On-manifold robust tracking control of a free-flying space robot with input saturation and thruster misalignment

This article is concerned with the nonlinear dynamics and tracking control on a differentiable manifold for a free-flying space robot with multiple constraints, such as uncertain parameters, external disturbances, input saturation, and thruster misalignment. Unlike the global parametric modeling methods suffering from singularity, ambiguity, and complexity issues, in this study the robot dynamics are formulated uniquely, globally, and analytically by matrix Lie groups and Lie algebras. By designing a configuration error function on 𝑆 ⁢ 𝐸 ⁡ ( 3 ) × ℝ 𝑛 , the tracking error dynamics are derived on the tangent bundle of the differentiable manifold. Then, a geometric terminal sliding mode control (GTSMC) strategy is newly proposed to enable the predefined-time trajectory tracking in the presence of uncertain parameters and external disturbances. Moreover, to improve the applicability of the control algorithm to practical space robotics, this work also addresses the issues of actuator saturation and thruster misalignment which are often encountered in space missions. Finally, numerical simulations are carried out to verify the effectiveness and performance of the developed geometric control scheme.