By Tyler Brown
Learning how to control a car as a race driver does, at its very limits of handling, can ultimately assist ordinary drivers who enter a turn too quickly or are driving on a wet road and don’t realize when they need to brake. DGPS and inertial sensors drive feedback and feedforward speed controllers on a twisting test track to the top of Pikes Peak.
Stanford professor Chris Gerdes and his Dynamic Design Lab have outfitted and trained a white Audi to roar up the Pikes Peak International Hill Climb, a 12.5-mile racecourse to the top of the 14,110-foot Rocky Mountain summit.
Without a driver.
Officially known as the Autonomous Audi TTS Pikes Peak, the car has been nicknamed Shelley by its crew, in honor of Michele Mouton, the first woman to win the Hill Climb, in 1984, also in an Audi.
The team of graduate and Ph.D. students and Volkswagen’s Palo Alto research lab have spent two years conceptualizing and modifying the car to make the solo climb. They have just returned from tests of the car’s DGPS and other sensors on the course. International [human] racers competed on June 30, with the fastest just missing the course record of 10 minutes, 1.408 seconds, established in 2007, by a mere 10.082 seconds. That’s an average speed of 75 miles per hour over a course with 156 turns, many of them hairpins, an elevation gain of 4,721 feet, and both paved and gravel surfaces. Speeds at the Pikes Peak Hill Climb, often described by drivers as racing against the mountain more than other vehicles, top out around 165 miles per hour.
Shelley, not specifically built as a racecar, does not have the horsepower to hit that speed, but she aims for respectable rates all the same. “We are ultimately going for the fastest time we can get in a TTS and hope to establish that range in September and shoot for it in 2011,” wrote Gerdes from the mountain.
Safety the Goal. The team’s work is a variation on one theme: make Shelley drive faster, smarter — and safer.
“We believe that if we can learn how to control a car at its very limits of handling,” Gerdes said, “then we can also help ordinary drivers who enter a turn too quickly or are driving on a wet road and don’t realize when they need to brake. That’s ultimately where we hope this goes: safety systems.”
“Average drivers sometimes end up involved in road accidents due to their inability to control a vehicle at its limits,” Gerdes and Krisada “Mick” Kritayakirana wrote in a 2009 paper, from which the following results and figures are drawn, “yet racecar drivers routinely operate a vehicle at its limits without losing control. The difference could come from two key characteristics that racecar drivers have acquired.
“First, a racecar driver has the ability to estimate the friction between the tire and the road surface. Second, a racecar driver can utilize all of the actuators to control the vehicle at its limits, such as using the throttle and brakes to steer the vehicle, which could be counterintuitive to a typical driver. If a controller could imitate a racecar driver, perhaps this same concept could be applied to a vehicle safety system to assist drivers when they are on the verge of losing control. The controller could utilize every actuator to assist the driver, and real-time friction estimation could help predict the control authority that each actuator has. The goal of this research is to create a controller that captures these two key characteristics of a racecar driver.”
Feedforward, Feedback. Before entering a corner, a racecar driver anticipates the speed and steering angle that he or she would use. Similarly, in the Gerdes/Kritayakirana research, a feedforward controller is used to predict the speed and steering commands. While cornering, a racecar driver adjusts actuator commands (steering, throttle, and brake) to cope with any disturbances or driver’s perception mismatches (modeling errors). A feedback controller is designed to imitate a racecar driver making corrections during cornering. As a consequence, the desired steering and speed commands are calculated from the sum of feedforward and feedback controllers.
Robustness Tests. At Stanford, preliminary testing of Shelley’s control systems on the student-built P1 by-wire research vehicle provided a proof of concept. As with Shelley, P1’s DGPS and inertial sensors determine path-tracking errors that can be used to implement the steering feedback controller. A large parking lot with gravel over asphalt provided the ideal proving grounds for these tests. The inconsistent surface provided varying friction in the range of 0.4 to 0.6 and therefore presented a control challenge. The steering control had to be robust enough to ensure that this variation did not result in instability and the vehicle spinning.
The vehicle trajectory in Figure 1 shows performance of the steering feedback tested in isolation with an arbitrarily chosen constant accelerator input. Because the vehicle enters the curve much faster than the friction between the tire and the road can support, large deviations from the desired path (in this particular case, a maximum lateral error of 10.7 meters, and maximum heading error of 18.73 degrees) occur.
Although it swings wide of the desired path, P1 remains stable and does not spin out. The ability to maintain control of the car even when there is a misjudgment in the friction conditions is vitally important to both the Pikes Peak climb and future safety systems.
Demonstrating the robustness of the steering control both analytically and experimentally on P1 gave the team confidence to use it as a central part of Shelley’s control logic.
Combined Controllers. The current control scheme running on Shelley adds the feedforward steering and both feedforward and feedback speed control elements to the simple steering controller demonstrated in Figure 1.
This combination can track the desired path around the corner quite closely, as shown by the trajectory in Figure 2. This plot shows the performance on a rough dirt track with a friction coefficient again between 0.4 and 0.6 and therefore a maximum possible acceleration of between 4 and 6 meters/second2.
To demonstrate that Shelley is operating at the limits of friction, a g-g diagram is depicted in Figure 3. These diagrams, which are typically used to evaluate racecar driver performance, plot the longitudinal and lateral acceleration of the vehicle. An expert driver will achieve the maximum possible longitudinal acceleration in braking and the maximum lateral acceleration in cornering.
