Embodiments of a friction drive system include a battery, a drive motor, a control unit, and a speed wheel. When the friction drive system is mounted on a wheeled vehicle, the speed wheel provides an accurate measurement of the vehicle speed by maintaining contact with a tire of the vehicle. An automatic traction control system, which may be part of the control unit, compares the speed of the speed wheel with the speed of the drive motor to determine whether slippage is occurring. If slippage is detected, then embodiments of an automatic traction control system automatically increase an amount of normal force between a contact surface on the drive motor and the tire, by advancing a position of the drive motor relative to a fixed mounting point. If no slippage is detected, then embodiments of an automatic traction control system automatically reduce the amount of normal force, by retracting a position of the drive r elative to a fixed mounting point. In embodiments of a friction drive system, the relative position of the drive motor may be controlled by powering a worm gear motor attached to a worm gear in response to commands from the control unit.