1. Performance Guarantees for Collision Avoidance Eric Rossetter Group Talk 5/17/02

2. Outline Motivation Recap of linear results Lyapunov function for linear system Simulation results Conclusions/Future Work

3. Motivation and Goals Potential field framework for collision avoidance How do we guarantee collision avoidance?

4. Potential Field Summary Incorporate collision avoidance into driver assistance systems Control forces are derived from potential functions Vehicle handling characteristics are not changed

6. 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

7. 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!

8. Linear System F

9. Linear Stability Results 1.Control force must be applied in front of Neutral Steer Point 2.Control Force must come from a projection into the potential function

10. Candidate Lyapunov Function In order to be a Lyapunov function it must be positive definite The condition on the last term is: Potential Energy Kinetic Energy Other Stuff

11. Lyapunov Function Derivative where,

12. Lyapunov Function Derivative Given a quadratic potential function If we choose the lookahead distance to be Using Sylvester’s Criterion

13. 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

14. Simulation Potential Function Gain Chosen to Avoid Obstacle 0.75m away with initial conditions: V=40 m/s  Degrees

15. 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