Automated trajectory control for proximity operations using relative orbital elements

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Spencer, David Allen
Braun, Robert D.
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This dissertation develops a methodology for automated trajectory control of a spacecraft about a non-maneuvering target. The methodology utilizes relative orbital elements (ROEs), combined with guidance laws based upon artificial potential functions (APFs), to perform automated trajectory planning and maneuver design. The investigation provides a definitive reference on the definition and use of ROEs for relative proximity operations. The detailed derivation of ROEs is provided, along with transformations between ROEs and relative Cartesian state elements, characteristics of unforced motion in terms of ROEs, and the effect of impulsive maneuvers on ROEs. Operationally-useful guidance algorithms utilizing ROEs are developed and demonstrated. These ROE-based algorithms for rendezvous, circumnavigation and station-keeping provide a toolkit for relative proximity operations mission planning. A new approach for APF formulation using ROEs as the target variables is developed. While previous approaches allowed targeting of a specified relative position, the present approach allows the targeting of relative orbit geometries. The approach capitalizes upon the orbital dynamics represented through the ROEs, and retains the computational simplicity offered by the APFs. Formulations for the APF targeting of individual ROEs, as well as simultaneous targeting of a set of ROEs, are established. An approach for combining ROE targeting using APFs with obstacle avoidance is presented. The trajectory guidance algorithm performance is evaluated using a flight-like guidance, navigation and control simulation environment, including orbital perturbations. Algorithm performance is established through a set of operationally relevant scenarios. The guidance algorithms are shown to be capable of correcting for environmental disturbances, while meeting the targeted relative orbits in an automated fashion.
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