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Real Time Shape Reconstruction for Near Earth Asteroid Landing Open Access

Small solar system bodies, such as asteroids and comets, are of significant interest to the scientific community. These small bodies offer great insight into the early formation of the solar system. Of particular interest are those near-Earth asteroids (NEA) which inhabit heliocentric orbits in the vicinity of the Earth. These easily accessible bodies provide attractive targets to support space industrialization, mining operations, and scientific missions. Furthermore, these asteroids are of keen interest for more practical purposes. The recent meteor explosions in 2002 over Tagish Lake, Canada or over Chelyabinsk, Russia in 2013 are clear evidence of the risk of asteroid impacts on the Earth. These asteroids, which released an energy equivalent to 5 kt of TNT, are estimated to strike the Earth on average every year [1]. Larger bodies, such as the 60 m object that exploded over Tunguska, Russia in 1908, release the energy equivalent to 10 Mt of TNT and will occur on average every 1000 years. In spite of the significant interest in asteroid deflection, and the extensive research by the community, the operation of spacecraft in their vicinity remains a challenging problem. Research Question In this work, we develop an orbit and landing scheme for spacecraft onto an asteroid. The main objective is to construct the coupled equations of motion of a rigid spacecraft about an asteroid. This accurate dynamic model is then used to derive a nonlinear controller for the tracking of a landing trajectory. In contrast to much of the previous work, we explicitly consider the gravitational coupling between the orbit and attitude dynamics. In addition, we utilize a polyhedron potential model to represent the shape of the asteroid, which results in an exact closed form expression of the gravitational potential field [4, 5]. In order to determine the shape of the asteroid, we model a laser ranging sensor (LIDAR) on a maneuvering spacecraft. The LIDAR is able to provide depth measurements of the surface of the asteroid. Given a set of depth measurements it is possible to compute the shape, and hence gravitational potential of the asteroid. Computing the shape of the asteroid on a continual basis avoids the long delay and computational complexity of current asteroid operations. Furthermore, the updated gravitational model enables a spacecraft to autonomously transition from a mapping orbit directly to landing.

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