Adaptive Nonlinear Control of Multiple Spacecraft Formation Flying

Thispaperconsiderstheproblemofrelativepositioncontrolformultiplespacecraftformatione ying.Specie cally, the full nonlinear dynamics describing the relative positioning of multiple spacecraft formation e ying are used to develop a Lyapunov-based, nonlinear, adaptive control law that guarantees global asymptotic convergence of the position tracking error in the presence of unknown, constant, or slow-varying spacecraft masses, disturbance forces, and gravity forces. Simulation results are included to illustrate the controller performance. that compensated for unknown, constant disturbances while pro- ducing globally asymptotically decaying position tracking errors. This controller, however, required exact knowledge of the space- craft parameters. In this paper we consider the full nonlinear dynamics describ- ing the relative positioning of MSFF for control design purposes. Using Lyapunov-based control design and stability analysis tech- niques, we develop a nonlinear adaptive control law that guarantees global asymptotic convergence of the spacecraft relative position to any sufe ciently smooth desired trajectory, despite the presence of unknown, constant, or slow-varying spacecraft masses, disturbance forces, and gravity forces. In the case when the parameters are ex- actlyknown,theproposedcontrolstrategyyieldsglobalexponential convergence of the tracking errors. In comparison to the work of Refs. 11 and 12, the proposed controller ensures stronger stability resultsandaccountsforawiderclassofparametricuncertainties.As inRefs.11-13, we will consider in this paper the idealized scenario where the spacecraft actuators are capable of providing continuous- time control efforts, as opposed to being of pulse type. 9 We note that the problem of pulse-type, nonlinear control design for MSFF constitutes an open research problem and is beyond the scope of this paper. The paper is organized as follows. Section II presents the non- linear dynamic model derivation. The control objective is stated in Sec. III. The control design and closed-loop stability analysis are presented in Sec. IV. Simulation results are provided in Sec. V, whereas some concluding remarks are given in Sec. VI.