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U of M College of Engineering Control Seminar Series Sponsored by Eaton, Ford, General Motors, and Whirlpool |
An Energy-Based Approach to Driver
Assistance Systems
Professor J.
Christian Gerdes
Design Group
Department of
Mechanical Engineering
Stanford University
Abstract:
Each year there are approximately 40,000 fatalities on
US roadways, 40% of which result from a collision with a fixed obstacle in the
environment. Thousands of lives,
therefore, could be saved by simply helping the driver keep the vehicle in the
lane. This talk describes an
approach to driver assistance based on artificial potential fields that define
the lane boundaries as hazards with the minimum hazard in the center of the
lane. Analogous to a marble
rolling in a valley, the lanekeeping assistance system attempts to move the
vehicle back to the minimum hazard.
Mathematically, the system can be formulated in terms of Lagrangian
dynamics with the lankeeping system adding a force corresponding to the
gradient of the hazard potential on top of the existing vehicle dynamics. When the driver is tracking the lane,
the car feels exactly how it would without any assistance; as the driver
deviates from the center, the car gently adds an additional steering command,
producing an effect much like running in a shallow trough or being attached to
the road with a light spring.
Ideally, such a system provides only enough resistance
to keep the vehicle in the lane.
The energy theoretic foundation provides a way to guarantee this by
rigorously bounding the deviation from the lane center. This requires designing the controller so that a lower
dimensional subspace inherits the Lagrangian structure, ensuring the kinetic
energy in the longitudinal direction does not transfer into potential energy or
lane deviation. The bounds
provided are very tight, making this a practical design tool. In addition, the result is very
general, in essence bounding the effects of disturbances on Lagrangian systems
through the use of a strict Lyapunov function.
The system has been implemented on a 1997 Chevrolet
Corvette with differential GPS and steer-by-wire vehicle and performs as
predicted, demonstrating that the
approach is not only mathematically interesting but also practical. Thoughts on extending this energy-based
approach to other accident scenarios such as rollover conclude the talk.
3:30 – 4:30 p.m.