Relative Sensing, Control Precision, and Mission Delta- Trade-Offs for Precision Formation Flying in Planetary Orbit

Abstract

As control precision for Earth-orbiting formations increases, the required can quickly become infeasible. Missions have demonstrated approximately for 10-m control (TanDEM-X), but that quickly grows to approximately for 1.5-m control (CanX-4/5). Previous research has shown that formation reference trajectories must use high-fidelity relative orbital dynamics; otherwise, is spent rejecting modeling errors. However, even with a perfect reference trajectory, feeding back relative state estimation errors can drive . This paper presents a linear time-invariant analysis approach that quantifies the three-way trade-off between mission , control precision, and estimation error for approximately circular orbits and verifies the approach through high-fidelity simulations, including tracking an ideal reference trajectory that eliminates the cost of modeling errors. Because Linear Quadratic Regulator control is used, the resulting can be considered a lower bound on the required , assuming linear control and quadratic cost. Using reference trajectories based on simplified dynamics, such as without differential J2, would only increase . Using this analysis approach, for example, the minimum required capability of a relative sensing and estimation system could be determined given a mission concept’s capability and control requirements for science.