Multi-wheel statically-stable mobile robots tall enough to interact meaningfully with people must have low centers of gravity, wide bases of support, and low accelerations to avoid tipping over. These conditions present a number of performance limitations. Ballbot is a single spherical wheeled mobile robot which can move fast in different directions. This kind of robot has the same height, width, and weight of a person and a high center of gravity. Unlike balancing 2-wheel platforms which must turn before driving in some directions, the single-wheel robot can move directly in any direction. Ballbot is an underactuated system with two nonholonomic velocity constraints. In order to deal with the real situations, in this thesis a spatial model of ballbot will be presented. Then trajectory planning and robust control of the robot will be applied on the achieved model. First, a 3D dynamic model of the ballbot is derived by using Lagrange method for nonholonomic systems. Using the null space of constraint coefficients matrix, Lagrange multipliers are omitted from the equations. Then to deal with input coupling, a change of variables will be used. Since ballbot is an underactuated system, finding a normal form of equations could be helpful in the control point of view. Therefore, its equations of motion are examined to find whether there is a simple normal form or not. However, it can be seen that there is no normal form for these motion equations. Next an offline trajectory planning is proposed to move the robot between two static configurations. This strategy is also used to move among several configurations while the sphere velocity is non zero at midpoints. The most important challenge in trajectory planning and control of the ballbot is to make the cylindrical body upright while moving the sphere on the ground. Thus, the offline trajectory is proposed for unactuated joints (cylinder angles) with limited amplitudes and unknown parameters. Using optimization techniques in evaluating the unknown parameters, the least error at final desired configuration is derived. In order to track the planned trajectory in the presence of uncertainties and disturbances, two different controllers (computed torque and sliding mode controllers) are applied to the system. An online trajectory planning is also suggested using fuzzy logic to track the desired time dependent sphere trajectories on the ground. The inputs of the fuzzy blocks are tracking errors of the sphere angles while the outputs are desired cylinder angles which are to be tracked by feedback controllers. The tracking of cylinder angles leads to track desired trajectories of the robot on the ground. This method is applied to the system to track different paths like a straight line and round paths. Computed torque method and sliding mode controllers are used beside fuzzy trajectory planning to help tracking of the desired trajectory. To consider uncertainties and disturbances, some simulations are performed, the result of which show that sliding mode controller demonstrate much better performance compared with computed torque controller. On the other hand, when such unfavorable conditions do not exist, the computed torque method is the candidate showing less tracking error than the sliding controller. Keywords Ballbot, Spatial Dynamic Modeling, Nonholonomic Systems, Trajectory Planning, Sliding Mode Controller, Computed Torque Controller, Fuzzy.