A spherical tractor operating mobile platform (STOMP) is provided for internally propelling and steering along an external surface. The STOMP includes a spherical shell having interior and exterior surfaces, an internal chassis containing an electrical power supply and a propulsion controller; a tractor drive system and an overhead wheel assembly. The tractor drive system provides propulsion and steering of the shell along the surface. The drive system includes a frame that connects to the chassis from below and contains a motor unit. The frame includes port and starboard sides that support respective wheel sets surrounded by corresponding continuous tracks. These tracks engage the shell's interior surface. Each wheel set includes a drive wheel, an idler wheel and a tension wheel for engaging a corresponding track. The overhead wheel assembly connects to the chassis from above to maintain the chassis and the drive system in compression with the shell. To propel the shell, the propulsion controller commands the motor unit to provide torque to both the port and starboard drive wheels. For steering the shell towards starboard, the motor provides torque to the port drive wheel. For steering the shell towards port, the motor provides torque to the starboard drive wheel.