Expected Shortest Paths for Landmark-Based Robot Navigation Amy Briggs Carrick Detweiler Daniel...
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Transcript of Expected Shortest Paths for Landmark-Based Robot Navigation Amy Briggs Carrick Detweiler Daniel...
Expected Shortest Paths for Landmark-Based Robot Navigation
Amy BriggsCarrick DetweilerDaniel ScharsteinAlexander Vandenberg-Rodes
Department of Computer ScienceMiddlebury College
Student collaborators
Carrick Detweiler ‘04
David Ehringer ‘03
Deniz Sarioz ‘01
Alexander Vandenberg-Rodes
Lily Fu ‘03
Fafa Paku ‘02
Student collaborators
Darius Braziunas ‘00
Victor Dan ‘03
Huan Ding ‘03
Dan Knights ‘01
Jeff Lanza ‘01
Pete Wall ‘01
Related Work Fennema et al. 1990
Kavraki & Latombe 1994 Lazanas & Latombe 1995 Simmons & Koenig 1995 Taylor & Kriegman 1995 Nickerson et al. 1998 Owen & Nehmzow 1998 Blei & Kaelbling 1999 Mani et al. 1999 Thrun et al. 2000
Navigation using visual landmarks
Explore mode: build graph of landmark locations and visibility information Navigate mode: use graph to plan paths between landmarks
B
C
AD
Exploration Algorithm
Find an initial landmark and servo to it While untraversed edges exist in the graph, do: While current landmark has an untraversed
outgoing edge, do: Perform an observation Travel the shortest untraversed edge to another
landmark Update graph
Use ESP algorithm to go to the closest landmark with an untraversed outgoing edge
Navigation Algorithm
While not at destination landmark, do: Run ESP algorithm to find expected
shortest path Try to go to first landmark in path If that fails, do until successful:
Try next most optimal path If unable to leave current landmark:
Perform an observation, update graph, and rerun ESP algorithm
Localization Algorithm
Perform a “partial explore” to build a graph based on the robot’s internal coordinatesCompare new graph with previously built graph of environmentCalculate x, y, and theta offsets between the two graphs
Relation to MDPs
Problem is a special instance of aMarkov decision process (MDP)
Each visibility scenario is one state(2d states per node)
Our algorithms correspond to1. Value iteration2. Policy iteration
G
A
B
5
2
3
1.0
0.5 0.5
AGE Expected length of shortest path from A to G
)5,3,2min(25.0
)3,2min(25.0
)5,2min(25.0
)2(25.0
BGAG
BGAG
AG
AGAG
EE
EE
E
EE
Two Competing Algorithms
Value Iteration Evaluates system of equations Many iterations
Policy Iteration Solve linear system of equations Matlab sparse matrix solver
Algorithmic Evaluation
Generated realistic graphs (50,000+) Corridor graphs Multi-room graphs
Varied parameters Number of nodes and edges
Up to 25,000 nodes Range of edges: sparse to dense
Probability of edges Very low (.0001-.001) to full (.0001-1)
Results
Value Iteration Many iterations to converge Very slow on sparse graphs
Policy Iteration Runtime only slightly affected by density Real-time performance on most graphs Higher memory requirements O(N2)
Acknowledgments
Thanks to Steve Abbott and Deniz Sarioz for insightful contributions, and to Darius Braziunas, Victor Dan, Cristian Dima, Huan Ding, David Ehringer, Lily Fu, Dan Knights, Jeff Lanza, Fafa Paku, and Peter Wall for their work on the implementation of the navigation framework.
Supported in part by NSF grants IIS-0118892, CCR-9902032, CAREER grant 9984485, POWRE grant EIA-9806108, by Middlebury College, by the Howard Hughes Medical Institute, and by the Council on Undergraduate Research.