In transition between braking and cornering, the best drivers will use all available friction, giving the ideal curve a roughly circular shape. The g-g diagram for this test illustrates that Shelley continually operates at the limits of friction. As a result, the curve bears some resemblance to the behavior of an expert racecar driver. More precise comparisons with expert drivers driving the same course are planned for the future.
A Rich Legacy
Shelley follows in the tracks of other Stanford robot cars such Junior, an autonomous Volkswagen Passat. “Junior was a perceptual challenge,” Gerdes recalled. Junior and its predecessor Stanley, under the direction of Stanford professor Sebastian Thrun, were designed to perceive the environments around them, understand signs and recognize the driving situation of nearby vehicles, then logically respond to what they saw. Both competed in the Defense Advanced Research Projects Agency (DARPA) Grand Challenges.
Stanley and Junior, while possessing a much higher level of autonomy than Shelley and able to handle a range of environments, crept along at speeds well below the average driver’s comfort level, and placed little emphasis on driving dynamics. Shelley is highly focused on the dynamics issue.
“They’re all autonomous vehicles to some extent, but they have very different scopes, and I guess you could say, very different personalities as well,” Gerdes said.
“Can we go around turns as fast as possible, brake at the last possible minute, and accelerate out as soon as we’re steering out of a turn?” Gerdes asked. This became the group’s goal for Shelley.
Rami Hindiyeh had the task of crafting Shelley’s judgment. He writes software designed to mimic a rally car driver’s mind with a series of mathematical analyses that predict how the car should control itself in different situations. He looked at “ways to slide Shelley through turns like a rally car racer would.” Mick Kritayakirana is in charge of the autonomous racing controller to govern Shelley “at the limits, like racecar drivers race on the pavement.”
The Audi TTS’s steering, brakes, gears, and throttle are all controlled electronically, so Shelley required few mechanical modifications to integrate her systems into a controller area network that allows the vehicle’s components to communicate. The network enables the team to individually switch each component from manual to automatic so the team can test its reliability.
Shelley’s most critical components are GPS antennas and receivers coupled to an inertial system that determines speed and sideways motion. The INS controls the car’s direction during GPS signal interruptions, giving up to 200Hz updates on car position.
While the combined effects of Shelley’s systems are complex, the computer in the trunk that processes the data isn’t any faster than one you could buy a decade ago. Most calculations are done separately within the GPS and in the vehicle electronics. “We don’t need a whole lot of computational power to run the driving and racing algorithms,” Gerdes said.
“We have to spend a lot of time trying to make the car listen to what we command,” Kritayakirana added.
The Pikes Peak course was plotted on a GPS map for the car to follow, and based on that information and how much friction the computer predicts, it has an idea of how fast it can take turns at different angles and with varying road surfaces. The computer refines its speed and steering with each test turn to figure out what Gerdes calls Shelley’s “braking point.”
“When a human is driving a car and they see a turn coming up, they can, at a constant rate, so to speak, just try to turn the wheel towards that curve preemptively,” said team member David Hoffert. “And that works because roads are designed with certain mathematical geometric properties that if you do that, [you] follow the path.”
As the team nears the finish line, members continue to closely collaborate with Volkswagen’s research group. They have weekly meetings “where we talk about our current status and evaluate the hardware and software,” said Marcial Hernandez, senior research engineer at Volkswagen. The team aims to have Shelley back on the mountain in September. “We’d really like to send the car pretty close to its capability, certainly much, much faster than people would be comfortable driving unless they were highly skilled racecar drivers,” Gerdes said.
Pre-Race Tests
The team’s trip to Pikes Peak in July enabled the group to experience the International Hill Climb and watch some of the best racers in the world tackle the mountain. Following the hill climb, the project team devoted a couple of days to gathering GPS data on Pikes Peak. This included scouting locations for base stations to broadcast DGPS corrections and determining the availability of corrections at different points along the highway. In addition, the team took measurements of the road boundaries and profiles for developing digital maps of the course.
Line-of-sight issues for the GPS base stations and interference of other voice and DGPS users on the broadcast frequencies used by the team present challenges for racing on the mountain. The group made significant progress on these issues during the June experiments and has scheduled additional GPS testing for July. Travis Wolgram, a test engineer at the Association of American Railroads in Pueblo, Colorado, joined the group to discuss using the High Accuracy National DGPS system in future testing. With a prototype base station now operational at the Federal Railroad Administration’s Transportation Technology Center, 50 miles southeast of Pikes Peak, there is a unique opportunity to harness these corrections for the project.
Shelley should return to Pikes Peak in September, with the goal of driving the entire course slowly and selected segments at full race speed. With proper analysis of this data during the winter months when snow is on the mountain, the team should be prepared to make a full run at race speed in 2011.
Manufacturers
The Autonomous Audi TTS Pikes Peak uses an Applanix POS LV420 GPS and inertial measurement unit, with OmniStar HP service for 10-centimeter or better accuracy, Trimble SPS851 GPS receiver for the base station, two Trimble HPB450 transmitters for RTK signal transmission from the base station, and a Pacific Crest ADL Vantage receiver in the vehicle to receive the RTK corrections.
Tyler Brown is a Stanford undergraduate. An earlier version of this story appeared in the Stanford Daily; it has been updated and expanded here by the Dynamic Design Lab and GPS World staff.
