Linear vs. nonlinear control techniques for the reconfiguration of satellite formations

Abstract

This paper investigates several linear and nonlinear feedback control methods for satellite formation reconfigurations and compares them to a near optimal open loop, discrete-time, impulsive maneuver. The reconfigurations are done in terms of a set of relative parameters that define an orbit about the leader satellite (or center reference position if a leader satellite does not exist at the center of the formation). The purpose of the study is two-fold, to compare the control usage of continuous feedback control methods versus a discrete burn method and to determine if nonlinear control techniques offer significant improvement over more conventional linear control laws. Linear Quadratic Regulators (LQR), LQR with linearizing feedback, and State Dependent Riccati Equation (SDRE) are used. Simulations showed that reconfigurations for small relative orbits were adequately controlled using linear techniques. Nomenclature r relative position in the radial direction c relative position in the cross track direction o relative position in the out of plane direction uj angular frequency of the leader orbit k0 radius of the leader orbit vc control