Linear Multi-step Prediction and Correction Algorithm of 6-DOF Space Manipulator for Continuous Trajectory Tracking

In this paper, the generalized Jacobian matrix and the improved Milne-Hamming linear multi-step prediction and correction algorithm are combined for solving the space manipulator trajectory tracking problem. First of all, controlling end-effector tracks a known trajectory by the method of pseudo inverse of generalized Jacobian matrix. However, due to the accuracy of the solution of this approach inversely with the step-size of numerical integration, we need larger calculation to get more precise solutions. To increase the accuracy in fixed step-size of calculation, Milne-Hamming linear multi-step prediction and correction algorithm is combined with the methods that mentioned above. Then, we utilize the Runge-Kutta method to evaluate the first four solutions of Milne-Hamming algorithm result. We don’t have enough parameters to initialize the algorithm until step five. Finally, the validity of the algorithm is verified by computer simulation.