Spacecraft (SC) formation flying is a new technology which plays an important role in the future space missions such as NASA’s Terrestrial Planet Finder (TPF) Mission and Space Telescope assembly [76, 77], the European Space Agency’s (ESA) simi-lar mission, called Darwin [78], among many others. Several algorithms have been proposed for the attitude and/or position synchronization and control of multiple SC in deep space and in low orbit [16, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91].
In this thesis, we consider attitude synchronization and tracking, therefore, we re-view recent literature on this topic in this subsection. Position synchronization
problem for spacecraft formation flying missions is not considered in this thesis.
The single SC attitude control and fault-tolerant attitude control with/without using angular velocity measurement is also studied in the literature [92, 93, 94, 95, 96]. Reference [79] is one of the earliest papers on coordinated attitude control of SC. This paper investigates the use of one-leader, multiple-leader, and barycenter coordination strategies. The one-leader coordination strategy requires that one SC serves as the reference SC, the leader, for the rest of the SC, the followers, in the formation. The followers then track the leader, possibly with a constant offset. The multiple-leader approach involves splitting the formation into two or more groups and assigning one or more fleet leaders. In this case, the fleet leaders act as the reference SC for the group leaders, which in turn, act as the reference SC for the group followers. This approach results in a hierarchical communication topology.
The most interesting coordination strategy discussed is the barycenter strategy. In this strategy, the j-th SC uses the position information of the neighboring SC to determine the barycenter of their locations. The barycenter is then used as the desired location of the j-th SC. In a subsequent paper [80] the authors use the same type of formulation to develop one-leader based coordinated control laws for position and attitude control of a SC formation. The interesting addition of this paper is the application of the one leader coordinated control strategy to the problem of Michelson stellar interferometry.
The authors in [84] developed a distributed controller for the SC formation at-titude control problem that they term the coupled dynamics controller. The coupled dynamics controller uses a ring communication topology, where each SC knows the state of two other SC in the formation. The desired state and the state of the two other SC are used to determine the appropriate control torque. A convergence proof
is provided; however the proof does not ensure global convergence of the forma-tion attitude. It requires that the SC begin with no angular rate and that the initial formation error is below a certain limit.
In [86] the authors developed a passivity-based controller for the SC forma-tion attitude control problem. The passivity-based controller uses only attitude in-formation to determine control actions, thus alleviating the need for angular rate measurements. The authors also analytically determine the domain of attraction for the passivity-based controller and the coupled dynamics controller. Later in [16] a more general architecture for SC formation attitude control is introduced by the same authors. The architecture is designed to subsume the leader-follower, behavior-based, and virtual-structure coordination strategies. The authors claim that the architecture is “amenable to analysis via control theoretic methods.” A brief descriptive list of some formation control problems that can be analyzed using the architecture is given. The authors demonstrate the usefulness of the architecture by applying it to the practical problem of Michelson stellar interferometry.
In [97] the authors investigate a centralized implementation of virtual struc-ture coordination strategy using the general architecstruc-ture. The primary contribution of the paper is the addition of formation feedback to the SC formation. The authors prove the virtual structure control law guarantees the stability and convergence of the system.
A fundamentally difference approach is proposed in [82] for dealing with the SC formation control problems. In this paper, each SC in the formation uses its cur-rent desired state and state information communicated by the other SC to determine a quasi-desired state using the reference projection. The quasi-desired state is then used by the SCs attitude controller to determine the appropriate control action. Dif-ferent types of coordination are possible using the appropriate reference projection.
In the paper, a reference projection is developed for the leader-follower, general-ized leader-follower, and the virtual desired attitude coordination strategies. The leader-follower reference projection for the leader is the desired state of the forma-tion, and the current state of the leader is the reference projection for the follower SC. The generalized leader-follower strategy differs in that the reference projection for the followers is a compromise between the desired state and the current state of the leader. The only truly decentralized coordination strategy is the virtual desired attitude strategy, where the reference projection for each SC is a compromise be-tween the desired state and the average state of the SC in the formation. In a later paper [90], the authors discuss applying the idea of reference projections to tracking control and in [91] the authors investigate the idea further and present simulation results.
More recently, [98] introduce a distributed algorithm for SC formation atti-tude control. The authors consider unit-quaternion in their analysis, which enables large attitude maneuvers. However, the authors consider fixed communication net-work and full state measurement in their analysis. Communication delays are con-sidered in [99], which extends the results in [98]. Modified Rodriguez Parameters (MRP) are also used in the controller design for SC formation flying in [100]. Com-munication time-delays are considered in [101]. However, when using MRP SC full attitude rotation maneuvers cannot be executed.
SC attitude synchronization and coordination control without requiring angu-lar velocity feedback is very useful specially when this information is not available due to sensor failure. This problem is considered recently in the literature. Specifi-cally, authors in [89] developed a velocity free attitude tracking algorithm for SC by using leader-follower approach. Consequently, failure of the leader SC will result in failure of the mission.
More recently, [88] developed an attitude synchronization and tracking al-gorithm for multiple SC formation by using MRP for attitude representation. The advantage of these two studies ([89] and [88]) is that they do not require sharing the estimate of the angular velocity among the SC in the formation, and this con-siderably reduces the communication load in the formation. Another recent study on velocity-free attitude control of SC formation is reported in [87]. In this paper, the authors use unit-quaternion to describe the SC attitude and extend the results reported in [94] for velocity control of a single SC to SC formation flying. How-ever, in this algorithm it is required that an estimate of the angular velocity is shared among the SC in the formation. Therefore, the algorithm does not reduce the com-munication among the SC in the formation. However, it is interesting to note that in this algorithm boundedness of the control effort is guaranteed.