This study explores a method for the dynamic modeling of soft robots, focusing on enhancing the deep learning-based Lagrangian modeling approach through the attention mechanism, which enriches the training process by allocating focused attention and analytical weighting to critical state features, thereby increasing the model's sensitivity to changes in the robot's state. We compared our method through simulation, demonstrating that the model is effective in long-term prediction and noise rejection.

This letter investigates the direct trajectory optimization of the free-floating space manipulator (FFSM). The main purpose is to plan the joint space trajectories to reduce the spacecraft motion due to the joint rotation during the FFSM performing tasks. To improve the calculation efficiency, the adaptive Radau pseudospectral method (A-RPM) is applied to discretize the system dynamics and transform the formulated optimal problem into a nonlinear programming problem (NLP). By adaptively subdividing the current segment and assigning collocation points according to the solution error, high-degree interpolation polynomials are avoided. To verify the effectiveness of the proposed method, a ground micro-gravity platform of the FFSM system is designed by using the air-bearing technique, on which experiments are carried out. The results show that the variation of the base spacecraft is dramatically reduced if the joints rotate along the optimized trajectories.