Rapid and accurate rendezvous and proximity operations for spacecraft are crucial to the success of most space missions. In this paper, a sequential convex programming method, combined with the first-order and second-order Birkhoff pseudospectral methods, is proposed for the autonomous rendezvous and proximity operations of spacecraft. The original nonlinear and nonconvex close-range rendezvous problem with thrust constraints and no-fly zone constraints is converted into its convex version by using the sequential convexification techniques; then, the Birkhoff pseudospectral method is used to transcribe the dynamic constraints into a series of linear algebraic equality constraints, in other words, a convex second-order conic programming problem with a relatively small condition number. Thus, the resulting problem can be accurately and efficiently solved by a convex solver. The simulation results indicate that the proposed methods, especially the second-order Birkhoff pseudospectral method, have obvious advantages over other methods in computational efficiency and sensitivity.

Most studies on map segmentation and recognition are focused on architectural floor plans, while there are very few analyses of shopping mall plans. The objective of the work is to accurately segment and recognize the shopping mall plan, obtaining location and semantic information for each room via segmentation and recognition. This work can be used in other applications such as indoor robot navigation, building area and location analysis, and three-dimensional reconstruction. First, we identify and match the catalog of a mall floor plan to obtain matching text, and then we use the two-stage region growth method we proposed to segment the preprocessed floor plan. The room number is then obtained by sending each segmented room section to an OCR (optical character recognition) system for identification. Finally, the system retrieves the matching text to match the room number in order to obtain the room name, and outputs the needed room location and semantic information. It is considered a successful detection when a room region can be successfully segmented and identified. The proposed method is evaluated on a dataset including 1340 rooms. Experimental results show that the accuracy of room segmentation is 92.54%, and the accuracy of room recognition is 90.56%. The total detection accuracy is 83.81%.