recently, the two-wheeled inverted pendulum has drawn the attention of robotic community in view of a plethora of applications, such as transport vehicles: segway, teleconferencing robots, and electronic network-vehicle. as a widely-used personal transportation vehicle, a two-wheeled inverted pendulum robot has the advantages of small size and simple structure. moreover, with the advent of modern control technology, these kinds of platforms with safety features and sophisticated control functions can be cost down, so that they have high potential to satisfy stringent requirements of various autonomous service robots with high speed. at the same time, it is of great interest from control point of view as the inverted pendulum is a complicated, strongly coupled, unstable and nonlinear system. therefore, it is an ideal experimental platform for various control theories and experiments. to understand such a complex system, the lagrangian equation has been introduced to develop a dynamic model. and following the mathematical model, linear quadratic regulator control and fuzzy adaptive method are proposed for upright stabilization, velocity control and position control of the system. however, sometimes these kinds of robots need to move on a slope, so an advanced linear quadratic regulator controller and a modified fuzzy adaptive controller have been proposed to achieve position control on a slope for the robot while stabilizing its body in balance. in addition, trajectory tracking control using proportional integral derivative control and sliding mode control with fuzzy adaptive backstepping method is also designed to make the robot autonomously navigate in two dimensional plane. simulation results indicate that the proposed controllers are capable of providing appropriate control actions to steer the vehicle in desired manners. then, a couple of real time experiments have been conducted to verify the the effectiveness of the developed control strategies.