Direct trajectory optimization of coupled constrained system formed by the space manipulator and the flexible structure

This paper investigates the dynamics modeling and trajectory optimization of a coupled constrained system consisting of a space manipulator and a flexible structure. The objective is to plan the joint-space trajectory that guides the manipulator to a desired configuration, while minimizing vibration and deformation of the flexible structure. The trajectory is simultaneously strictly constrained to the manifold defined by the geometric constraint. Firstly, the augmented Lagrangian approach is adopted to model the coupled constrained dynamics. The space manipulator and the flexible structure are formulated together as a differential-algebraic system with Lagrange multipliers. The multipliers are used as the optimization decision variables to construct the coupled constrained dynamic state equations. Then, the trajectory planning is formulated as an optimal control problem with the geometric constraint and transcribed into a nonlinear optimization problem via a direct collocation method. To address trajectory drift caused by discretization errors, a correction strategy combining the relaxation mechanism and orthogonal projection is proposed. Moreover, a residual-based mesh refinement strategy is introduced. It increases time resolution in segments with high residuals and applies warm-started optimization to improve efficiency. Simulation results show that the proposed method maintains both dynamic consistency and geometric accuracy. It effectively suppresses structural vibration and improves overall feasibility and solver robustness.