Real-Time Combinatorial Tracking of a Target Moving Unpredictably Among Obstacles

1. Hector H. Gonzales-Banos, Cheng-Yu Lee and Jean-Claude Latombe Real-Time Combinatorial Tracking of a Target Moving Unpredictably Among Obstacles Presented By: Amit Jain NUS CS5247

2. NUS CS5247 Outline • Introduction • Problem Statement • Approach • Evaluation • Future Work • Conclusion

3. NUS CS5247 Introduction Consider a scenario involving... Team of autonomous robots Performing independent tasks At a remote location Requirements for ideal debugger: Dynamic Environment Unmapped Territory

4. NUS CS5247 Problem Statement Maximize Escape Time Unknown Environment Nondeterministically uncertain target

5. NUS CS5247 Approach Acts = {} For each EscapePath ep ∈ SEP Acts = Acts ∪ maximizeEscapeTime(ep) BestAction = combine(Acts)

6. NUS CS5247 Approach: maximizeEscapeTime Basic Approach Maximize escape time Pros Directly addresses the problem Cons Computationally expensive to calculate Alternatives/Proxies Shortest Distance to Escape as proxy Risk Function as proxy

7. NUS CS5247 Approach: SDE Maximize Shortest Distance to Escape Pros Correct in holonomic case Related in non-holonomic case Cons Non-linear Relationship

8. NUS CS5247 Approach: Risk Function Minimize risk Pros: Polynomial relationship with SDE Considers pursuer's position

9. NUS CS5247 Approach • Acts = {} • For each EscapePath ep ∈ SEP • Acts = Acts ∪ maximizeEscapeTime(ep) • BestAction = combine(Acts)

10. NUS CS5247 Approach: Combining Actions Naive Approach: Average over actions Pros: Easy to Implement Intuitive Cons: Over Representation of Escape Paths Alternative Approach: Average over EPTs

11. NUS CS5247 Evaluation Influence of escape paths on risk Transient response of target tracker Tracking over long time

12. NUS CS5247 Future Work Extending to 3-D Learning the map

13. NUS CS5247 Conclusion Reactive target follower Novelties: Linear time calculation of escape path New proxy for escape time Avoids localization issues

14. NUS CS5247 Questions

15. NUS CS5247 Thank You