In the last twenty years, spherical mobile robots have been noticed. herical robots, due to their special abilities and their symmetrical shape, do not overturn during operation and have better maneuverability, also the closed cover of the robot protects its internal system from dust and other harmful factors and enables the robot to perform missions in environments where humans or other robots are unable to pass through these places. Mathematical modeling is always an important part of robotics therefore, at first, the kinematics modeling of the spherical robot was done with three rotor mechanisms. Afterwards, the dynamic modeling of the spherical robot was performed using two different constrained Lagrange and Newton methods. Subsequently, Lagrangian and Newtonian dynamics of the robot were examined on an inclined plane, and the Lagrangian dynamics of the spherical robot were also analyzed when the robot slipping. Some works were done on Newtonian dynamics to prepare the dynamic equations for controlling the system. The robot was then controlled using computed torque, fuzzy computed torque, adaptive fuzzy computed torque, sliding mode, and fuzzy sliding mode methods and the results of these five control methods were compared. At the end of this section, the undetermined dynamics of the robot were estimated using neural network and the control was done based on the neural network. Finally, a linear and circular path were designed for the robot and the robot's motion on the inclined plane was investigated and the probability of slippage on the inclined plane was also considered. The results of the linear path that was designed in this study were verified by a previous research. The results of these two studies were compatible with each other.All simulations were done with MATLAB and Simulink software. One of the innovations of this study is that the Lagrangian dynamics of spherical robot with three inertial wheels has been thoroughly studied for the state of pure rotation, furthermore, when the robot slips, the robot's dynamics on the inclined plane are completely derived from two different methods, and using fuzzy algorithms the solutions were improved and the undetermined dynamics of the system has been estimated using adaptive neural network algorithms. The uncertain dynamics were well estimated and the robot was well controlled. One of the benefits of a neural network estimator was that the control of the robot was done well, this is mainly because the undetermined dynamics were estimated, therefore, this process did not required much knowledge about nonlinear dynamics . Another topics addressed in this study was the investigation of the spherical robot slipping on an inclined plane because when the robot moves on an inclined plane and for example when it goes up, it may slip. Keywords: Spherical robot, inertia disk, Newton-Euler, Constrained Lagrangian, quaternion, fuzzy logic, computed torque control, sliding mode, neural network, inclined plane, slipping