This paper analyzes the impact of sensing noise on formation flying control algorithms that have been developed for distributed spacecraft systems. The key issue is that the sensing errors cause uncertainty in the initial conditions of the trajectory planning process which is at the core of the fuel-optimization algorithm. For example, the relative velocity measurements using a carrier-phase differential GPS sensor are predicted to be accurate to approximately 2 mm/sec, but a 2 mm/sec error in the intrack velocity corresponds to approximately 30 m/orbit secular drift rate in the relative positions between two spacecraft. This large drift rate is comparable to the values expected from differential J2 disturbances, so its impact on the fuel used to perform formation flying is an important concern. To account for these sensing errors, modifications are presented to the station-keeping optimization algorithms that have been developed using linear programming. The approach robustifies the design of the control inputs to velocity errors, but this is achieved at the expense of using much shorter design horizons. The modified control approach has been demonstrated using a realistic nonlinear simulation environment. The results from these simulations confirm that noise in the relative velocity measurements will play a crucial role in the fleet performance and/or the fuel cost.
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November 24, 2002