Ph.D Thesis

Ph.D StudentJin Hui-Liang
SubjectModeling and Control of a Robotic Yoyo
DepartmentDepartment of Mechanical Engineering
Supervisor PROF. Miriam Zacksenhouse


The original contribution of this thesis includes three parts: 1) modeling the dynamics of yoyo, 2) control: model-based approach, 3) control: oscillator-based approach. The first part is conducted due to the lack of appropriate models. The two control approaches are based on different types of feedback and the resulted difference in performance is compared.

      Modeling. A two-DOF (degree-of-freedom) dynamic model of the yoyo is first proposed in this project. The flight of the yoyo can be divided into four different phases, namely, the constrained motion phase, the bottom phase, the free motion phase, and the transition phase. During the bottom and the transition phases a sequence of collisions between the yoyo and the string is observed. It is asserted and experimentally verified that the energy loss due to these collisions dominates the total energy loss. Based on the two-DOF model, a simplified one-DOF model is proposed. The one-DOF model can be used to construct a state observer to estimate the angular velocity and the angular position of the yoyo, thereby facilitating the development of the model-based control.

      Model-based control. A simple control algorithm for coordinating the motion of the robot with that of the yoyo is proposed. The stability of the closed-loop system was investigated by analyzing a discrete return map derived from the original continuous system. The stabilizing power of the control algorithm is successfully demonstrated on a real-time robotic yoyo playing system. Theoretical predictions regarding the fixed point of the return map are experimentally confirmed. This part of the project provides a further verification of the one-DOF model developed in the previous part as well as a preparation for the next part---oscillator-based control of yoyo playing.

      Oscillator-based control. Several simple forms of neural oscillators for closed-loop control of the yoyo are studied, namely, the leaky integrate-and-fire (LIF) oscillator and the phase-lock loop (PLL) oscillator, each with either an excitatory or an inhibitory connection. The steady-state working curves of the four oscillators are investigated with respect to that of the yoyo and it is rigorously shown that only the inhibitory PLL oscillator may stabilize the yoyo. The theoretical predictions are verified by numerical simulation.

       The above results have been formulated into several papers. The thesis concludes with a discussion that addresses some basic issues regarding the project and with suggestions for future research.