# Sensorless Posture Detection of Reluctance Spherical Motor Based on Mutual Inductance Voltage
## 3 Particle Swarm Optimization Algorithm for 3-DoF Attitude Recognition  
### Identification Principle  
According to the monotonous correspondence within a range of 30\({}^{\circ}\) between the mutual inductance voltage generated in the coil and rotor teeth misalignment angle, each group of coils can be regarded as a sensor for detecting the rotor teeth. Figure 10 shows the detection range of twelve coil groups of the upper, middle, and lower layers in the range of 0\({}^{\circ}\) to 180\({}^{\circ}\) east longitude of the stator, and the western half of the sphere is symmetrical. In the figure, the center of each coil's detection range is the installation position of the coil on the stator. Each ellipse represents the maximum detection range of a coil., and the filled circles represent the positions of the three rotor teeth located in the eastern hemisphere surface at a rotor random position. Theoretically, as long as any two of the three rotor teeth can be determined, the 3-DoF position angle of the rotor can be calculated. It is the simplest to calculate the spherical position of rotor teeth by the trilateration method [17; 18], judging the position of rotor teeth by the distance from rotor tooth to three stator coils with known positions. However, due to the number of rotor teeth in the prototype, the period of coil mutual inductance voltage is too short, which makes the detection range of each coil detector too small. As shown in Figure 10, the coincidence of the detection ranges of the third, fourth, and seventh coils is only a small piece of black zone, and the condition of  
Figure 8: Mutual inductance voltage measurements for yaw and pitch motion in the 30\({}^{\circ}\) range of the layer coil. Figure 9: Contour diagram of mutual inductance voltage (mV) distribution. traliteration is met only when the rotor teeth are located in this area. However, the area that meets this condition only accounts for a small part of the possible positions of the whole rotor tooth. On the other hand, according to the contour map of the coil mutual inductance voltage obtained in advance, the theoretical value of the coil mutual inductance voltage can be conveniently obtained from the positional relationship between the rotor magnetic pole and coil axis. However, if the position of the rotor magnetic pole according to the value of the mutual inductance voltage is reversed, a position set represented by a contour line instead of a certain position value would be obtained. Therefore, it is impossible to directly calculate the rotor position from the mutual inductance voltage. Instead, it is necessary to constantly test whether a hypothetical rotor position can bring about the mutual inductance voltage that is consistent with the actual situation, that is, to invert the rotor position through the information of the mutual inductance voltage. If the assumed rotor 3-DoF position can bring the assumed values of the mutual inductance voltage of all coils close enough to the measured values, it can be considered that the assumed position of the rotor is approximately equal to the actual position. According to this train of thought, in the process of rotor position inversion, the measured values of the mutual inductance voltage of all coils are measured and recorded online on the one hand, assuming the 3-DoF position angle of the rotor on the other hand. Then, determine the assumed position of each rotor magnetic pole in combination with the design structure and obtain the assumed value of the mutual inductance voltage of each coil at this assumed position according to the known contour map of mutual inductance voltage. An intelligent optimization algorithm is used to optimize the assumed value of the rotor 3-DoF position angle, and the assumed value that minimizes the error between the predicted value and the measured value of all mutual inductance voltages is found as the final rotor position inversion result.