# Sensorless Posture Detection of Reluctance Spherical Motor Based on Mutual Inductance Voltage
## 1 Introduction  
Under the development of industrial automation demand for a multi-degree-of-freedom (DoF) motion mechanism, a motion mode for motors has been developed from simple one-dimensional rotation to a multi-degree-of-freedom motion. Due to the compact structure, no accumulation of motion bias, and a flexible motion mode [1], the spherical motor is especially suitable for installation and narrow motion space and has a wide application prospect in robot arms, joints, and other fields. However, due to its 3-DoF motion characteristics, the spherical motor cannot be driven in an open-loop manner. Whatever the motion is should be based on accurate attitude detection. Until now, scholars from all over the world have made extensive explorations in the position detection and drive control of spherical motors and have achieved outstanding results. However, the reported research still has some defects in position detection, especially in sensorless detection. As a result, the volume advantage of a spherical motor over a multi-DoF motion mechanism formed by a combination of multiple single-DoF motors is completely offset by a huge and complex detection mechanism, which has since become a great obstacle for spherical motors to enter actual industrial applications.  
According to whether the detection device is in contact with the rotor of the spherical motor, the rotor position detection method can be divided into contact detection method and non-contact detection method. All the contact detection methods need to add a mechanical detection mechanism to the rotor, driving the encoder through the contact structure, such as the sensing systems described in [2; 3; 4]. Although the detection mechanism adopted has good detection accuracy, it occupies too much space and interferes with the rotor motion. In order to avoid the defects of the contact detection method, the works in [5; 6; 7] use the Hall element for non-contact position detection in their research process for spherical motors, locating the rotor by detecting the magnetic field of the permanent magnet in the rotor. The works in [8; 9] adopted a pseudo-random array color checkered pattern coding method, through the color information detected by optical sensors, cooperating with known rotor coating code and detecting the rotor position by Machine vision. In the sensorless position detection of spherical motors, [PERSON] uses the induced voltage generated in the stator coils of the permanent magnet spherical motor rotor flux to first realize the sensorless detection of the angular velocity and position increment of the spherical motor rotor as described in [10; 11]. Compared with the results from a gyroscope, it can achieve the same accuracy and a better signal-to-noise ratio, but the detection accuracy is lower at low speed or zero-speed since the reverse voltage is difficult to detect.  
In order to realize sensorless position detection of the spherical motor, a method is proposed in this paper to judge the 3-DoF position of the switched reluctance rotor by detecting the mutual inductance voltage of the stator coils. The numerical relationship between the misalignment of stator/rotor poles and the mutual inductance of coil is analyzed as the basic information to judge the spatial position of the rotor. In the process of on-line rotor position detection, according to the mutual inductance voltage information collected in real time, an intelligent optimization algorithm is used, combined with the mutual inductance voltage distribution pattern and constraints of the rotor structure to inverse the 3-Dof position angle of the rotor. Taking a 24/6 pole switched reluctance spherical motor as an experimental object as shown in Figure 1, the proposed sensorless position detection method is verified by comparing the results with the contact sensors at artificially preset posture points. The results prove the effectiveness of the method.