Output Feedback Control for Spacecraft Formation Flying with Coupled Translation and Attitude Dynamics Hong Wong, Haizhou Pan, and Vikram Kapila Mechanical, Aerospace, and Manufacturing Engineering, Polytechnic University, Brooklyn, NY 11201 Abstract— In this paper, we address an output feedback tracking control problem for the coupled translation and attitude motion of a follower spacecraft relative to a leader spacecraft. It is assumed that i) the leader spacecraft is tracking a given desired translation and attitude motion trajectory and ii) the translation and angular velocity measurements of the two spacecraft are not available for feedback. First, the mutually coupled translation and atti- tude motion dynamics of the follower spacecraft relative to a leader spacecraft are described. Next, a suitable high-pass filter is employed to estimate the follower spacecraft relative translation and angular velocities using measurements of its relative translational position and attitude orientation. Using a Lyapunov framework, a nonlinear output feed- back control law is designed that ensures the semi-global asymptotic convergence of the follower spacecraft relative translation and attitude position tracking errors, despite the lack of translation and angular velocity measurements of the two spacecraft. Finally, an illustrative numerical simulation is presented to demonstrate the effectiveness of the proposed control design methodology. I. Introduction Spacecraft formation flying (SFF) has the potential to enhance space-based imaging/interferometry missions through the use of distributed apertures. Specifically, by combining the imaging apertures placed on several separated spacecraft and by appropriately configuring the formation geometry, the sensing aperture can be enlarged beyond the capability of a single spacecraft. However, effective utilization of the SFF technology necessitates highly maneuverable spacecraft to be pre- cisely controlled in a formation so as to maintain a meaningful separation and orientation. Thus, develop- ment of a systematic SFF control design framework incorporating the six degree-of-freedom (DOF) coupled translation and attitude motion dynamics of spacecraft is of paramount importance. The study of dynamics and control for six-DOF spacecraft has received scant attention in the current literature. Some recent exceptions include [8], [9]. These control methods require the use of translation and an- gular velocity measurements of spacecraft for feedback. Unfortunately, cost/weight constraints may not permit the use of translation and angular velocity sensors. In prior research, several authors have addressed the Research supported in part by the National Aeronautics and Space Administration–Goddard Space Flight Center under Grant NGT5-151 and the NASA/New York Space Grant Consortium under Grant 32310-5891. problem of output feedback control of spacecraft. Specif- ically, using the four-parameter quaternion represen- tation of the spacecraft attitude, an adaptive output feedback attitude tracking controller was developed in [3]. Furthermore, in [10], an adaptive output feedback position tracking controller was developed for SFF. However, the output feedback control problem for the six-DOF coupled translation and attitude motion of spacecraft formations remains to be addressed. In this paper, we address the output feedback track- ing control problem for the six-DOF motion of a follower spacecraft relative to a leader spacecraft using the coupled translation and attitude dynamics of a leader- follower spacecraft pair developed in [7]. A high-pass filter is employed to generate a velocity-related signal from the translational position and attitude orientation measurements. A judicious modification of the generally recommended [4] filter is implemented to overcome the complexity arising from the mutual coupling of the follower spacecraft translation and attitude mo- tion dynamics. Using a suitable Lyapunov function, our nonlinear output feedback control law guarantees asymptotic convergence of the translation and attitude position tracking errors, despite the lack of translation and angular velocity feedback. II. Mathematical Preliminaries Throughout this paper, several reference frames are employed to characterize the translation and attitude motion dynamics of a spacecraft. Each reference frame used in this paper is assumed to consist of three basis vectors which are right-handed, mutually perpendicular, and of unit length. Let F denote a reference frame and let → i , → j , and → k denote the three basis vectors of F . Then → F △ =  → i → j → k  denotes the vectrix of the reference frame F [5]. A vector → A can be expressed in the reference frame F as → A △ = a 1 → i +a 2 → j +a 3 → k , where a 1 ,a 2 , and a 3 denote the components of → A along → i , → j , and → k , respectively. Frequently, we will assemble these components as A △ = [a 1 a 2 a 3 ] T . Using the above vectrix formalism and the usual vector inner product, a vector → A can be expressed in the reference frame F as → A= A T → F = → F T A. The vectrix → F has the following two properties: i) → F · → F T = I 3 , where “·” denotes the usual vector 2005 American Control Conference June 8-10, 2005. Portland, OR, USA 0-7803-9098-9/05/$25.00 ©2005 AACC ThB04.6 2419