Control of a Spherical Robot with a Nonholonomic Omniwheel Hinge Inside

This study investigates the rolling along the horizontal plane of two coupled rigid bodies: a spherical shell and a dynamically asymmetric rigid body which rotates around the geometric center of the shell. The inner body is in contact with the shell by means of omniwheels. A complete system of equations of motion for an arbitrary number of omniwheels is constructed. The possibility of controlling the motion of this mechanical system along a given trajectory by controlling the angular velocities of omniwheels is investigated. The cases of two omniwheels and three omniwheels are studied in detail. It is shown that two omniwheels are not enough to control along any given curve. It is necessary to have three or more omniwheels. The quaternion approach is used to study the dynamics of the system.