Continuous-Thrust Transfer with Control Magnitude and Direction Constraints Using Smoothing Techniques

Abstract

This paper treats the satellite formation and reconfiguration problem under constraints on control magnitude and direction. An optimal controller with these constraints is derived using a continuous smoothing method, in which a sequence of unconstrained optimal control problems is solved according to Pontryagin’s minimum principle by introducing barrier functions to the original performance index. The solutions converge to the solution of the original problem and strictly satisfy the treated constraints as the coefficients of the functions approach zero. Optimal controllers are successfully formulated in - and -norm problems. The magnitude and direction constrained solution is naturally extended from the solution with only magnitude constraints. Numerical simulations demonstrate that a successive optimal controller with such a multiconstraint can be obtained by solving a two-point boundary value problem using the shooting method in a noncoplanar circular orbit and a coplanar eccentric orbit.