Research Description

Motivation

Automobiles have become indispensable in our modern society. Consequently, vehicle safety has tremendous importance in our everyday lives. For some perspective, according to a report published by NHTSA in 2008, motor vehicle crashes continue to be the leading cause of death for children, teens, and young adults in the United States. Worldwide, an estimated 1.2 million people are killed in road crashes each year and as many as 50 million are injured. Projections by the World Health Organization in 2004 indicate that these figures will increase by about 65% over the next 20 years unless there is new commitment to prevention.

Over the past few decades, vehicle control systems have been developed to enhance vehicle handling and passenger safety. These systems seek to prevent unintended vehicle behavior through active vehicle control and assisting drivers in maintaining control of their vehicles. Among them, Anti-lock Brake Systems (ABS), Traction Control Systems (TCS), and Electronic Stability Control (ESC) are examples of automotive braking technologies that have improved handling and helped drivers avoid potentially dangerous situations.

Unfortunately, current systems are limited by the lack of knowledge of the vehicle's state and operating conditions. Knowledge of the vehicle's sideslip angle, which is the angle between the vehicle's heading direction and actual velocity, is important information that is largely unavailable for current safety systems. The tire's lateral handling limits, which is the maximum grip a tire has on the road during a turn, are also generally unknown.

As a result of this limited information, production stability control systems rely on detecting a difference between intended and actual vehicle yaw rate before the system can intervene. In other words, current systems are reactive; they must detect a problem before corrective action can be taken. If onboard systems had accurate knowledge of sideslip angle (and therefore tire slip angle) and could predict the peak lateral force limits, control systems could anticipate rather than react to loss of control situations, further enhancing vehicle handling and increasing passenger safety.

Exploring the Benefit of Steering Torque for Estimation

Recently, researchers have looked at utilizing a new source of information for detecting the vehicle’s lateral limits: steering torque. Steering torque is the total torque about a tire's steer axis resulting from tire forces, the driver, and system actuators. Steering torque measurements are available in research vehicles with steer-by-wire or production vehicles with Electric Power Steering (EPS) or Active Steering. Just as a skilled race car driver can sense the limits of tire adhesion through the steering wheel feel, steering torque is a promising new source of information for estimating the vehicle's lateral handling capability for safety systems.

Why is steering torque useful for lateral limit detection? Steering torque has the potential to provide information about the tire's lateral limits because it includes the moment induced by lateral tire force.

The figure below illustrates how lateral force is generated from tire deformation, both for a high friction and a low friction surface, assuming a parabolic pressure distribution in the contact patch. It depicts the tire traveling towards the right, starting on the left with zero lateral deformation (traveling straight) and ending on the right at the point where the required lateral force exceeds the available friction (skidding out of the page, towards the reader). The angle of tire deformation, or the difference between the tire's heading and velocity, is referred to as slip angle.

Lateral Force Generation as Slip Angle Grows

As slip angle increases, the lateral force distribution grows in area, which is represented by a shaded triangular area under the tire. However, the lateral force obtained is ultimately limited by the friction limit of the road, which is the product of the tire-road friction coefficient and the tire normal force.

We also observe from the figure that the effective lateral force does not act directly at the center of the contact patch. Rather, it acts at a distance known as the tire pneumatic trail, which induces a moment (known as self-aligning moment). As slip angle increases, the effective lateral force moves toward the center of the patch. This results in pneumatic trail vanishing once the force distribution reaches the limit of tire adhesion, the rate of which depends on the available peak friction.

From this illustration, it is clear why pneumatic trail information contained in steering torque is so advantageous for estimation – its dependence on the friction limits is apparent even at small slip angles, which opens up the possibility to estimate your vehicle’s lateral limits of adhesion even at modest lateral accelerations.

Recognizing the benefits of pneumatic trail information in steering torque for estimation, our main focus is the development and experimental validation of estimation methods which utilize the early lateral limit information contained in steering torque measurements. We have constructed a nonlinear observer for estimating tire slip angle and the peak lateral force limits (and the tire-road coefficient of friction if normal force is known). The method relies on sensors available in many production vehicles, eliminating the need for costly sensor technologies. Mathematically guaranteed to converge in the presence of estimation error, the method has also been validated experimentally. Testing conditions include maneuvers performed on dry, flat paved road at Moffett Field (see picture below), as well as on lower-friction, dry gravel at the Shoreline parking lot.

For more information on these estimation methods, as well as details on the nonlinear observer, we invite you to browse our publication list.

