1. Department of Mechanical
Stability Issues Using a ‘Virtual’ Forces Approach for Lanekeeping Assist Systems
Eric Rossetter
J. Christian Gerdes
Stanford University
Department of Mechanical
Engineering

2. Outline Motivation Potential Field Approach ‘Virtual’ Forces Analogy
Video Clip
‘Virtual’ Forces Analogy
Stability Issues Using Virtual Forces
Location of Virtual Force
Projection into Potential
Conclusions
Dynamic Design Lab
Stanford University
Stability Issues Using a ‘Virtual’ Forces Approach for Lanekeeping Assist Systems

3. 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.
Dynamic Design Lab
Stanford University
Stability Issues Using a ‘Virtual’ Forces Approach for Lanekeeping Assist Systems

4. 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
Dynamic Design Lab
Stanford University
Stability Issues Using a ‘Virtual’ Forces Approach for Lanekeeping Assist Systems

5. Lanekeeping Assistance on a 1997 Corvette C5
Dynamic Design Lab
Stanford University
Stability Issues Using a ‘Virtual’ Forces Approach for Lanekeeping Assist Systems

6. 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
Dynamic Design Lab
Stanford University
Stability Issues Using a ‘Virtual’ Forces Approach for Lanekeeping Assist Systems

7. Control Law Final System: Driver Controlled Forces (steering, braking)
Mass
Matrix
Uncontrolled
Forces (rear tire)
Replace with
Virtual Forces
Final System:
Dynamic Design Lab
Stanford University
Stability Issues Using a ‘Virtual’ Forces Approach for Lanekeeping Assist Systems

8. Creating a Virtual Force
The virtual control force can be created using a combination of steering and differential braking
Dynamic Design Lab
Stanford University
Stability Issues Using a ‘Virtual’ Forces Approach for Lanekeeping Assist Systems

9. Linear Stability Analysis
Linearize the system about a constant longitudinal velocity
Use a quadratic potential function
Dynamic Design Lab
Stanford University
Stability Issues Using a ‘Virtual’ Forces Approach for Lanekeeping Assist Systems

10. Stability Factors Using ‘Virtual’ Forces
Lateral stability is affected by several factors
Location of the control force
Vehicle dynamics
Lookahead into the potential
Dynamic Design Lab
Stanford University
Stability Issues Using a ‘Virtual’ Forces Approach for Lanekeeping Assist Systems

11. Control Force Location
For stability the control force must be applied in front of the neutral steer point of the vehicle
Neutral Steer
Point
Dynamic Design Lab
Stanford University
Stability Issues Using a ‘Virtual’ Forces Approach for Lanekeeping Assist Systems

12. 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
Dynamic Design Lab
Stanford University
Stability Issues Using a ‘Virtual’ Forces Approach for Lanekeeping Assist Systems

13. Lookahead
Projection into the potential will provide an adequate system response
Dynamic Design Lab
Stanford University
Stability Issues Using a ‘Virtual’ Forces Approach for Lanekeeping Assist Systems

14. 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
Dynamic Design Lab
Stanford University
Stability Issues Using a ‘Virtual’ Forces Approach for Lanekeeping Assist Systems

15. Ideal Lookahead Lookahead varied from 0-60m Dynamic Design Lab
Stanford University
Stability Issues Using a ‘Virtual’ Forces Approach for Lanekeeping Assist Systems

16. 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
Dynamic Design Lab
Stanford University
Stability Issues Using a ‘Virtual’ Forces Approach for Lanekeeping Assist Systems

17. 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
Dynamic Design Lab
Stanford University
Stability Issues Using a ‘Virtual’ Forces Approach for Lanekeeping Assist Systems

18. 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
Dynamic Design Lab
Stanford University
Stability Issues Using a ‘Virtual’ Forces Approach for Lanekeeping Assist Systems