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

October 31, Motivation Terrain representation Smugglers and border guards

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

October 31, 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, Brute Force Comparison x100 test cases Average path length difference of 0.1% Average speed up of over % Chebyshev Heuristic Brute Force

October 31,

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

October 31, 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 Advanced Signal Processing Algorithms, Architectures, and Implementations XVII, San Diego CA, 27 August International Society for Optical Engineering. paper

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

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

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

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

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

October 31, 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, 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.