Formation Control of Multiple Autonomous Vehicle Systems

6 Formation Control of Space Systems

This chapter will introduce how to apply the adaptive formation control strategy proposed in Section 5.7 to formations of spacecraft, and show the simulation results of two typical applications: motion synchronization among multiple axes of one spacecraft, and/or any given axis of multiple spacecraft while realizing the convergence of position tracking errors.

The proposed synchronization framework uses a Lagrangian formulation because of its simplicity when dealing with complex systems involving multiple dynamics. We first briefly recall the derivation of equations of the Lagrangian form (6.1), and then show that the rotational dynamics of a rigid spacecraft can be written in this form, which implies that the approaches introduced in the foregoing chapter can be applied to the rotational synchronized tracking problem of multiple spacecraft. However, we do not dwell on such applications since we are mainly concerned with the formation control problem in this chapter. To address the position synchronization of formations of spacecraft, we first set out the relative translational dynamics of multiple spacecraft in the Lagrangian form, and then apply the control strategy proposed in Section 5.7. Simulation results are presented to show the effectiveness of the strategy.

6.1 Lagrangian Formulation of Spacecraft Formation

6.1.1 Lagrangian Formulation

Consider the Euler–Lagrange equations

(6.1)

where the Lagrangian function