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# Decomposition Algorithm for Global Reachability on a Time-Varying Graph

- Monday, 01 November 2010

### This method sequentially solves a series of small problems instead of a single large problem.

A decomposition algorithm has been developed for global reachability analysis on a space-time grid. By exploiting the upper block-triangular structure, the planning problem is decomposed into smaller subproblems, which is much more scalable than the original approach.

Recent studies have proposed the use of a hot-air (Montgolfier) balloon for possible exploration of Titan and Venus because these bodies have thick haze or cloud layers that limit the science return from an orbiter, and the atmospheres would provide enough buoyancy for balloons. One of the important questions that needs to be addressed is what surface locations the balloon can reach from an initial location, and how long it would take. This is referred to as the global reachability problem, where the paths from starting locations to all possible target locations must be computed.

The balloon could be driven with its own actuation, but its actuation capability is fairly limited. It would be more efficient to take advantage of the wind field and “ride” the wind that is much stronger than what the actuator could produce. It is possible to pose the path planning problem as a graph search problem on a directed graph by discretizing the space-time world and the vehicle actuation.

The decomposition algorithm provides reachability analysis of a time-varying graph. Because the balloon only moves in the positive direction in time, the adjacency matrix of the graph can be represented with an upper block-triangular matrix, and this upper block-triangular structure can be exploited to decompose a large graph search problem. The new approach consumes a much smaller amount of memory, which also helps speed up the overall computation when the computing resource has a limited physical memory compared to the problem size.

*This work was done by Yoshiaki Kuwata of Caltech for NASA’s Jet Propulsion Laboratory. For more information, contact This email address is being protected from spambots. You need JavaScript enabled to view it.. NPO-46941*