This book presents the achievements of the author s team in the research of a special underactuated system called mobile wheeled inverted pendulum MWIP developed over recent years It focuses on a combination of theory and practice and almost all algorithms are verified on the real MWIP system Taking the dynamic modeling control and simulation as the mainline this book first introduces the particularity control challenges and applications of the MWIP system Then Lagrange function is adopted to model the dynamics of two dimensional and three dimensional MWIP systems Then based on the special characteristics of the MWIP s dynamics a new high order disturbance observer is designed and a control strategy is proposed by combining the high order disturbance observer with a novel design of sliding mode manifold Furthermore several methods to overcome the chattering problem of the traditional sliding mode control are presented in detail Besides some intelligent algorithms related to the interval type 2 fuzzy logic control are applied to the MWIP system Finally the future development of underactuated robot has been prospected This book is intended for researchers and engineers in robotics and control It can also be used as supplementary reading for nonlinear systems theory at the graduate level The in depth theory and detailed platform construction provide an excellent convenience for readers to build their platforms and learn the knowledge they need