Minimum-jerk trajectory generation and global optimal control for permanent magnet spherical actuator

The study in this paper covers minimum-jerk trajectory generation and global optimal control for the Permanent Magnet Spherical Actuator(PMSA). The generated trajectory is guaranteed to minimize the end-actuator jerk in order to improve the smoothness and stability of rotor motions. A novel three-dimensional Euclidean space orientation representation method based on Rotation group SO(3) is proposed to promote the trajectory generation of the rotor. A union of dynamics and inverse torque model is well established and then global optimal control algorithm is developed to improve trajectory tracking ability without excessive control-energy expenditure. To verify the effectiveness and robustness of the proposed algorithm, simulations and experiments are conducted on the spherical actuator. The results indicate that by using minimum-jerk trajectory generation, a union of dynamics and inverse torque model, and the global optimal control can be supplied into the spherical actuator to achieve ideal motions performance.