Abstract: Unlike permanent magnet spherical motors, the design inspiration for reluctance spherical motors comes from switched reluctance motors. The presence of a doubly salient structure can cause significant torque ripple, thereby affecting the stable operation of the motor. In order to suppress the torque ripple of a reluctance spherical motor, a constant torque control method is proposed from a control perspective. By analyzing and studying its spin, tilt, and arbitrary direction motion, the torque ripple suppression of a reluctance spherical motor during spin, tilt, and arbitrary direction motion is achieved. The main work of this article is as follows. Firstly, the motion process and energization situation of a reluctance spherical motor are analyzed, and a method for solving the driving current—torque current fitting polynomial method is proposed. Then, the constant torque control method is used to suppress torque ripple of the reluctance spherical motor during spin, tilt, and any direction motion. Finally, the torque ripple suppression at different positions is verified through simulation and experiments, and the verification results show the effectiveness of the proposed method.