2-Dimensional Dynamical Modeling and Control of Spherical Robot Driven by Inner Car

Spherical robots have been studied by many researchers because of its high mobility and robustness against the surrounding environments due to the symmetric shapes and sealed driving mechanisms. The major driving techniques are the moving weight and reaction torques ones, most of which need the complex mechanisms easy to be at fault. On other hand, the inner car driving technique exceptionally results in simple mechanism, where the cars are used only to change the center of mass to generate the gravitational driving forces. In this paper, the 2-dimensional modeling and control of the spherical robot which is directly driven by the inner car with the wheel's torque. In the modeling, the rolling constraints between the outer sphere, the inner car's wheel and the ground are considered while the geometric constraint to support the car on the sphere is also considered. In the control, a linear regulation controller of the sphere's position with stabilizing the inner car's orientation is derived based on the reduced system, which are given by eliminating the constraint forces from the equations of motion of the whole system. The effectiveness of the controller is shown by a numerical simulation where the original system is considered.