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At present, the output shaft of a permanent magnet spherical actuator (PMSA) is a rigid structure, which has the problems of small load weight ratio and high energy consumption. It is difficult to meet the application requirements of lightweight, high speed, and low energy consumption. In this paper, a PMSA is proposed as the driving motor for the rigid-flexible coupling system (R-FCS) of the robotic manipulator, and a flexible mechanical arm is used to replace the rigid output shaft of the PMSA to connect the hand claw to form a spherical joint. Firstly, the partial differential dynamics model of the robotic manipulator in the coordinate system is established based on the Hamilton method, and the R-FCS is constructed according to the momentum conservation equation combined with the rigid axis dynamics model of the PMSA. Then, a backstepping sliding mode controller (BSMC) is designed to form a closed-loop control system by selecting an appropriate nonlinear gain function to estimate the unknown disturbances of the system, and the stability of the controller is guaranteed by the Lyapunov theory. Finally, the simulation and experimental results verify that the R-FCS can achieve better trajectory tracking and provide an effective driving method for robotic manipulator spherical joint. [ABSTRACT FROM AUTHOR]

This study proposes an adaptive sliding‐mode control strategy based on trajectory re‐planning for a permanent magnet spherical actuator (PMSA) to address the large overshoot caused by substantial initial error while maintaining tracking precision. The proposed re‐planning technique reconstructs a local trajectory without the preceding knowledge of the desired position in the future, which makes this technique more suitable for reconstructing trajectory given online. First, a re‐planning cool‐down term is added to maximize the capability of controller to improve the precision and speed of tracking. Moreover, a smooth switching technique is also applied to further improve the precision of trajectory tracking and stop redundant re‐planning when the system enters satisfactory state. Finally, the proposed trajectory re‐planning strategy is combined with a robust adaptive sliding‐mode controller (RASC), which effectively reduces friction, delay, and external uncertainty disturbances. The effectiveness of the proposed control design is verified by both simulation and experiment on PMSA, which can provide reference for the further engineering application of multi‐degree‐of‐freedom system. © 2023 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

Permanent magnet spherical motors (PMSMs) operate on the principle of the dc excitation of stator coils and three freedom of motion in the rotor. Each coil generates the torque in a specific direction, collectively they move the rotor to a direction of motion. Modeling and analysis of the output torque are of critical importance for precise position control applications. The control of these motors requires precise output torques by all coils at a specific rotor position, which is difficult to achieve in the three-dimension space. This article is the first to apply the Gaussian process to establish the relationship of the rotor position and the output torque for PMSMs. Traditional methods are difficult to resolve such a complex three-dimensional problem with a reasonable computational accuracy and time. This article utilizes a data-driven method using only input and output data validated by experiments. The multitask Gaussian process is developed to calculate the total torque produced by multiple coils at the full operational range. The training data and test data are obtained by the finite-element method. The effectiveness of the proposed method is validated and compared with existing data-driven approaches. The results exhibit superior performance of accuracy. [ABSTRACT FROM AUTHOR]