Performance Guarantees for Collision Avoidance

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Performance Guarantees for Collision Avoidance

• Eric Rossetter
• Group Talk 5/17/02

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Outline

• Motivation
• Recap of linear results
• Lyapunov function for linear system
• Simulation results
• Conclusions/Future Work

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Motivation and Goals

• Potential field framework for collision avoidance
• How do we guarantee collision avoidance?

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Potential Field Summary

• Incorporate collision avoidance into driver
  assistance systems
• Control forces are derived from potential
  functions
• Vehicle handling characteristics are not changed

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Bounding Lateral Motion

• Given initial vehicle states how far will it move
  laterally
• Lyapunov Approach
• Create and energy like function of the states
• Show that the derivative of this function is
  negative semi-definite

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Hurdles in Finding Lyap. Functions

• Lateral motion is non-linear
• Total Energy is not a good bound for lateral
  motion
• The sum of kinetic and artificial potential
  energy in the lateral and yaw directions is not a
  Lyap. Function
• We know that one exists from the linear analysis!

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Linear System
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Linear Stability Results

• Control force must be applied in front of Neutral
  Steer Point

1. Control Force must come from a projection into
   the potential function

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Candidate Lyapunov Function
Potential Energy
Kinetic Energy
Other Stuff

• In order to be a Lyapunov function it must be
  positive definite
• The condition on the last term is

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Lyapunov Function Derivative
where,
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Lyapunov Function Derivative
Given a quadratic potential function
If we choose the lookahead distance to be
Using Sylvesters Criterion
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Non-linear Lyapunov Function

• Bounds the non-linear system
• Given knowledge of the states a potential
  function gain can be chosen to avoid a lateral
  obstacle

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Simulation
Potential Function Gain Chosen to Avoid Obstacle
0.75m away with initial conditions V40 m/s
y5 Degrees
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Conclusions/Future Work

• The presented Lyapunov function bounds the
  lateral motion of a vehicle
• Guarantees collision avoidance with fixed lateral
  obstacles
• Inclusion of road curvature and external
  disturbances