Nonlinear Orbital Dynamic Equations and State-Dependent Riccati Equation Control of Formation Flying Satellites
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Nonlinear Orbital Dynamic Equations and StateDependent Riccati Equation Control of Formation Flying Satellites Chang-Hee WonI and Hyo-Sung Ahrr' Abstract Precise maneuvers of formation flying satellites require a general orbital dynamic equation and an effective nonlinear control method. In this paper, nonlinear orbital dynamics of relative motion equations are derived for a constant distance separation formation flying problem. This general orbital dynamic equation allows elliptic, noncoplanar, and large separation distances between spacecraft as well as traditional circular, coplanar, and small separation distance cases. Furthermore, for the in-plane formation flying scenario with large constant angle of separation between satellites, we derive the change in position and velocity equations. A nonlinear control method called the state-dependent Riccati equation control method is utilized to solve the formation flying control problem. This novel control method for a nonlinear system allows the intuitive design tradeoff between the control action and the state error similar to the classical linear-quadratic-regulator control method. Two numerical simulations demonstrate the effectiveness of the new state-dependent Riccati equation control method with the newly developed relative motion equations.
Introduction Multiple spacecraft formation flying is one of the key technologies of current and future space missions. The National Aeronautical and Space Administration's Earth Observing-l satellite demonstrated formation flying technology by flying in a formation one minute behind Landsat-7 in November 2000, and Jet Propulsion Laboratory is planning the Deep Space-3 mission to formation fly three separate spacecraft to take space optimal interferometer measurements. The objective of formation flying is to autonomously control two or more satellites relative to another satellite with minimum ground control station involvement. There are two main challenges in formation flying technology. First, there has to be a general nonlinear 'Assistant Professor, Department of Electrical Engineering, University of North Dakota. 2Graduate Student, Department of Electrical Engineering, University of North Dakota. 433
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Won and Ahn
relative motion equation and second, there has to be an appropriate nonlinear control method to design an optimal controller. So, in this paper, we derive a nonlinear orbital dynamic equation and we propose to use the State-Dependent Riccati Equation (SDRE) control method to solve the formation flying problem. On the orbital dynamic side of formation flying, various studies have been reported. In 1985, Vassar and Sherwood studied formation keeping for a pair of satellite in a circular orbit in spite of disturbances such as aerodynamic drag and solar radiation pressure [1]. Kapila et al. developed and used linear Clohessey-Wiltshire (CW) equation for circular orbit formation flying in their paper [2]. They utilized linear pulse control method in their example. In 2000, Yedavalli and Sparks studied satell
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