Estimated-State Adaptive Sliding Mode Control and Disturbance Observation Using Second-Order Surfaces for Spacecraft Formation Reconfiguration

Abstract

This paper presents a two-phase relative orbit control framework for spacecraft formation flying that combines analytic energy-optimal transfer with robust adaptive sliding mode tracking. In the first phase, a chaser is transferred from an arbitrary initial relative state to a projected circular orbit (PCO) under the Clohessy--Wiltshire dynamics. Rather than selecting the PCO entry phase by numerical sweeping, the transfer cost is parameterized by the phase angle, and the stationarity condition is reduced to a quartic polynomial whose real roots yield all candidate entry phases. In the second phase, the chaser maintains the PCO in the presence of external disturbances. An adaptive sliding mode controller (ASMC) and a sliding mode disturbance observer (SMDO) are employed in both phases to provide robust tracking and disturbance compensation. The observer reduces the lumped disturbance to a bounded residual, while the controller updates its adaptive gain from an estimated-state second-order sliding variable. The second-order surface tightens the ultimate tracking error bound, and a practical derivative estimation method reuses available reference velocity and acceleration signals, avoiding finite-difference noise amplification and additional differentiator tuning. Simulations demonstrate accurate tracking, effective disturbance rejection, and a smooth transition between the two phases.