Spatial Graphs Cost and Efficiency: Exploring Edges Competition by MCMC

Multivariate spatial central limit theorems with applications to percolation and spatial graphs

The Annals of Probability ◽

10.1214/009117905000000206 ◽

2005 ◽

Vol 33 (5) ◽

pp. 1945-1991 ◽

Cited By ~ 20

Author(s):

Mathew D. Penrose

Keyword(s):

Central Limit ◽

Limit Theorems ◽

Central Limit Theorems ◽

Spatial Graphs

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Robot navigation algorithms using learned spatial graphs

Robotica ◽

10.1017/s0263574700008559 ◽

1986 ◽

Vol 4 (2) ◽

pp. 93-100 ◽

Cited By ~ 54

Author(s):

S. S. Iyengar ◽

C. C. Jorgensen ◽

S. V. N. Rao ◽

C. R. Weisbin

Keyword(s):

Robot Navigation ◽

Sensor Data ◽

Two Dimensional ◽

Continuous Transition ◽

Spatial Graph ◽

Spatial Graphs ◽

Navigation Algorithms ◽

Sensor Information ◽

Navigation Planning ◽

Available Information

SUMMARYFinding optimal paths for robot navigation in a known terrain has been studied for some time but, in many important situations, a robot would be required to navigate in completely new or partially explored terrain. We propose a method of robot navigation which requires no pre-learned model, makes maximal use of available information, records and synthesizes information from multiple journeys, and contains concepts of learning that allow for continuous transition from local to global path optimality. The model of the terrain consists of a spatial graph and a Voronoi diagram. Using acquired sensor data, polygonal boundaries containing perceived obstacles shrink to approximate the actual obstacles surfaces, free space for transit is correspondingly enlarged, and additional nodes and edges are recorded based on path intersections and stop points. Navigation planning is gradually accelerated with experience since improved global map information minimizes the need for further sensor data acquisition. Our method currently assumes obstacle locations are unchanging, navigation can be successfully conducted using two-dimensional projections, and sensor information is precise.

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