Lyapunov-Based Control of Coupled Translational-Rotational Close-Proximity Spacecraft Dynamics and Docking

Abstract

This work presents a non-linear control strategy for the docking of two spacecraft in a leader-follower orbit pattern. The chief craft is assumed to be in a circular orbit around a celestial body. The deputy craft is assumed to have a separation distance from the chief that is small compared to the orbital radius of the chief. Furthermore, the relative dynamics of these crafts can be described by the Hill-Clohessy-Wiltshire equations. The control strategy developed is able to regulate the relative translational distance and velocity of the docking feature points on the two craft with globally asymptotic stability. Furthermore, the control strategy is able to regulate the relative rotational velocity and relative attitude, between the two craft, to that which it is required for successful docking. The rotational control is achieved with “almost” globally asymptotic stability, inclusive of an infinitesimally small unstable manifold. Other researchers in this field have shown that this unstable manifold is easily avoided using advanced control methods. These control laws are developed using Lyapunov’s Direct Method, and have asymptotic stability claims per the use of the Mukherjee-Chen theorem. Numerical Monte-Carlo simulation shows asymptotic stability for a subset of the domain of convergence for the developed control laws. Un-modeled torques and accelerations are later imposed on the system. The control laws are then augmented with integral feedback terms, and the closed loop system, with the augmented control laws, retains the asymptotic stability claims.