Design of relative motion and attitude profiles for three-dimensional resident space object imaging with a laser rangefinder

This paper focuses on the aerospace application of a single beam laser rangefinder (LRF) for 3D imaging, shape detection, and reconstruction in the context of a space-based space situational awareness (SSA) mission scenario. The primary limitation to 3D imaging from LRF point clouds is the one-dimensional nature of the single beam measurements. A method that combines relative orbital motion and scanning attitude motion to generate point clouds has been developed and the design and characterization of multiple relative motion and attitude maneuver profiles are presented. The target resident space object (RSO) has the shape of a generic telecommunications satellite. The shape and attitude of the RSO are unknown to the chaser satellite however, it is assumed that the RSO is un-cooperative and has fixed inertial pointing. All sensors in the metrology chain are assumed ideal. A previous study by the authors used pure Keplerian motion to perform a similar 3D imaging mission at an asteroid. A new baseline for proximity operations maneuvers for LRF scanning, based on a waypoint adaptation of the Hill-Clohessy-Wiltshire (HCW) equations is examined. Propellant expenditure for each waypoint profile is discussed and combinations of relative motion and attitude maneuvers that minimize the propellant used to achieve a minimum required point cloud density are studied. Both LRF strike-point coverage and point cloud density are maximized; the capability for 3D shape registration and reconstruction from point clouds generated with a single beam LRF without catalog comparison is proven. Next, a method of using edge detection algorithms to process a point cloud into a 3D modeled image containing reconstructed shapes is presented. Weighted accuracy of edge reconstruction with respect to the true model is used to calculate a qualitative “metric” that evaluates effectiveness of coverage. Both edge recognition algorithms and the metric are independent of point cloud densit- , therefore they are utilized to compare the quality of point clouds generated by various attitude and waypoint command profiles. The RSO model incorporates diverse irregular protruding shapes, such as open sensor covers, instrument pods and solar arrays, to test the limits of the algorithms. This analysis is used to mathematically prove that point clouds generated by a single-beam LRF can achieve sufficient edge recognition accuracy for SSA applications, with meaningful shape information extractable even from sparse point clouds. For all command profiles, reconstruction of RSO shapes from the point clouds generated with the proposed method are compared to the truth model and conclusions are drawn regarding their fidelity.