# Sensorless Posture Detection of Reluctance Spherical Motor Based on Mutual Inductance Voltage
## 3 Particle Swarm Optimization Algorithm for 3-DoF Attitude Recognition
### Experimental Verification  
In order to verify the effectiveness of the sensorless detection method proposed in this paper, experimental verification is carried out by using artificially preset posture points and comparing them with the detection results of contact sensors. According to the readings of rotary encoders installed on three rotating shafts on the 3-DoF contact position detection bench as shown in Figure 3, it is considered that the rotor of the spherical motor is adjusted to a given position. Then, the mutual inductance voltage values of all twelve groups of coils are detected on a tour inspection using the detection circuits shown in Figure 4. These voltage values are put into the position recognition program for algorithmic recognition. The recognition results are compared with the actual readings of the contact sensor. The main parameters of the algorithm are set as follows: swarm size is 200, iteration algebra is 50, and fitness function is described in the previous section. Two motion tracks are designed for the test. The first is to fix the roll angle of the rotor around the X-axis at \(-10^{\circ}\), the pitch angle around the Y-axis increases from \(-10^{\circ}\) to \(10^{\circ}\) in steps of \(2^{\circ}\), and the yaw angle around the Z-axis synchronously decreases from \(20^{\circ}\) to \(-20^{\circ}\) in step of \(4^{\circ}\). The experimental results are shown in Figure 11. The dashed line is the actual value of the position angle obtained by the contact position sensor, and the dotted line is the detection value of the position angle obtained by inversion according to the mutual inductance voltage. The second experimental trajectory is as follows: all three degrees of freedom rotate synchronously in a step of 3\({}^{\circ}\), in which the pitch angle around the Y axis and the yaw angle around the Z axis decrease from 15\({}^{\circ}\) to \(-\)15\({}^{\circ}\), and the pitch angle around the Y axis increases from \(-\)15\({}^{\circ}\) to 15\({}^{\circ}\). The experimental results are shown in Figure 12.  
From the comparison between the set value and the detected value of the 3-DoF position angle in Figures 11 and 12 and Tables 1 and 2, it can be seen that the proposed sensorless detection method has a good on-line detection effect; the maximum detection  
Figure 11: Result of experiment 1: (a) experimental result, (b) error distribution. Figure 12: Result of experiment 2: (a) experimental result, (b) error distribution. error is within \(\pm 4^{\circ}\), and the population standard deviation is within \(1.8^{\circ}\). It can be used for replacing the position detection method with sensors. The main causes of experimental biases are as follows:  
1. The bias brought from inconsistent magnetic circuits caused by the manufacturing process and assembly accuracy of the spherical motor. In the process of testing and drawing the contour lines of the mutual inductance voltage, it is found that the contour lines obtained by selecting different rotor pole as regulating object have certain differences. In this regard, this paper takes the median processing of the mutual inductance voltage contour lines obtained from the different rotor pole tests. The difference between this median and the actual measurement value would be reflected in the bias of the final result. This part of bias can be reduced by improving the manufacturing process of the motor and improving the consistency of the magnetic circuit. 2. The bias brought by the algorithm termination condition. In order to ensure the output speed of the algorithm, a coercive termination condition according to evolutionary algebra is set. This may lead to some cases in which the fitness of the output results is not high enough. Therefore, it is necessary to further improve the efficiency of the algorithm, reduce the amount of computation, and improve the convergence speed. 3. The deviation of the preset position angle during the experiment.