Geometric methods for control of nonholonomic mechanical systems with applications to the control moment gyroscope and wheeled mobile robots

The advantage of geometric dynamics analysis over the classical analysis method is that geometric method is independent of the choice of coordinates. The work, presented here, applies differential geometry for analysis and control of underactuated dynamical systems which include mobile robots, aircraft systems, underwater vehicles, satellites and many more systems. In the first part we will model a class of wheeled mobile robots and for which geometric method is applied to trajectory tracking. In the second part of the dissertation, geometric method is applied to the control moment gyroscope mounted on an inverted pendulum. The control moment gyroscope inverted pendulum is originally modeled at Embry-Riddle Aeronautic University by Dr. Douglas Isenberg. Stability analysis and control law design is proposed. The first solution proposed uses collocated partial feedback linearization and then the dynamics are transformed into strict feedback form, a form suitable to apply backstepping method. This work appears in the Springer series Advances in Intelligent Systems and Computing [6]. The application of collocated partial feedback linearization due to Mark Spong, makes it easy to transform the system into a cascade of a linear and a nonlinear subsystems. Peaking phenomenon is an issue which is inherently present in interconnected subsystems; the manifestation of this phenomenon is sometimes observed as finite time escape. Finite time escape can excite unstable modes in the nonlinear subsystem. Peaking phenomenon is studied and a solution is proposed.;[6] Yawo H Amengonu, Yogendra P Kakad, and Douglas R Isenberg. The control moment gyroscope inverted pendulum. In Advances in Systems Science, pages 109--118. Springer, 2014.