Advanced guidance algorithms for spacecraft formation-keeping

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Abstract
This paper presents advanced formation-keeping guidance algorithms that use linear programming (LP) to determine fuel-optimal control inputs and state trajectories. The overall formation-keeping problem is analyzed in terms of two key issues: (i) what dynamics model should be used to specify the desired state to maintain a passive aperture; and (ii) what dynamics model should be used in the LP to represent the motion about this state. Several linearized models of the relative dynamics are considered in this analysis, including Hill's equations for circular orbits, modified linear dynamics that partially account for the J/sub 2/ effects, and Lawden's equations for eccentric orbits. A controller is developed for formation-keeping using each of these models. A modified LP formulation is presented to include robustness to sensor noise while ensuring a feasible solution. The guidance algorithms are implemented in numerous very detailed nonlinear simulations that demonstrate effective control in the presence of all expected disturbances and sensor noises. The average fuel cost for the formation-keeping maneuvers over a two week simulation is on the order of 4 mm/s per orbit.

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