Precise control of robots and object’s orientation while balancing them is an important issue in robotics and control science. Humanoids, some of traortation vehicles, robots with two wheels and inverse pendulum are several examplcs in which balancing is crucial. In most of these robots, restricting one or two degrees of freedom, the robot balance is qacquired. In these robots, different actuators are used for balancing. In this thesis, based on the inertial momentum of the wheel and iired from inverse pendulum, a selfbalancing three-dimensional cube is introduced. This cube can balance on edges and corners. Moving from one position to another, (i.e. from one edge or corner to another edge or corner) is of the capabilies of this cube. This cube moves and balances itself via three perpendicular inertail wheels actuated by three electrical motors. This system consists of six degrees of freedom; three of which is related to the orientation of the cube with respect to inertal frame and the next three is of rotaion of the inertial wheels. The dynamics of the cube is highly nonlinear and nonlinear control techniques are required for controlling it. This cube is used in free-floating systems and balancing objects similar to inverse pendulum. In this work equations of the cube are obtained using Lagrangain and Newton-Euler methods in six degrees of freedom and are compared to each other for verifying the results. Two controllers based on fuzzy logic and computed torque methods are designed for this cube and simulations are conducted in MATLAB/Simulink. This system is designed in CATIA and the data for simulation are obtained from it. The results of the controllers are compared to each other and finally the fabrication and parts selection are discussed. Keywords: self-balancing cube with inertail wheels, nonlinear control, fuzzy control, six degree of freedom dynamics equations, three dimensional inverse pedulum