Connectivity preservation and collision avoidance control for spacecraft formation flying in the presence of multiple obstacles

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This paper addresses connectivity preservation and collision avoidance problem of spacecraft formation flying with multiple obstacles and parametric uncertainties under a proximity graph. In the proximity graph, each spacecraft can only get the states of the neighbor spacecraft within its sensing region. Connectivity preservation of a graph means that the connectivity of the graph should be preserved at all times during spacecraft formation flying. We consider two cases: (i) the obstacles are static, and (ii) the obstacles are dynamic. In the first case, a distributed continuous control algorithm based on artificial potential function and equivalent certainty principle is proposed to account for the unknown parameters and the static obstacles. In the second case, a sliding surface combined with a distributed adaptive control algorithm is proposed to tackle the influence of the dynamic obstacles and the unknown parameters at the same time. With the distributed control algorithms, the desired formation configuration can be achieved while the connectivity of the graph is preserved and the collisions between the spacecraft and the obstacles are avoided. Numerical simulations are presented to illustrate the theoretical results.