Formation Keeping and Attitude Alignment for Multiple Spacecraft Through Local Interactions

A DVANCES in networking and distributed computing enable numerous applications for multivehicle systems including space-based observations, future combat systems, smart homes, enhanced surveillance systems, hazardous material handling systems, and reconfigurable sensing systems. In some applications, it is desirable that multiple vehicles maintain a geometric configuration and achieve relative attitude alignment. One example is deep-space interferometry (see [1,2] and references therein), where a fleet of networked spacecraft are required to perform a sequence of formationmaneuverswhilemaintaining relative attitudes accurately. In multivehicle coordination, the interplay between informationexchange topologies and control plays an important role. In [3] information-exchange techniques are studied to improve stability margins and accuracy for vehicle formations, where an information flow filter provides each vehicle with the formation center so that this information can be used by each vehicle as a reference. In [4–6] consensus algorithms for single-integrator dynamics are studied in the context of undirected or directed switching informationexchange topologies. Extensions to double-integrator dynamics are discussed in [7,8], in which flocking algorithms are addressed to guarantee separation, alignment, and cohesion behaviors in a group of vehicles under undirected information exchange. In the area of spacecraft formation flying, [9–11] study the problem of formation keeping and attitude alignment for multiple spacecraft via information exchange with one or two adjacent neighbors. In [9], a leader–follower approach is applied, where each spacecraft tracks its leader’s position and attitude, and information only flows from leaders to followers. Although the leader–follower approach is easy to understand and implement, there are limitations. For example, the unique team leader, to which the reference state for the formation is only available, is a single point of failure for the whole group. In addition, there is no explicit feedback from the followers to the leaders: if the follower is perturbed by disturbance, formation keeping and attitude alignment cannot be maintained. In [10,11], the control law for each spacecraft is a function of the states of its two adjacent neighbors. As a result, group feedback is introduced in the team through coupled dynamics between the spacecraft. However, [10,11] require a bidirectional ring communication topology, which is rather restrictive in the sense that each spacecraft needs to explicitly identify its two adjacent neighbors in the group to form the ring. In addition, [10,11] require that the reference state for the formation be available to every group member, which may not be realistic in the presence of communication bandwidth and range limitations. The main purpose of this note is to address the problem of formation keeping and attitude alignment under a general directed information-exchange topology when the reference state for the formation may only be available to a part of the group members and these group member may not have a directed path to all of the other spacecraft. The contributions of the current note are twofold. First, we propose a formation keeping control law that guarantees that multiple spacecraft can maintain a given formation configuration during formation maneuvers with local neighbor-to-neighbor information exchange when the time-varying reference position and velocity for the virtual center of the formation are only available to a part of the group members. Second, we propose a attitude alignment control law that guarantees that multiple spacecraft can follow a given time-varying reference attitude with local neighbor-toneighbor information exchange when the reference attitude is only available to a part of the group members. It is worthwhile to mention that althoughwe study the problem of formation keeping and attitude alignment in the context of deep-space spacecraft formation flying, the results hereafter are valid for other rigid bodies that satisfy the same dynamics. Compared to other work in spacecraft attitude control (e.g., [12]), the emphasis of this note lies in the analysis of how interspacecraft information exchange plays a key role in formation keeping and attitude alignment. Compared to [7,8], the proposed formation keeping control law takes into account the general case of directed information exchange in the presence of a time-varying reference state. In addition, the proposed attitude alignment control law extends the consensus algorithms from singleor double-integrator dynamics as addressed in [3–8] to rigid-body rotational dynamics while taking into account the general case of directed information exchange in the presence of a time-varying reference state. The proposed control laws allow information to flow from any spacecraft to any other spacecraft to introduce information feedback and coupling between neighboring spacecraft so as to increase redundancy and robustness to the whole group in the case of failures of certain information-exchange links, which generalizes the leader–follower approach (e.g., [9]) and the behavioral approach requiring a bidirectional ring information-exchange topology (e.g., [10,11]).