A Repeatable Motion Scheme for Kinematic Control of Redundant Manipulators.

To achieve closed trajectory motion planning of redundant manipulators, each joint angle has to be returned to its initial position. Most of the repeatable motion schemes have been proposed to solve kinematic problems considering only the initial desired position of each joint at first. Actually, it is very difficult for various joint angles of the robot arms to be positioned in the expected trajectory before moving. To construct an effective kinematic model, a novel optimal programming index based on a recurrent neural network is designed and analyzed in this paper. The repetitiveness and timeliness are presented and analyzed. Combining the kinematic equation constraint of manipulators, a repeatable motion scheme is formulated. In addition, the Lagrange multiplier theorem is introduced to prove that such a repeatable motion scheme can be converted into a time-varying linear equation. A finite-time neural network solver is constructed for the solution of the motion scheme. Simulation results for two different trajectories illustrate the accuracy and timeliness of the proposed motion scheme. Finally, two different repetitive schemes are compared and verified the optimal time for the novelty of the proposed kinematic scheme.