1. 1 Target Tracking u u Real Time Tracking of an Unpredictable Target Amidst Unknown Obstacles by Cheng Yu Lee, Hector Gonzalez-Banos and Jean Claude Latombe u u Real-time Combinatorial Tracking of a Target Moving Unpredictably Among Obstacles by Cheng Yu Lee, Hector Gonzalez-Banos and Jean Claude Latombe

2. 2 The Problem observer target observer target observer’s visibility region Goal: Keep the target in field of view despite obstacles No prior map of workspace Unknown target’s trajectory

3. 3 The Problem

4. 4 Corner Example: Pure visual servoing

5. 5 Corner Example: Anticipating Occlusion

6. 6 Steps of Tracking Algorithm Acquire visibility region / Locate target Compute shortest escape paths Associate risk with every shortest escape path and compute risk gradient Compute motion command as recursive average of risk gradients

7. 7 Acquisition of Visibility Region Target using horizontal laser scanner

8. 8 Steps of Tracking Algorithm Acquire visibility region / Locate target Compute shortest escape paths Associate risk with every shortest escape path and compute risk gradient Compute motion command as recursive average of risk gradients

9. 9 Shortest Escape Path (SEP) u Property of the SEP: ray of visibility from observer cut at most ones by each SEP. u We can use a ray sweep algorithm to build the SEP incrementally. (cf. theorem) Target Observer

10. 10

11. 11 Steps of Tracking Algorithm Acquire visibility region / Locate target Compute shortest escape paths Associate risk with every shortest escape path and compute risk gradient Compute motion command as recursive average of risk gradients

12. 12 Initial Risk-Based Strategy v e observer target Risk = 1/length of shortest escape path

13. 13 v p e observer target e’ p’ Initial Risk-Based Strategy Risk = 1/length of shortest escape path

14. 14 e observer target Improved Risk-Based Strategy (other case) look-ahead component v

15. 15 v p e observer target e” p”  i Improved Risk-Based Strategy reactive component look-ahead component

16. 16 Generic Risk Function v e observer target r h f(1/h) = ln ( + 1) h2h2h2h2 1  = = = =c r2r2r2r2 f(1/h) reactive look-ahead

17. 17 Results

18. 18 Steps of Tracking Algorithm Acquire visibility region / Locate target Compute shortest escape paths Associate risk with every shortest escape path and compute risk gradient Compute motion command as recursive average of risk gradients

19. 19 Computing the motion command  Basic idea: motion = -  e, but which escape path?

20. 20

21. 21 Example

22. 22 Corner Example

23. 23 Imagine yourself tracking a moving target in an unknown environment using a flashlight projecting only a plane of light!

24. 24 Transient Obstacles

25. 25 Steps of Tracking Algorithm Acquire visibility region / Locate target Compute shortest escape paths Associate risk with every shortest escape path and compute risk gradient Compute motion command as recursive average of risk gradients 0.1s

26. 26 Extension: adjustments for Real Robot Observer and target are modeled as disks Observer’s sensor has limited range (8m) and scope (180dg) Observer is nonhololomic with zero turning radius

27. 27 Conclusion Observer successfully tracks swift targets despite paucity of its sensor Fast computation of escape-path tree and risk gradient (control rate is ~ 10Hz) Future work: Multiple observers and multiple targets, more dynamic environments Could take into account the map it is building