Chang’E-4 (CE-4) was the first mission to accomplish the goal of a successful soft landing on the lunar farside. The landing trajectory and the location of the landing site can be effectively reconstructed and determined using series of images obtained during descent when there were no Earth-based radio tracking and the telemetry data. Here we reconstructed the powered descent trajectory of CE-4 using photogrammetrically processed images of the CE-4 landing camera, navigation camera, and terrain data of Chang’E-2. We confirmed that the precise location of the landing site is 177.5991°E, 45.4446°S with an elevation of −5935 m. The landing location was accurately identified with lunar imagery and terrain data with spatial resolutions of 7 m/p, 5 m/p, 1 m/p, 10 cm/p and 5 cm/p. These results will provide geodetic data for the study of lunar control points, high-precision lunar mapping, and subsequent lunar exploration, such as by the Yutu-2 rover.
Differential search (DS) is a recently developed derivative-free global heuristic optimization algorithm for solving unconstrained optimization problems. In this paper, by applying the idea of exact penalty function approach, a DS algorithm, where an S-type dynamical penalty factor is introduced so as to achieve a better balance between exploration and exploitation, is developed for constrained global optimization problems. To illustrate the applicability and effectiveness of the proposed approach, a comparison study is carried out by applying the proposed algorithm and other widely used evolutionary methods on 24 benchmark problems. The results obtained clearly indicate that the proposed method is more effective and efficient over the other widely used evolutionary methods for most these benchmark problems.
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