Performance Guarantees for Hazard Based Lateral Vehicle Control Eric Rossetter J. Christian Gerdes Stanford University Department of Mechanical Engineering

Performance Guarantees for Hazard Based Lateral Vehicle Control Outline Motivation for Lanekeeping Assistance Systems Potential Field Approach ‘Artificial’ potential functions in control Implementing control forces derived from the potential Video Recap Linear Stability Results Linear Lyapunov Bounding Function Simulation Conclusions/Future Work Dynamic Design Lab Stanford University Performance Guarantees for Hazard Based Lateral Vehicle Control

Performance Guarantees for Hazard Based Lateral Vehicle Control Motivation and Goals A large percentage of vehicle fatalities are caused by lane departures. Active lanekeeping assistance systems can help the driver remain in the lane What performance guarantees can be placed on these systems? Dynamic Design Lab Stanford University Performance Guarantees for Hazard Based Lateral Vehicle Control

Potential Field Approach ‘Artificial’ potential energy is analogous to hazard level Control forces are derived from artificial potential functions Control inputs are added on top of driver commands Dynamic Design Lab Stanford University Performance Guarantees for Hazard Based Lateral Vehicle Control

Performance Guarantees for Hazard Based Lateral Vehicle Control Control Law Driver Controlled Forces (steering, braking) Inertial Forces Uncontrolled Forces (rear tire) Replace with Control Forces Final System: Dynamic Design Lab Stanford University Performance Guarantees for Hazard Based Lateral Vehicle Control

Creating a Virtual Force Steering & Differential Braking Dynamic Design Lab Stanford University Performance Guarantees for Hazard Based Lateral Vehicle Control

Creating a Virtual Force Steering only: Moment applied is dependent on the side force Dynamic Design Lab Stanford University Performance Guarantees for Hazard Based Lateral Vehicle Control

Performance Guarantees for Hazard Based Lateral Vehicle Control Potential Field Video Dynamic Design Lab Stanford University Performance Guarantees for Hazard Based Lateral Vehicle Control

Bounding Lateral Motion By design, the potential field controller is not a tracking controller Desirable to bound the lateral motion of the vehicle Question: Given a set of initial conditions, how should the potential function be scaled to avoid a collision or lane departure? Dynamic Design Lab Stanford University Performance Guarantees for Hazard Based Lateral Vehicle Control

Performance Guarantees for Hazard Based Lateral Vehicle Control Lyapunov Approach Create an energy-like function of the states positive definite negative semi-definite Dynamic Design Lab Stanford University Performance Guarantees for Hazard Based Lateral Vehicle Control

Controlled Vehicle Dynamics F Dynamic Design Lab Stanford University Performance Guarantees for Hazard Based Lateral Vehicle Control

Recap of Linear Stability Results Control force must be applied in front of the neutral steer point Control force must come from a projection into the potential function Dynamic Design Lab Stanford University Performance Guarantees for Hazard Based Lateral Vehicle Control

Creating a Candidate Lyapunov Function Are these derivable from a potential? Generalized Damping Forces Dynamic Design Lab Stanford University Performance Guarantees for Hazard Based Lateral Vehicle Control

Candidate Lyapunov Function All our forces are derivable from the potential or are generalized damping forces Candidate Lyapunov Fcn: Dynamic Design Lab Stanford University Performance Guarantees for Hazard Based Lateral Vehicle Control

Lyapunov Function Conditions Two conditions must be checked Condition 1: Using Sylvester’s Criterion: Dynamic Design Lab Stanford University Performance Guarantees for Hazard Based Lateral Vehicle Control

Performance Guarantees for Hazard Based Lateral Vehicle Control Lyapunov Conditions Condition 2: Using Sylvester’s Criterion: Therefore, is a Lyapunov function Dynamic Design Lab Stanford University Performance Guarantees for Hazard Based Lateral Vehicle Control

Using the Lyapunov Fcn. To Bound Lateral Motion How do we use this Lyapunov function to avoid collisions? Dynamic Design Lab Stanford University Performance Guarantees for Hazard Based Lateral Vehicle Control

Performance Guarantees for Hazard Based Lateral Vehicle Control Simulation Potential Function Gain Chosen to Avoid Obstacle 0.75m away with initial conditions: Ux=40 m/s, =5 Degrees Dynamic Design Lab Stanford University Performance Guarantees for Hazard Based Lateral Vehicle Control

Performance Guarantees for Hazard Based Lateral Vehicle Control Conclusions The presented Lyapunov function gives an analytic expression that yields useful bounds for lateral vehicle motion The structure of this function is useful in finding bounds for certain non-linearities Large heading angles Higher order potentials Dynamic Design Lab Stanford University Performance Guarantees for Hazard Based Lateral Vehicle Control

Performance Guarantees for Hazard Based Lateral Vehicle Control Future Work Add time varying external disturbances to the bounding function Road Curvature Driver Inputs Experimentally verify the results on the steer-by-wire test vehicle Dynamic Design Lab Stanford University Performance Guarantees for Hazard Based Lateral Vehicle Control