Path Planning on a Compressed Terrain

1. Path Planning on a Compressed Terrain Daniel M. Tracy, W. Randolph Franklin, Barbara Cutler, Franklin T. Luk, Marcus Andrade, Jared Stookey Rensselaer Polytechnic Institute

2. Motivation • Terrain representation • Smugglers and border guards October 31, 2008

3. Terrain Compression • Must evaluate the information loss of the compression • Reconstitute the terrain from the compressed data to obtain the alternate representation • Compare the alternate representation against the original • Simple metrics such as RMS and max elevation error • More complex metrics such as visibility and path planning October 31, 2008

4. Outline • New path planning algorithm • Account for complex cost metric • Allow for full range of Euclidean motion on a 2D grid • Efficient on hi-res data • Novel error metrics to evaluate terrain compression October 31, 2008

5. Siting & Path Planning • Border guard placement: Multiple Observer Siting • Smuggler’s Path: Find the shortest path between two given points while trying to avoid detection by the observers. • A* algorithm • Add penalty for going uphill. October 31, 2008

6. Cost Metric • Cost of moving from one cell to an adjacent cell: • h is the horizontal distance. • v is the elevation difference. • SlopePenalty is when going uphill and 1 otherwise. • VisibilityPenalty is 1 if the new cell is not visible and 100 otherwise. October 31, 2008

7. Range of Motion Chebyshev Euclidean A straightforward application of the A* algorithm results in the Chebyshev distance being minimized, rather than the Euclidean distance. October 31, 2008

8. Path Planning • New approach: Two pass system • First pass: Plan a path that minimizes Chebyshev distance. • Second pass: Only include points from the first path in the search space. • Not guaranteed to be optimal, but in practice it often is. October 31, 2008

9. Brute Force Comparison Heuristic Chebyshev Brute Force • 100 100x100 test cases • Average path length difference of 0.1% • Average speed up of over 100. 92% October 31, 2008

10. October 31, 2008

11. Test Data(400x400 DTED II) W111 N31 subsets Hill2 Hill1 Hill3 W121 N38 subsets Mtn2 Mtn3 Mtn1 October 31, 2008

12. Error Metrics Path Cost Error: Difference of the costs of the paths computed on the original and alternate representations. Alternate Original D. M. Tracy, W. R. Franklin, B. Cutler, M. A. Andrade, F. T. Luk, M. Inanc, and Z. Xie. Multiple observer siting and path planning on lossily compressed terrain. In Proceedings of SPIE Vol. 6697 Advanced Signal Processing Algorithms, Architectures, and Implementations XVII, San Diego CA, 27 August 2007. International Society for Optical Engineering. paper 6697-16. October 31, 2008

13. Hill 3 Elevation range: 500 m Elevation stdev: 59 m Original Alternate October 31, 2008

14. Mtn 1 Elevation range: 1040 m Elevation stdev: 146 m Original Alternate October 31, 2008

15. Mtn 2 Elevation range: 953 m Elevation stdev: 152 m Original Alternate October 31, 2008

16. Ottawa LIDAR Data • 2000x2000 grid • 19 minutes on 2.4 GHz CPU with 4 GB memory • peak memory usage 360 MB October 31, 2008

17. Multiple Queries • Sample a larger portion of the terrain by performing multiple path planning queries October 31, 2008

18. Future Work • Scale visibility penalty by distance from observer • Make sure that the hidden areas are disconnected • Moving observers: Compute paths for tourists, smugglers • Red/Blue games: The blue team tries to hide; the red team tries to find them October 31, 2008

19. Summary Path Planning Algorithm • Accounts for complex cost metrics • Full range of Euclidean motion • Efficient on hi-res terrain • New error metrics derived from smugglers and border guards for evaluating terrain compression. October 31, 2008