An adaptive sliding mode spacecracft attitude control strategy on SO(3) modelled dynamics for VLEO scenario

This paper introduces a novel Sliding Mode Control (SMC) strategy based on SO(3) attitude representation for spacecraft in Very Low Earth Orbit (VLEO). The VLEO environment is attractive due to the lower communication latency between satellite and ground station and reduced launch costs, but it also poses significant challenges, as the poor modelling available of environmental perturbations. Due to these challenges and potential benefits, space missions in VLEO environment are a timely research topic, with many aspects still to be investigated. This is the context for this work, in which we aim to address the problem of attitude control of a satellite in VLEO, thus including the particular disturbances encountered in such environment. In our approach, the spacecraft’s attitude dynamics are modelled as rotations within the special orthogonal group SO(3), and a SMC strategy is employed to robustly stabilize the orientation in the presence of unknown perturbations and model uncertainties. The design process of a SMC consists of defining a control law to enclose the closed-loop dynamics on the sliding surface. A key innovation of our design is the dynamic adaptation of the sliding variable parameters, which results in a time-varying sliding manifold that improves the robustness of the controller by accelerating the reaching phase. Once the system reaches the sliding manifold, the adaptive law is modified to track the desired reference while adhering to mission constraints, such as limits on control effort and manoeuvre duration. Furthermore, in our formulation the sliding variable is defined as a function of the system states on the tangent bundle, and by leveraging a kinematic control law on Lie Groups along with a suitable group operation, it is possible to define a sliding subgroup that enhances the overall control performance. This methodology is particularly well-suited for autonomous spacecraft missions in VLEO, where the accurate modelling of atmospheric disturbances is challenging. Indeed, by utilizing a sliding mode technique, the proposed controller offers both robustness to external disturbances and adaptability to uncertainties in the VLEO environment. Extensive simulations show the effectiveness of our controller, and comparative analyses with traditional control methods further highlight its performance advantages. This work thus contributes a promising solution for reliable spacecraft attitude control in the regime of VLEO. This research was carried out within the Space It Up! project funded by the Italian Space Agency (ASI) and the Italian Ministry of University and Research (MUR) under contract No. 2024-5-E.0, CUP No. I53D24000060005. 4000060005.