Decentralized Robust Adaptive Control for Attitude Synchronization Under Directed Communication Topology

Abstract

T HE need to maintain accurate relative orientation between spacecraft is critical in many satellite formation missions. For instance, in interferometry application, the relative orientation between spacecraft in a formation is required to be maintained precisely during formation maneuvers. In interspacecraft laser communication operation, the participating spacecraft are also required to maintain accurate relative attitude throughout the communication process. This control problem, commonly referred to as attitude synchronization in the literature, has attracted much research attention. Various solutions have been proposed and these can be broadly classified according to the advocated techniques: leader– follower [1–4], virtual structure [5,6], behavior-based [7–11], and graph-theoretical approach [12–15]. In particular, the graph-theoretical approach has been actively studied for cooperative control of multi-agent system using limited local interaction [16,17] and was adopted for attitude synchronization problem in [12–15]. In the above-cited decentralized attitude synchronization results, except [14,15], it is assumed that the interspacecraft communication links are undirected (i.e. bidirectional). However, in practice, the interspacecraft communication topology may be restricted to be directed, such as in unidirectional satellite laser communication system. The control problem of attitude synchronization under directed communication topology is more challenging as compared with the case with undirected communication topology. This issue was studied in [14] but the proposed control law requires derivative of the angular velocity, which may introduce additional noise into the system. Furthermore, the attitude-tracking performance analysis in [14] is applicable only to the casewhere the directed graph can be simplified to a graph with only one node. This constraint on communication topology is relaxed in [15], which uses modified Rodriguez parameters and Euler– Lagrange system to describe the satellite attitude dynamics. However,modifiedRodriguez parameters contain singularity and are thus not suitable for the development of globally stabilizing control algorithms. This Note proposes a decentralized adaptive sliding-mode control lawwhich regulates attitude and angular velocity errors of individual spacecraft with respect to reference commands and minimizes relative attitude and angular velocity errors between spacecraft. Thus, the proposed control law ensures that each spacecraft attains desired time-varying attitude and angular velocity while maintaining attitude synchronization with other spacecraft in the formation even in the presence of model uncertainties and external disturbances. Moreover, the design is applicable to general communication topology and is not restricted to ring topology or undirected communication topology. In the following section, unit quaternion representation will be introduced into the satellite attitude control problem and algebraic graph theory will be applied to describe general directed communication topology.