Computing and Visualizing Reachable Volumes for Maneuvering Satellites
LAWRENCE LIVERMORE NATIONAL LAB CA
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Detecting and predicting maneuvering satellites is an important problem for Space Situational Awareness. The spatial envelope of all possible locations within reach of such a maneuvering satellite is known as the Reachable Volume RV. As soon as custody of a satellite is lost, calculating the RV and its subsequent time evolution is a critical component in the rapid recovery of the satellite. In this paper, we present a Monte Carlo approach to computing the RV for a given object. Essentially, our approach samples all possible trajectories by randomizing thrust-vectors, thrust magnitudes and time of burn. At any given instance, the distribution of the point-cloud of the virtual particles defines the RV. For short orbital time-scales, the temporal evolution of the point-cloud can result in complex, multi-reentrant manifolds. Visualization plays an important role in gaining insight and understanding into this complex and evolving manifold. In the second part of this paper, we focus on how to effectively visualize the large number of virtual trajectories and the computed RV. We present a real-time out-of-core rendering technique for visualizing the large number of virtual trajectories. We also examine different techniques for visualizing the computed volume of probability density distribution, including volume slicing, convex hull and isosurfacing. We compare and contrast these techniques in terms of computational cost and visualization effectiveness, and describe the main implementation issues encountered during our development process. Finally, we will present some of the results from our end-to-end system for computing and visualizing RVs using examples of maneuvering satellites.
- Unmanned Spacecraft