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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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