Global reachability and path planning for planetary exploration with montgolfiere balloons

Aerial vehicles are appealing systems for possible future exploration of planets and moons such as Venus and Titan, because they combine extensive coverage with high-resolution data collection and in-situ science capabilities. Recent studies have proposed the use of a montgolfiere balloon, which controls its altitude by changing the heating rate or venting gas from the balloon, but has no actuation capability in the horizontal plane. A montgolfiere can use the variation in wind with altitude to guide itself to a desired location. This paper considers the problems of determining the altitude profile that the montgolfiere should follow in order to reach its target most quickly. We provide a new method that solves this path planning problem for all possible target locations, thereby providing a reachability analysis for the entire globe. The key idea is to perform a principled simplification and decoupling of the dynamics of the montgolfiere. We then discretize the search space, converting the planning problem into a graph search problem, and use Dijkstra´s algorithm to calculate the minimum-time path from the start location to every possible location in the graph. We demonstrate the approach on a possible Titan mission scenario.