Chaotic Vibration Prediction of a Free-Floating Flexible Redundant Space Manipulator

The dynamic model of a planar free-floating flexible redundant space manipulator with three joints is derived by the assumed modes method, Lagrange principle, and momentum conservation. According to minimal joint torque's optimization (MJTO), the state equations of the dynamic model for the free-floating redundant space manipulator are described. The PD control using the tracking position error and velocity error in the manipulator is introduced. Then, the chaotic dynamic behavior of the manipulator is analyzed by chaotic numerical methods, in which time series, phase plane portrait, Poincare map, and Lyapunov exponents are used to analyze the chaotic behavior of the manipulator. Under certain conditions for the joint torque optimization and initial values, chaotic vibration motion of the space manipulator can be observed. The chaotic time series prediction scheme for the space manipulator is presented based on the theory of phase space reconstruction under Takens' embedding theorem. The trajectories of phase space can be reconstructed in embedding space, which are equivalent to the original space manipulator in dynamics. The one-step prediction model for the chaotic time series and the chaotic vibration was established by using support vector regression (SVR) prediction model with RBF kernel function. It has been proved that the SVR prediction model has a good performance of prediction. The experimental results show the effectiveness of the presented method.