Dynamic modeling and trajectory optimization for detumbling malfunctioning spacecraft using a flexible rod

A servicing spacecraft equipped with a flexible rod-type deceleration device has emerged as a promising solution for detumbling malfunctioning satellites. However, existing rigid-body simplifications of the servicing spacecraft fundamentally obscure the underlying multibody coupling mechanisms, and the gap between detumbling strategies and manipulator motion planning restricts operational feasibility. To address these issues, this paper establishes a systematic rigid-flexible coupled dynamic model, in which the free-floating space manipulator and the large-deformation flexible rod are unified within a differential-algebraic system with Lagrange multipliers. To accurately calculate the contact dynamics and improve the computational efficiency of detumbling simulations, an effective contact detection algorithm combining global bounding-volume screening and local minimum distance optimization is designed. Furthermore, a multi-stage trajectory optimization scheme is proposed to bridge the gap between ideal contact strategies and physical feasibility, decomposing the detumbling trajectory planning task into contact point optimization, configuration optimization, and trajectory generation, thereby transforming highly nonlinear task-space requirements into configuration-space constraints and reducing the complexity of the optimization problem. Numerical simulations demonstrate that the proposed model accurately captures the coupled dynamics and contact characteristics during the detumbling process. The contact detection algorithm reduces the computational time by approximately 38% compared to the conventional algorithm. Moreover, the optimization scheme is capable of generating collision-free and dynamically feasible trajectories, enabling the servicing spacecraft to simultaneously suppress the rotation and nutation of the tumbling target, thereby ensuring safe and efficient detumbling operations.