Stabilization of an inverted pendulum using control moment gyros

Gyroscopes have played an important role in the science community with uses ranging from simple classroom demonstrations to cutting edge technological advancements. They offer a unique source of torque that has been proven useful in a wide range of applications. One common educational demonstration calls for a person to stand on a pivoting platform, and hold a spinning bicycle wheel with one hand on each side of the axle. As the person rotates their arms, causing precession of the bicycle tire, they begin to spin on the platform. This is due to the dynamic effect of the gyroscope and is a perfect example of a control moment gyro. This paper presents the use of control moment gyros as a compact way of dynamically controlling an inverted pendulum. The dynamic characteristics are derived for a dual-gyroscope configuration that generates torque proportional to the velocity about the gimbal axis. Classical control theory is used to design a controller that not only stabilizes the pendulum, but also controls the gyroscopes to return to a neutral steady state position. Control gains are adjusted to account for noise effects and to compensate for parameter errors, and an accelerometer is used to replace the potentiometer measuring the vertical angle. With the theory and background in place, experimental results are presented to verify the predicted response and validate the control approach. The end result is a stable system that is resilient to a broad range of external influences and erroneous measurements

Single wheel robot: gyroscopical stabilization on ground and on incline.

by Loi-Wah Sun.Thesis (M.Phil.)--Chinese University of Hong Kong, 2000.Includes bibliographical references (leaves 77-81).Abstracts in English and Chinese.Abstract --- p.iAcknowledgments --- p.iiiContents --- p.vList of Figures --- p.viiList of Tables --- p.viiiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Motivation --- p.1Chapter 1.1.1 --- Literature review --- p.2Chapter 1.1.2 --- Gyroscopic precession --- p.5Chapter 1.2 --- Thesis overview --- p.7Chapter 2 --- Dynamics of the robot on ground --- p.9Chapter 2.1 --- System model re-derivation --- p.10Chapter 2.1.1 --- Linearized model --- p.15Chapter 2.2 --- A state feedback control --- p.16Chapter 2.3 --- Dynamic characteristics of the system --- p.18Chapter 2.4 --- Simulation study --- p.19Chapter 2.4.1 --- The self-stabilizing dynamics effect of the single wheel robot --- p.21Chapter 2.4.2 --- The Tilting effect of flywheel on the robot --- p.23Chapter 2.5 --- Dynamic parameters analysis --- p.25Chapter 2.5.1 --- Swinging pendulum --- p.25Chapter 2.5.2 --- Analysis of radius ratios --- p.27Chapter 2.5.3 --- Analysis of mass ratios --- p.30Chapter 3 --- Dynamics of the robot on incline --- p.33Chapter 3.1 --- Modeling of rolling disk on incline --- p.33Chapter 3.1.1 --- Disk rolls up on an inclined plane --- p.37Chapter 3.2 --- Modeling of single wheel robot on incline --- p.39Chapter 3.2.1 --- Kinematic constraints --- p.40Chapter 3.2.2 --- Equations of motion --- p.41Chapter 3.2.3 --- Model simplification --- p.43Chapter 3.2.4 --- Linearized model --- p.46Chapter 4 --- Control of the robot on incline --- p.47Chapter 4.1 --- A state feedback control --- p.47Chapter 4.1.1 --- Simulation study --- p.49Chapter 4.2 --- Backstepping-based control --- p.51Chapter 4.2.1 --- Simulation study --- p.53Chapter 4.2.2 --- The effect of the spinning rate of flywheel --- p.56Chapter 4.2.3 --- Simulation study --- p.58Chapter 4.2.4 --- Roll up case --- p.58Chapter 4.2.5 --- Roll down case --- p.58Chapter 5 --- Motion planning --- p.61Chapter 5.1 --- Performance index --- p.61Chapter 5.2 --- Condition of rolling up --- p.62Chapter 5.3 --- Motion planning of rolling Up --- p.65Chapter 5.3.1 --- Method I : Orientation change --- p.65Chapter 5.3.2 --- Method II : Change the initial velocities --- p.69Chapter 5.4 --- Wheel rolls Down --- p.70Chapter 5.4.1 --- Terminal velocity of rolling body down --- p.73Chapter 6 --- Summary --- p.75Chapter 6.1 --- Contributions --- p.75Chapter 6.2 --- Future Works --- p.76Bibliography --- p.7

Control of the Gyrover: A Single-Wheel Gyroscopically Stabilized Robot

The definitive article is published in Advanced Robotics, located at http://brill.publisher.ingentaconnect.com/content/vsp/arb (DOI: 10.1163/156855300741951). © Brill Academic PublishersThe Gyrover is a single wheel gyroscopically stabilized mobile robot developed at Carnegie Mellon University. An internal pendulum serves as a counter weight for a drive motor that causes fore/aft motion, while a large gyroscope on a tilt-mechanism provides for lateral balance and steering actuation. In this paper, we develop a detailed dynamic model for the Gyrover, and use this model in an extended Kalman filter to estimate the complete state. A linearized version of the model is used to develop a state feedback controller. The design methodology is based on a semi-definite programming procedure which optimize the stability region subject to a set of Linear Matrix Inequalities that capture stability and pole placement constraints. Finally, the controller design combined with the extended Kalman filter are verified on the robot prototype

Control of the Gyrover: A Single-Wheel Gyroscopically Stabilized Robot

This paper was presented at the 1999 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS'99), Kyongju, Korea, October 17-21. The definitive paper is located at: http://ieeexplore.ieee.org (DOI: 10.1109/IROS.1999.813001). © IEEE.The Gyrover is a single wheel gyroscopically stabilized mobile robot developed at Carnegie Mellon University. An internal pendulum serves as a counterweight for a drive motor that causes fore/aft motion, while a tilt-mechanism on a large gyroscope provides a mechanism for lateral actuation. In this paper, we develop a detailed dynamic model for the Gyrover, and use this model in an extended Kalman filter to estimate the complete state. A linearized version of the model is used to develop a state feedback controller. The design methodology is based on a semi-definite programming procedure which optimizes the stability region subject to a set of Linear Matrix Inequalities that capture stability and pole placement constraints. Finally, the controller design combined with the extended Kalman filter are verified on the prototype.Institute for Complex Engineered Systems at Carnegie Mellon UniversityDefense Advanced Research Projects Agency (Contract # DABT63-97-1-0003)

Control of the Gyrover : a single-wheel gyroscopically stabilized robot

The Gyrover is a single wheel gyroscopically stabilized mobile robot developed at Carnegie Mellon University. An internal pendulum serves as a counter weight for a drive motor that causes fore/aft motion, while a tilt-mechanism on a large gyroscope provides a mechanism for lateral actuation. In this paper we develop a detailed dynamic model for the Gyrover and use this model in an extended Kalman filter to estimate the complete state. A linearized version of the model is used to develop a state feedback controller. The design methodology is based on a semi-definite programming procedure which optimize the stability region subject to a set of linear matrix inequalities that capture stability and pole placement constraints. Finally, the controller design combined with the extended Kalman filter are verified on the prototype