# Real Time Shape Reconstruction for Near Earth Asteroid Landing


Knowledge of the shape of an asteroid is crucial for spacecraft operations. The standard method of determining the gravitational potential, through the use of a polyhedron potential model, is dependent on the shape model. Furthermore, accurate landing or low altitude operations requires accurate knowledge of the surface topology. The typical approach to shape determination requires an extensive mapping’’ phase of the mission over which extensive measurements are collected and transmitted for Earth-based processing. Instead, we present an efficient method for estimating the shape of an asteroid in real time. Range measurements of the surface are used to incrementally correct an initial shape estimate according to Bayesian framework. Then, an optimal guidance scheme is proposed to control the vantage point of the range sensor to construct a more accurate model of the asteroid shape. This shape model is then used in a nonlinear controller to track a desired trajectory about the asteroid. % Finally, a multi resolution approach is presented which enables for a higher fidelity shape representation in a specified location while avoiding the inherent burdens of a uniformly high resolution mesh. This approach enables for an accurate shape determination around a potential landing site. We demonstrate this approach using several radar shape models of asteroids and provide a full dynamic simulation about asteroid 4769 Castalia.