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

摘要

As control precision for Earth-orbiting formations increases, the required Delta V can quickly become infeasible. Missions have demonstrated approximately 5 m/s/yr for 10-m control (TanDEM-X), but that quickly grows to approximately 90 m/s/yr for 1.5-m control (CanX-4/5). Previous research has shown that formation reference trajectories must use high-fidelity relative orbital dynamics; otherwise, Delta V is spent rejecting modeling errors. However, even with a perfect reference trajectory, feeding back relative state estimation errors can drive Delta V. This paper presents a linear time-invariant analysis approach that quantifies the three-way trade-off between mission Delta V, 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 Delta V cost of modeling errors. Because Linear Quadratic Regulator control is used, the resulting Delta V can be considered a lower bound on the required Delta V, assuming linear control and quadratic cost. Using reference trajectories based on simplified dynamics, such as without differential J2, would only increase Delta V. 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 Delta V capability and control requirements for science.