Mathematical model based on nonlinear differential equations and its control algorithm

A practical examination of the traditional robotic arm (RA) in operation revealed a significant limitation in its ability to control the position of motion. This underscores the urgent need to enhance the current RA’s position control capabilities. Therefore, this study proposes the use of nonlinear differential equations (NDEs) to establish a mathematical model and the design of NDE-based RA motion control algorithms in conjunction with a central pattern generator neural network. A comparison of the control effects showed that the proposed method was highly fitted to the target trajectory. The joint node (JN) motion tracking trajectories of the three RAs were similar, up to 90–85% to the target trajectories of the JNs. In addition, the control of the motion position was similar up to 95–98% to the target motion position trajectories. The motion control algorithm based on NDEs was effective in improving the average execution time of the Pareto optimal frontier of the RA by 58.29%. The joint velocity and angle changes of the three types of RAs under the NDE control algorithm exhibited a high degree of similarity to the fluctuations observed in the expected and predicted curves. These observations contribute to an understanding of the effectiveness of the system observer in observing the joint angle changes. This indicates that the motion control based on NDEs can effectively enhance the tracking effectiveness of the JN positions of the RA, improve the control ability of the RA motion, and increase the joint stability of the RA.