1160 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 20, NO. 5, SEPTEMBER 2012 Attitude Coordination Control for a Group of Spacecraft Without Velocity Measurements An-Min Zou, Krishna Dev Kumar, Senior Member, IEEE, and Zeng-Guang Hou, Senior Member, IEEE Abstract—This paper investigates the problem of velocity-free attitude coordination control for a group of spacecraft with attitude represented by modified Rodrigues parameters. The communication flow among neighbor spacecraft is described by an undirected connected graph. Two velocity-free attitude coordination control schemes are proposed. By employing linear reduced-order observers, robust control and Chebyshev neural networks, the first velocity-free control scheme allows a group of spacecraft to simultaneously align their attitude and track a time-varying reference attitude even in the presence of unknown mass moment of inertia matrix and external disturbances, where all spacecraft have access to the common reference attitude. The second control law guarantees a group of spacecraft to track a time-varying reference attitude without requiring velocity mea- surements even when the common reference attitude is available only to a subset of the group members. Furthermore, the sta- bility of the overall closed-loop system for both control laws is guaranteed by a Lyapunov-based approach. Finally, numerical simulations are presented to demonstrate the performance of the proposed controllers. Index Terms—Adaptive control, attitude coordination, Cheby- shev neural networks (CNNs), spacecraft formation flying (SFF), without velocity measurements. I. INTRODUCTION D URING the past few years, the problem of attitude co- ordination control for spacecraft formation flying (SFF) has received wide attention [1]–[9]. SFF is expected to be an applicable technology for many space missions such as mon- itoring of the Earth and its surrounding atmosphere, geodesy, deep space imaging and exploration, and in-orbit servicing and maintenance of spacecraft. The concept of SFF is to replace a large spacecraft with a group of smaller, less-expensive, coop- erative spacecraft. In particular, the major advantage of SFF lies in flexibility and modularity. A review of previous work on the field of SFF is given in [10]. Several approaches have been presented for the space- craft formation control. These approaches can be catego- Manuscript received February 17, 2011; accepted July 19, 2011. Manuscript received in final form July 25, 2011. Date of publication August 30, 2011; date of current version June 28, 2012. Recommended by Associate Editor M. Mes- bahi. This work was supported in part by the Ryerson University Post-Doctoral Fellowship (RPDF) Program, by the Ontario Early Researcher Award Program, and by the Canada Research Chair program. The work of Z.-G. Hou was sup- ported in part by the National Natural Science Foundation of China under Grant 60 775 043. A.-M. Zou and K. D. Kumar are with the Department of Aerospace Engi- neering, Ryerson University, Toronto, ON M5B 2K3, Canada (e-mail: anmin. zou@ia.ac.cn; kdkumar@ryerson.ca). Z.-G. Hou is with the State Key Laboratory of Intelligent Control and Man- agement of Complex Systems, Institute of Automation, The Chinese Academy of Sciences, Beijing 100190, China (e-mail: zengguang.hou@ia.ac.cn). Digital Object Identifier 10.1109/TCST.2011.2163312 rized according to their control architectures as multi-input multi-output (MIMO), leader-follower (LF), virtual structure (VS), and behavioral [10]. In the LF approach, some spacecraft are designated as leaders, whereas others are considered as followers. The leaders track predefined trajectories, and the followers track the leaders according to given schemes. In the VS approach, the entire formation is treated as a single larger and virtual rigid body. The virtual structure can evolve as a whole in a given direction with some given orientation and maintain a rigid geometric relation among multiple agents. In the behavioral approach, the control action for each individual spacecraft in the formation is defined by a weighted average of the control corresponding to each desired behavior for the individual spacecraft. The behavioral approach is a decentralized strategy, and has the advantages such as flexibility, reliability, and robustness. In [1], a decentralized attitude coordination control algorithm based on state-dependent Riccati equation technique was pro- posed for satellite formation flying. Based on the decentralized control and the virtual structure approach, a decentralized formation scheme was presented for the spacecraft formation [3]. Later, the work of [4] extended the previous synchronized spacecraft rotation results reported in [2] and [3], where several control laws were proposed for a team of spacecraft through local information exchange with consideration of three dif- ferent cases. A class of decentralized coordination tracking control laws was developed in [5], which could guarantee global asymptotic stability and convergence of the attitude of spacecraft within a formation. In [6], a decentralized variable structure controller was proposed for the attitude coordination control of multiple spacecraft in the presence of modeling uncertainties, external disturbances, and intercommunication time delays. In [11], a decentralized synchronization tracking control law was proposed for a class of Lagrangian systems when the common desired trajectory was available to each member in the group, and the present control scheme was gen- eralized and extended to multirobot systems with nonidentical dynamics, linear coupling control, partial state coupling, undi- rectional coupling, and adaptive control. However, the above aforementioned cooperative control approaches require full state measurements (i.e., both attitude/position and velocity). In [2], a passivity-based formation control law, which was model independent and required a bi-directional ring topology, was presented for maintaining attitude alignment among a group of spacecraft without velocity measurements. More recently, Ren [7] extended the work of [2] to the case of a general undirected connected communication topology, where modified Rodrigues parameters (MRPs) were used for attitude representations. In both works, only constant reference attitude was considered, 1063-6536/$26.00 © 2011 IEEE