A new algorithm of solving for ranges during the final translation phase of spacecraft rendezvous and docking using computer vision system was presented to determine relative attitude and position between target and chase spacecraft by Quaternion Estimation. In this algorithm for ranges, a weighted objective function was constructed according to target pattern and geometry feature and used for solving for ranges. For both non-planar (such as three-point T-type and five-point pyramid type) and co-planar patterns (such as square, rectangle and rhombus), the objective function contained terms concerning ratios of distances between the target spots; but for co-planar targets, the objective function had another terms which describe co-planar feature. Gauss-Newton method was applied to solve for the optimum range solutions of the least squares problem. For quadrilateral patterns, the initial values for iterations were given by coordinates of virtual image of the intersection point of two diagonal lines. Extensive simulations, conducted for various target patterns with image coordinates errors, show that the range algorithm presented is quite effective for the relative state determination.
Mukundan R, Ramakrishnan K R. A quaternion solution to the pose determination problem for rendezvous and docking simulations[J].Mathematics and Computers in Simulation.1995, 39(2):143-153
Calboun P, Dabney R. A solution to the problem of determining the relative 6DOF state for spacecraft automated rendezvous and docking Fowski W J, Birnbaum M M. Proceedings of SPIE Space Guidance, Control and Tracking II. Orlando USA:SPIE Press, 1995:175-184