Path Planning on a Compressed Terrain

Daniel M. Tracy, W. Randolph Franklin, Barbara Cutler, Franklin T. Luk, Marcus Andrade, Jared StookeyRensselaer Polytechnic Institute

October 31, 2008 2

Motivation

• Terrain representation

• Smugglers and border guards

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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

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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

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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.

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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.

PenaltyVisibilitytySlopePenalvhCost )( 22

h

v1

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Range of Motion

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

Chebyshev Euclidean

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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.

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Brute Force Comparison

100 100x100 test cases•Average path length difference of 0.1%•Average speed up of over 100.92%

ChebyshevHeuristicBruteForce

Chebyshev Heuristic Brute Force

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Test Data(400x400 DTED II)

Hill1

Mtn1

Hill2

Mtn2

Hill3

Mtn3

W111 N31

subsets

W121 N38

subsets

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Error Metrics

Path Cost Error: Difference of the costs of the paths computed on the original and alternate representations.

Alternate OriginalD. 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.

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Hill 3

Original Alternate

Elevation range: 500 mElevation stdev: 59 m

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Mtn 1

Original Alternate

Elevation range: 1040 mElevation stdev: 146 m

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Mtn 2

Original Alternate

Elevation range: 953 mElevation stdev: 152 m

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Ottawa LIDAR Data

• 2000x2000 grid• 19 minutes on

2.4 GHz CPU with 4 GB memory

• peak memory usage 360 MB

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Multiple Queries

• Sample a larger portion of the terrain by performing multiple path planning queries

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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

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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.