NONLINEAR DYNAMICS AND CONTROL OF MULTI-BODY ELASTIC SPACECRAFT SYSTEMS Firdaus E. Udwadia University of Southern California, Viterbi School of Engineering, Los Angeles, California, 90089 email: fudwadia@usc.edu Aaron D. Schutte The Aerospace Corporation, El Segundo, California, 90245 email: aaron.d.schutte@aero.org Try Lam Jet Propulsion Laboratory, Pasadena, California, 91109 email: trylam@jpl.nasa.gov ABSTRACT This paper deals with the dynamics and control of multi-body systems in which their linear, rotational, and elastic motions are coupled. We model a multi-body spacecraft system as two rigid bodies that are connected by a nonlinear, elastic spring. It is assumed that the system travels in a planar orbit around a planet with a uniform gravitational field. The methodology developed in this paper leads to a simple nonlinear control law that allows us to control the coupled orbital, attitude, and elastic dynamics, and precisely maintain a prescribed tumbling trajectory. We show that complex motions like the precision tumbling of elastically vibrating spacecraft in orbit can be accomplished with considerable ease and accuracy. The proposed methodology reveals a systematic technique for controlling complex nonlinear, multi-body systems. 1. INTRODUCTION. The traditional method of analyzing spacecraft dynamics is to decouple the attitude motion of the spacecraft about its center of mass and that of the orbital motion. In general, this method works well, but for more complex space systems, such as those with massive appendages and booms, or for systems that are tethered, understanding the coupled dynamics and control becomes important, especially for precision-driven space missions. Perturbative forces on these complex systems cause them to torque, flex, compress, expand, and behave in other ways that affect the entire dynamics of the system. This requires one to study the motion of the system as a whole if high control authority is required. Some advancement has been made in recent years in trying to understand the dynamics of coupling the various motions between multi-body spacecraft systems. The station keeping, retrieval, and attitude control of tethered systems was studied in Refs. [1-3]. Studies of the coupled attitude and orbital dynamics of spacecraft were presented in Refs. [4-5]. The effect of gravitational gradient torques on the attitude behavior of a dumbbell-shaped spacecraft was studied in [6]. Orbital and attitude dynamics of a flexible spacecraft in the Jovian system including higher order gravity fields was worked on by Quadrelli, et. al. [7]. Sanyal et. al. [8-9] considered the control of orbital, attitude, and elastic motion for a dumbbell spacecraft in a planar orbit by linearizing a set of reduced equations of motion. In these previous studies, linearization and other approximations of the dynamics and/or control are involved. In this paper we develop a method to address the complete three-dimensional, nonlinear dynamics and control problem wherein we consider a new nonlinear control methodology for a spacecraft system that accounts for its coupled orbit, attitude, and elastic dynamics. The control approach is developed using principles rooted in analytical mechanics and adopted for the control of complex multi-body systems. It is based on the explicit set of equations of motion for general constrained mechanical systems discovered by Udwadia and Kalaba [10] and further developed in [11] for the control of nonlinear dynamical systems. An important contribution of the proposed method is that the control is obtained in closed form, and can therefore be computed in real time. Furthermore, no linearization in the system’s dynamics or in the control is involved. It has been shown [12-14] that the proposed methodology is easily applied to highly constrained astrodynamic problems.