Onboard driver view from test vehicle P1 during test run

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Envelope Control

Given early information of a vehicle's lateral limits, even with changing road conditions or tire properties, we can begin to imagine a more holistic approach to ensure vehicle safety. In aviation, a well-known integrated control strategy is envelope protection (also known as carefree handling). Envelope protection uses available actuators to prevent an aircraft from entering state or control regions outside of the safe flight regime. Limitations are often imposed on an aircraft's state, such as angle of attack, airspeed, bank angle and altitude

The idea of envelope protection, or envelope control, could similarly be extended to land vehicles. During normal driving, drivers would be able to freely maneuver the vehicle. However, if there is danger of crossing the limits, the steering controller would engage and assist the driver in staying within operating bounds.

Experimental Validation of Envelope Control System

Two experimental maneuvers are presented here from the combined observer and control system implemented onboard P1 on loose gravel at the Shoreline parking lot. During each of the following maneuvers, the nonlinear observer developed in the previous section is running in real-time, providing the controller with estimates of tire slip angle and the peak friction limits.

Controller Off

The first maneuver presented is a dropped throttle oversteer maneuver. You can view a video clip of this maneuver here (click 'save target as' to download and view the file) [.wmv].

What’s happening during this maneuver? By letting go of the throttle suddenly during the turn, the driver applies the regenerative brakes of the drive motors of the rear wheels, inducing longitudinal weight transfer to the front axle. Because the vehicle is already cornering near the limits of handling, braking causes the rear tires to lose traction, creating an oversteer condition. With the envelope controller off, the vehicle ends up in an unstable spin.

This maneuver demonstrates that in experiment, without a stabilizing controller or a well-timed driver countersteer, a dropped throttle oversteer results in an unstable spin (illustrated in the overhead view of the car trajectory in the figure below).

Dropped Throttle Vehicle trajectory, No Control

Controller On

The second experimental maneuver presented is a series of three consecutive dropped throttle oversteer maneuvers. For this maneuver, the controller is on. A video clip of this maneuver is available for view here (click 'save target as' to download and view the file) [.wmv].

Each drop throttle event highlights an important characteristic of the envelope control system. Let’s walk through each drop throttle separately.

1st Dropped Throttle
For the first dropped throttle event, the driver again engages the rear regenerative brakes during the turn. Without corrective action, this would result in the rear tires losing traction and pushing the car into an unstable spin similar to what was illustrated before. With the envelope control system on, however, the onboard estimator senses that the rear tire forces are near their limits of traction. Using the proportional feedback controller and steer-by-wire actuation, a steer angle is added on top of the driver command, resulting in a quick countersteer that brings the rear slip angle back into the safe operating envelope. This corrective action is similar to what race car drivers would do to stabilize their vehicle with steering commands.

2nd Dropped Throttle
In the second dropped throttle event, the driver initiates her own countersteering correction to stabilize the vehicle. Because the driver successfully counteracts the potential instability, the envelope controller's steering action is minimal and simply serves to marginally increase the magnitude of the countersteer.

3rd Dropped Throttle
The final dropped throttle event provides a good example of the controller having to make two steering corrections in quick succession (see figure below). In this maneuver, after the driver initiates the first dropped throttle, the controller senses the rear tire saturation and countersteers to immediately reduce yaw rate, which eventually decreases the sideslip angle and stabilizes the vehicle. However, shortly afterward, the driver speeds up, commanding an additional longitudinal drive force that reinitiates the rear axle slide. This produces a spike in rear slip angle, at which point the controller must countersteer for a second time and for a longer duration.

Dropped Throttle Vehicle trajectory, With Control

These results indicate that the combined controller and observer system is able to keep tire forces within their limits and prevent unstable vehicle motion. In instances where the driver makes a self-correction, these results suggest that the controller’s intervention is minimal.

Conclusions

Tire pneumatic trail is a valuable source of information for lateral tire characterization by enabling early detection of the limits before they are reached. Our work presented an estimation method that utilizes pneumatic trail information contained in steering torque measurements to characterize lateral tire force. Experimental results on two friction surfaces demonstrated that the limits of handling can be predicted once the tires have utilized only 50% of their maximum lateral force. In other words, this method has shown that friction limit detection is possible before the tires have exited the linear handling regime.

Ongoing work is aimed at integrating the estimation method with a stability controller to keep the vehicle operating in a safe handling envelope. The overall observer performance could be improved on P1 with the installation of rear axle load-cell sensors, which would enable direct sensing of the rear tire friction limits. Future work could also incorporate longitudinal tire forces and dynamics in the estimation models to enable accurate estimation when the car is braking or accelerating.

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