The problem on a motion design for a robot-snakeborder is investigated. The mechanical part of the robot includes a snakeboard and a flywheel, capable to perform the controllable motion relative to a crossbar of a snakeboard. The program laws of wheel axes control for improvement of prescribed traces of any point of a crossbar are developed. The angle acceleration of a flywheel control is designed for improvement of desirable regulation for a velocity of a crossbar centre of mass. The problem on maximum increment of velocity along the trace of the form of “eight” is solved.