1. Autonomous Vehicles: Boundary Tracking and Control Laws By Jackie Brosamer June 19, 2008

2. Boundary Tracking Goal given a density field, we want the vehicle to find the boundary (where d(k) = B) and track along it Basic algorithm rotate one way when inside the boundary and the opposite way when outside boundary

3. Problem: Large initial crossing angle

4. Solution: We modify our algorithm based on the time it takes to cross the boundary t and a predetermined reference angle

6. CUSUM filter But this modification relies on accurate record of the boundary crossing times, so we need to find a way to deal eliminate noise in our data We implement a cumulative sum algorithm to create a “high side” filter and a “low side” filter to increase accuracy

8. Multiple vehicle boundary estimation We assume the approximate boundary is a Markov model based on the state of the system s(k)

9. Optimization We then assume the boundary can be represented by an ellipse and formulate boundary estimation as an optimization problem

11. Steering Control Laws Steer by altering the curvature of the vehicle’s path

12. Coupling Control Laws Local coupling allows vehicles to follow other vehicles within their field of vision Also, stronger coupling between a designated leader and followers

13. Homotopy parameter Governs between global control law and local control law

14. Target Seeking Separate control law, does not guarantee swarming

15. Barrier Avoidance Average barrier direction given by: We add the following term to steering control law :