Hierarchical visibility for guaranteed search in large-scale outdoor terrain

Searching for moving targets in large environments is a challenging task that is relevant in several problem domains, such as capturing an invader in a camp, guarding security facilities, and searching for victims in large-scale search and rescue scenarios. The guaranteed search problem is to coordinate the search of a team of agents to guarantee the discovery of all targets. In this paper we present a self-contained solution to this problem in 2.5D real-world domains represented by digital elevation models (DEMs). We introduce hierarchical sampling on DEMs for selecting heuristically the close to minimal set of locations from which the entire surface of the DEM can be guarded. Locations are utilized to form a search graph on which search strategies for mobile agents are computed. For these strategies schedules are derived which include agent paths that are directly executable in the terrain. Presented experimental results demonstrate the performance of the method. The practical feasibility of our approach has been validated during a field experiment at the Gascola robot training site where teams of humans equipped with iPads successfully searched for adversarial and omniscient evaders. The field demonstration is the largest-scale implementation of a guaranteed search algorithm to date.

[1]  Richard E. Korf,et al.  Moving Target Search , 1991, IJCAI.

[2]  Jorge Cortes,et al.  Distributed Control of Robotic Networks: A Mathematical Approach to Motion Coordination Algorithms , 2009 .

[3]  T. D. Parsons,et al.  Pursuit-evasion in a graph , 1978 .

[4]  Jack Bresenham,et al.  Algorithm for computer control of a digital plotter , 1965, IBM Syst. J..

[5]  Richard M. Karp,et al.  Reducibility Among Combinatorial Problems , 1972, 50 Years of Integer Programming.

[6]  Giora Slutzki,et al.  Clearing a Polygon with Two 1-Searchers , 2009, Int. J. Comput. Geom. Appl..

[7]  Sourabh Bhattacharya,et al.  On the Existence of Nash Equilibrium for a Two-player Pursuit—Evasion Game with Visibility Constraints , 2010 .

[8]  Steven M. LaValle,et al.  Visibility-Based Pursuit-Evasion in an Unknown Planar Environment , 2004, Int. J. Robotics Res..

[9]  T. Shermer Recent Results in Art Galleries , 1992 .

[10]  Geoffrey A. Hollinger,et al.  Searching the Nodes of a Graph: Theory and Algorithms , 2009, ArXiv.

[11]  Rainer E. Burkard,et al.  Linear Assignment Problems and Extensions , 1999, Handbook of Combinatorial Optimization.

[12]  Alexander Kleiner,et al.  Real-time localization and elevation mapping within urban search and rescue scenarios: Field Reports , 2007 .

[13]  Leonidas J. Guibas,et al.  A Visibility-Based Pursuit-Evasion Problem , 1999, Int. J. Comput. Geom. Appl..

[14]  Stefano Carpin,et al.  On Weighted Edge-Searching , 2009 .

[15]  W. T. Tutte Graph Theory , 1984 .

[16]  Dariusz Dereniowski,et al.  Connected searching of weighted trees , 2010, MFCS.

[17]  Lynne E. Parker,et al.  Multi-Robot Systems: From Swarms to Intelligent Automata , 2002, Springer Netherlands.

[18]  Nathan R. Sturtevant,et al.  Partial Pathfinding Using Map Abstraction and Refinement , 2005, AAAI.

[19]  Stefano Carpin,et al.  Pursuit-Evasion on Trees by Robot Teams , 2010, IEEE Transactions on Robotics.

[20]  Richard M. Karp,et al.  Reducibility among combinatorial problems" in complexity of computer computations , 1972 .

[21]  Geoffrey A. Hollinger,et al.  GSST: anytime guaranteed search , 2010, Auton. Robots.

[22]  Ian D. Reid,et al.  Automatic partitioning of high dimensional search spaces associated with articulated body motion capture , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[23]  Charles Elkan,et al.  The paradoxical success of fuzzy logic , 1993, IEEE Expert.

