Self-organized control of spacecraft formation flying on irregular curves for cooperative observation

This paper comprehensively studies the self-organized deployment of a spacecraft cluster on a smooth irregular closed curve for cooperative on-orbit observation of a target spacecraft. The expected configuration curve is constructed by a set of control points through cubic B-spline interpolation, and it is closed and C2 continuous on the entire curve including its endpoints. As a necessary step for designing the control law, an efficient iterative algorithm for calculating the maneuvering spacecraft's nearest point on the curve is developed using Newton downhill method. Then the double-layer feedback controllers are designed, in which the inner controller makes the temporary target positions approximately uniformly converge to the curve, and the outer controller guides the actual positions to the temporary target positions. In this way, the spacecraft cluster can be accurately deployed on the desired curvilinear formation. The stability of the closed-loop system with the double-layer controller is also proved. Finally, a boat-shaped target configuration curve for comprehensively cooperatively observing a spherical target spacecraft is simulated and analyzed. The detailed results demonstrate that the designed self-organized control law can successfully achieve the desired formation flying with low control magnitude, acceptable accuracy, and reduce the influence of single spacecraft's failure to the final configuration's uniformity and the observation tasks.