Ph.D. Thesis Defense by Raye A. Sosseh
Tuesday, December 11, 2001

(Dr. Kok-Meng Lee, advisor)

"Finite Element Torque Modeling and Backstepping Control of a Spherical Motor"


The increasing demand for multi-degrees of freedom (DOF) actuators in a number of industries has motivated a flurry of research in the development of a series of non-conventional actuators, one of which is a ball-joint-like variable reluctance (VR) spherical motor.  This motor is capable of providing smooth and isotropic three-dimensional motion in a single joint.  Compared to conventional robotic manipulators that offer the same motion capabilities, the innovative spherical motor possesses several advantages.  Not only can the spherical motor combine 3-DOF motion in a single joint, it has a large range of motion with no singularities in its workspace.  The VR spherical motor is much simpler and compact in design than most multiple single-axis robotic manipulators.  The motor is also relatively easy to manufacture.  These unique characteristics of a spherical motor have potential contributions to a wide range of applications such as coordinate measuring, object tracking, material handling, automated assembling, welding, and laser cutting.

Most of these features have been demonstrated in previous research efforts at Georgia Tech.  The spherical motor, however, exhibits coupled, nonlinear and very complex dynamics that make the design and implementation of feedback controllers very challenging.  The orientation-varying torque generated by the spherical motor also contributes to the challenges in the controller design.  This thesis contributes to the on-going research effort by exploring alternate methods for controlling the motor.  This thesis addresses three issues related to the control of a spherical motor; (1) use of finite element (FE) methods to formulate an appropriate form of the torque model for real-time control, (2) use of a constrained Lagrangian formulation to derive the dynamics of an existing spherical motor prototype, and (3) the design and real-time implementation of a robust feedback controller.  The robust backstepping controller presented in this thesis is used to further demonstrate the appealing features exhibited by the spherical motor.