Nonlinear Orbital Dynamic Equations and State-Dependent Riccati Equation Control of Formation Flying Satellites

Abstract

Precise maneuvers of formation flying satellites require a general orbital dynamic equation and an effective nonlinear control method. In this paper, nonlinear orbital dynamics of relative motion equations are derived for a constant distance separation formation flying problem. This general orbital dynamic equation allows elliptic, noncoplanar, and large separation distances between spacecraft as well as traditional circular, coplanar, and small separation distance cases. Furthermore, for the in-plane formation flying scenario with large constant angle of separation between satellites, we derive the change in position and velocity equations. A nonlinear control method called the state-dependent Riccati equation control method is utilized to solve the formation flying control problem. This novel control method for a nonlinear system allows the intuitive design tradeoff between the control action and the state error similar to the classical linear-quadratic-regulator control method. Two numerical simulations demonstrate the effectiveness of the new state-dependent Riccati equation control method with the newly developed relative motion equations.