Experimental data were collected at Moffett Federal Airfield at a constant, moderate speed (13.6 m/s, or 30 mph) with standard tires. This video clip displays the right-hand ramp steer maneuver we performed from 0 to -10 degrees at the roadwheels (click 'save target as' to download and view the file) [.mpg] [.mov]. The resulting front lateral force and slip angle obtained from this manuever, and continual data fits performed to characterize the tire curve, are shown here [.avi].

Additional experimental data were obtained with Hoosier autocross racing tires at Altamont Motorsports Park. This video clip shows one of the test runs where P1 pulled 1.4 g's of lateral acceleration [.mov] [.avi] click 'save link as' to download and view the file). Notice the steel outriggers that were constructed and installed on P1 to prevent the danger of vehicle rollover.

Research Description

During everyday driving, a vehicle usually operates in the linear region of handling and responds predictably to the driver’s inputs. As the vehicle approaches its handling limits, for example during an aggressive or evasive emergency maneuver, the response is less predictable. If the front tires saturate first, the vehicle is said to limit understeer and may plow out of a curve. If the rear tires saturate first, the vehicle limit oversteers and may spin out. Race car drivers are very sensitive to these effects and carefully compensate for them with their steering commands. This allows them to routinely perform near the limits of handling while maintaining control of their vehicles. In contrast, because the average driver is not accustomed to operating in the nonlinear handling regime, both under- and oversteering responses are potentially very dangerous.

Current advances in vehicle sensing technology, such as GPS and steer-by-wire systems, allow us to actively compensate for under- and oversteering effects and enable any driver to drive up to the handling limits safely without loss of control. The overall approach is to: (1) sense if the tire forces are saturating, (2) use steer-by-wire steering inputs to actively compensate for saturating tire forces to achieve a predictable, stable vehicle response, and (3) saturate the driver steering input to keep the vehicle within control. The details of the control system are outlined below.

I. Tire Parameter Estimation

As the motion of a vehicle is governed by the forces generated between the tires and the road, knowledge of the tire forces is crucial to predicting vehicle motion. The lateral forces necessary for a vehicle to hold a curve arise as a result of tire deformation. Shown in the figure below, the relationship between the lateral force and slip angle is initially linear, with a constant slope of Ca, referred to as the cornering stiffness.

Lateral Force Tire Curve

When the force begins to saturate due to limited friction on the road, the tire enters the nonlinear operating region. The maximum lateral force available defines the vehicle’s handling limits. This peak force is the product of the coefficient of friction mu and the vertical tire load.
Since Ca and mu characterize the lateral force-slip relationship, real-time knowledge of these parameters enables the controller to predict vehicle motion, and thus is powerful information for purposes of vehicle control. Using a combination of GPS and INS sensors, it is possible to estimate the tire slip angle. In addition, sensors in a steer-by-wire system allow the self-aligning torque at the road wheels to be estimated. From this, we can find the lateral force on the front tires by modeling the pneumatic and mechanical trails.

With both the lateral force and slip angle of the front tires known, we have developed a method that applies an iterative technique, nonlinear least squares (NLS), that best fits data to the nonlinear tire model to estimate Ca. To estimate mu, the estimation technique is slightly more involved. First, the algorithm determines whether the tire has entered the saturation region. It fits the force-slip data to both a linear least squares (LS) line through the origin and applies a NLS fit to the nonlinear tire model (shown in the figure below). If the NLS fit error is sufficiently smaller than the linear fit error, the algorithm concludes that the tire is operating in the saturation regime and that there is enough information to estimate mu.

Experimental Tire Curve with LS and NLS Fits

II. Feedback Linearizing Controller

Given the estimate of Ca and mu, we can model the motion of the vehicle based on the nonlinear tire forces. The vehicle dynamics can be controlled using input-output state feedback linearization, a control technique that transforms known nonlinear dynamics into a simple linear system. For this application, feedback linearization uses steer-by-wire inputs to cancel out the nonlinearities of the vehicle model. In other words, the controller compensates for saturating tire forces with changes in the steer-by-wire steering commands. Once nonlinearities are eliminated, the system may be controlled to follow the desired trajectory using linear control theory. Since most drivers are accustomed to a vehicle response resulting from linear tire forces, the controller attempts linearize the dynamics to achieve a predictable, safe response.

III. Driver Input Saturation

Feedback linearization is feasible until the physical limits of the tire grip are reached. Once the slip angle grows too large, the controller implements a driver saturation algorithm to keep us in the linearizable handling region, maintaining the stability of the vehicle. Secondly, it also alerts the driver of the approaching limits of handling. Although the idea of limiting the driver steering input may be alarming at first, one must realize that the road will naturally saturate out the driver’s steering capability in the absence of a controller. The tire has finite grip to the road. At some point during an aggressive cornering maneuver, the available tire forces to complete the turn will saturate and the resulting vehicle motion will diverge from what the driver expects. This may result in an unstable spin out or an oscillatory trajectory. Unlike the road’s natural saturation effect, attenuation of the driver’s steering input in this algorithm allows the control system to safely limit the steering capability in a predictable manner.

Publications

Yung-Hsiang Judy Hsu and J. Christian Gerdes, "Stabilization of a Steer-by-wire Vehicle at the Limits of Handling Using Feedback Linearization." Proceedings of the 2005 ASME International Mechanical Engineering Congress and Exposition, Orlando, Florida. [pdf] [IMECE05 Presentation]

Yung-Hsiang Judy Hsu and J. Christian Gerdes, "A Feel For the Road: A Method to Estimate Tire Parameters Using Steering Torque" 2006 Symposium on Advanced Vehicle Control (AVEC), Taipei, Taiwan. [pdf] [AVEC06 Presentation]

Yung-Hsiang Judy Hsu, Shad Laws, Christopher D. Gadda, and J. Christian Gerdes, "A Method to Estimate the Friction Coefficient and Tire Slip Angle Using Steering Torque" Proceedings of the 2006 ASME International Mechanical Engineering Congress and Exposition, Chicago, Illinois. [pdf] [IMECE06 Presentation]

Yung-Hsiang Judy Hsu, Shad Laws, and J. Christian Gerdes, "Experimental Studies of Using Steering Torque Under Various Road Conditions for Sideslip and Friction Estimation" Proceedings of the 2007 IFAC Symposium on Advances in Automotive Control, Monterey, California. [pdf] [AAC07 Presentation]