Stability Issues Using a

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Stability Issues Using a Virtual Forces
Approach for Lanekeeping Assist Systems

• Eric Rossetter
• J. Christian Gerdes
• Stanford University
• Department of Mechanical
• Engineering

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Outline

• Motivation
• Potential Field Approach
• Video Clip
• Virtual Forces Analogy
• Stability Issues Using Virtual Forces
• Location of Virtual Force
• Projection into Potential
• Conclusions

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Motivation and Goals

• A large percentage of vehicle fatalities are
  caused by lane departures.
• Lanekeeping assistance systems can help the
  driver remain in the lane.

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Potential Field Approach

• Virtual control forces are derived from
  artificial potential functions
• Control inputs are added on top of driver
  commands
• Vehicle handling characteristics are unchanged

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Lanekeeping Assistance on a 1997 Corvette C5
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The Virtual Force Analogy

• Assume a potential function where
  are the global coordinates of
  the vehicle
• Apply a virtual
• control force to the
• vehicle based on the
• gradient of the potential function

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Control Law
Driver Controlled Forces (steering, braking)
Mass Matrix
Uncontrolled Forces (rear tire)
Replace with Virtual Forces
Final System
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Creating a Virtual Force

• The virtual control force can be created using a
  combination of steering and differential braking

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Linear Stability Analysis

• Linearize the system about a constant
  longitudinal velocity
• Use a quadratic potential function

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Stability Factors Using Virtual Forces

• Lateral stability is affected by several factors
• Location of the control force
• Vehicle dynamics
• Lookahead into the potential

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Control Force Location

• For stability the control force must be applied
  in front of the neutral steer point of the vehicle

Neutral Steer Point
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Control Force Location

• The control force must be in front of the neutral
  steer point for stability but it does not
  guarantee a stable or well behaved response

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Lookahead

• Projection into the potential will provide an
  adequate system response

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Lookahead

• Although lookahead is well known for lateral
  stability the amount necessary depends on the
  location of the control force as well as vehicle
  speed

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Ideal Lookahead
Lookahead varied from 0-60m
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Generalizing Virtual Forces

• This framework is an intuitive way for
  understanding stability for other systems
• Autonomous Vehicle using PD control
• Results are useful for coordinating multiple
  actuators
• Steering and differential braking
• Four wheel steering

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Conclusions

• Virtual forces concept is a useful framework for
  stability
• Two important conditions for lateral stability
• Control force location is in front of the neutral
  steer point
• Control force must be based on a projection into
  the potential function

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Current/Future Work

• These stability results can be used to find
  analytic bounds on the lateral motion of the
  vehicle
• Test the lanekeeping assist system at higher
  speeds (30-40 mph)
• Driver acceptance of the lanekeeping system