Basic Research Of A Permanent Magnet Spherical Stepper Motor For Humanoid Robot Joint Applications

Based on the analysis of the present research and development situation of the multi-degree-of-freedom motors, a novel spherical stepper motor for humanoid robot joint applications is analyzed and studied. The theory and analyzing methods for the magnetic field and torque calculation, kinetic modeling, steady-state thermal analysis and motion control are presented and derived. The particular three-dimensional spherical structure has made it different from those conventional motors in the theoretical research. As for this kind of motor, many problems have been seldom discussed and the relative literature is sparsely delivered, which shows the necessity and provides significant reference to the research of similar motors. Compared with ordinary multi-degree-of-freedom motors, the spherical stepper motor combines the merits of simple structure, relatively small volume, wider motion range and easy to be controlled. As an operation component, the spherical stepper motor can effectively overcome the intrinsic disadvantages of conventional connecting mechanisms by simplifying the complexity of the transmission, improving the dynamic and static performance. Therefore, the spherical stepper motor has been the front domain of current mechatronic driven actuator system research with intensive theoretical background, which caters to many applications.The main contribution of this dissertation can be discussed as follows.1. The magnetic field produced by the permanent magnet is analyzed and modeled. The integral equation method and the finite element method are used to compute the 3D air-gap magnetic field and derive its distribution respectively and compared. The solution results are used to the geometric design, optimization of the motor.2. The torque calculation model using the modified Maxwell Stress Tensor Method based on the Integral Equation Method solutions is developed and the typical torque characteristics are derived, which are compared with the results using the virtual work method based on the finite element solutions. It shows that the results by two methods agree well. Moreover, the single pair and adjacent rotor poles torque characteristics also with the detent torque characteristic are studied. Based on the linear analysis on the electromagnetic system, a simplified torque calculation method for the 3D real-time motion control has been derived. Finally the configuration parameters are analyzed and investigated, including the effect on the dynamic responses and torque characteristics, the optimization on the electromagnetic system using the experiment design method.3. In terms of the kinematics modeling, the rigid body kinematic models of single rotor and rotor with the gimbal guideway are derived, which provides the theory basis for the real-time orientation detection by using the gimbal guideway device. The rigid body dynamic model of the motor is derived based on the Euler's equation. Considering the attached payload and the non-linear friction, a complete non-linear system dynamic model has been proposed to perform the simulation of the dynamic response and control strategy. A detailed dynamic response by single stepping is simulated and analyzed. As for the steady-state thermal analysis, the studies focus on the discrete stepping mode and the continuous trajectory tracking control mode respectively. The relationships between the stator material, thickness, cooling modes with the temperature rise are presented and the computation results are given.4. A developed motion control algorithm for the spherical stepper motor is presented and simulated via a thorough analysis on the motion characteristic with feasibility and validity. The continuous trajectory tracking control mode is presented to overcome the disadvantages on the tracking precision. Based on the simplified torque calculation method and the non-linear system dynamic model, a controller based on the robust control principle has been developed to improve the trajectory tracking robust stability and overcome the undesired influence of the uncertainties. The analysis and simulation results show the applied importance of the presented model and control strategy.