A Feedback Guidance Scheme for Orbital Rendezvous
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A Feedback Guidance Scheme for Orbital Rendezvous 1 Craig A. Kluever" and Greg S. Tanck' Abstract A feedback guidance scheme for autonomous orbital rendezvous is presented. The guidance scheme is developed for spacecraft equipped with thrusters that operate in an on-off mode with constant thrust magnitude. The control law is obtained by solving the discretetime, steady-state linear quadratic regulator (LQR) problem. A parameter optimization method is used to obtain the optimal weighting matrices for the discrete-time LQR problem so that the total impulsive velocity increment (aV) is minimized. Several planar rendezvous maneuvers are presented for spacecraft equipped with electric propulsion thrusters and a range of sample periods (time between thruster firings) is investigated. The guidance scheme exhibits rapid convergence to minimum av solutions and the subsequent simulations show good closed-loop response characteristics.
Introduction Orbital rendezvous is a necessary maneuver for satellites in Earth orbit. On-orbit satellite repositioning maneuvers require a terminal guidance phase for proper orbit insertion. In addition, there are several types of space missions in which two or more spacecraft must maintain a prescribed distance with respect to each other. Examples include radio interferometry missions, Space Shuttle retrieval missions, and formation flying with respect to a space station. For each of these examples, an active control system is required for placing or keeping the spacecraft in a prescribed position in the desired orbit. Clohessy and Wiltshire [1] developed a terminal guidance scheme based on linearized equations of motion about a circular orbit. Vassar and Sherwood [2] presented a control scheme for maintaining a two-satellite formation in circular orbit. Lopez and McInnes [3] investigated an autonomous guidance IBased on Paper 97-624 presented at the AAS/AIAA Astrodynamics Specialist Conference, Sun Valley, Idaho, August 1997. 2Associate Professor, Department of Mechanical and Aerospace Engineering, University of MissouriColumbia, Columbia, MO 65211.
3Graduate Research Assistant, Department of Mechanical and Aerospace Engineering, University of Missouri-Columbia/Kansas City, Kansas City, MO 64110.
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scheme based on Lyapunov theory for performing on-orbit maneuvers. A terminal guidance phase for orbit insertion based on phase-plane analysis was presented by Yu [4]. Kellyet al. [5] and Chao and Bernstein [6] presented stationkeeping control strategies for geosynchronous satellites. In this paper, we develop a feedback guidance scheme for performing autonomous rendezvous with a target point in a circular orbit. The control law is developed for onboard thrusters that operate in an on-off mode with a constant thrust magnitude. The feedback control law is derived by using the discrete-time linear equations of motion relative to a reference circular orbit and the discrete-time, asymptotic linear quadratic regulator (LQR) approach. In addition, a parameter optimization
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