[24]  A. Volgenant,et al.  A shortest augmenting path algorithm for dense and sparse linear assignment problems , 1987, Computing.

[25]  Nathan R. Sturtevant,et al.  Evaluating Strategies for Running from the Cops , 2009, IJCAI.

[26]  Svetlana Lazebnik,et al.  Visibility-Based Pursuit-Evasion in Three-Dimensional Environments , 2011 .

[27]  Katia P. Sycara,et al.  Pursuit-evasion in 2.5d based on team-visibility , 2010, 2010 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[28]  G. Gallo,et al.  A multi-level bottleneck assignment approach to the bus drivers' rostering problem , 1984 .

[29]  Christos H. Papadimitriou,et al.  The complexity of searching a graph , 1981, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981).

[30]  Sebastian Thrun,et al.  Parallel Stochastic Hill- Climbing with Small Teams , 2005 .

[31]  D. R. Lick,et al.  Theory and Applications of Graphs , 1978 .

[32]  Hanan Samet,et al.  The Design and Analysis of Spatial Data Structures , 1989 .

[33]  Sven Koenig,et al.  Speeding up moving-target search , 2007, AAMAS '07.

[34]  Steven M. LaValle,et al.  Visibility-Based Pursuit-Evasion with Bounded Speed , 2008, WAFR.

[35]  Stefano Carpin,et al.  Multi-robot surveillance: An improved algorithm for the GRAPH-CLEAR problem , 2008, 2008 IEEE International Conference on Robotics and Automation.

[36]  Howie Choset,et al.  Coverage for robotics – A survey of recent results , 2001, Annals of Mathematics and Artificial Intelligence.

[37]  Masafumi Yamashita,et al.  Searching for a Mobile Intruder in a Polygonal Region , 1992, SIAM J. Comput..

[38]  Geoffrey A. Hollinger,et al.  Anytime Guaranteed Search using Spanning Trees , 2008 .

[39]  Ming Fan,et al.  A review of real-time terrain rendering techniques , 2004, 8th International Conference on Computer Supported Cooperative Work in Design.

[40]  Andrea S. LaPaugh,et al.  Recontamination does not help to search a graph , 1993, JACM.

[41]  Alexander Kleiner,et al.  Behavior maps for online planning of obstacle negotiation and climbing on rough terrain , 2007, 2007 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[42]  Dirk Schulz,et al.  A probabilistic approach to coordinated multi-robot indoor surveillance , 2005, 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[43]  Alexander Kleiner,et al.  Real‐time localization and elevation mapping within urban search and rescue scenarios , 2007, J. Field Robotics.

[44]  Paul D. Seymour,et al.  Monotonicity in Graph Searching , 1991, J. Algorithms.

[45]  Dimitrios M. Thilikos,et al.  An annotated bibliography on guaranteed graph searching , 2008, Theor. Comput. Sci..

[46]  Jeffrey J. P. Tsai,et al.  Route planning for intelligent autonomous land vehicles using hierarchical terrain representation , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[47]  T. C. Shermer,et al.  Recent results in art galleries (geometry) , 1992, Proc. IEEE.

[48]  J. Koenderink,et al.  The internal representation of solid shape with respect to vision , 1979, Biological Cybernetics.

[49]  Stefano Carpin,et al.  Extracting surveillance graphs from robot maps , 2008, 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[50]  Francesco Bullo,et al.  Distributed Control of Robotic Networks , 2009 .

[51]  Sven Koenig,et al.  Algorithms and Complexity Results for Pursuit-Evasion Problems , 2009, IJCAI.

[52]  Raymond E. Miller,et al.  Complexity of Computer Computations , 1972 .

[53]  Lali Barrière,et al.  Capture of an intruder by mobile agents , 2002, SPAA '02.

[54]  Boting Yang,et al.  Sweeping Graphs with Large Clique Number , 2004, ISAAC.