Control of the robot-wheel with a pendulum

A robot-wheel with a pendulum, which is described by a system of differential and algebraic equations, is considered. The problem of synthesizing control law is set that brings the system from an arbitrary initial position on a straight line to a given one, with the velocity of motion being limited. To solve this problem, a simpler, "reference," system of differential-algebraic equations is introduced the solutions of which satisfy the given phase and control constraints. Solutions of the reference system are taken to be the set of target trajectories for the original system. The feedback is found by numerical integration with projections of the original system together with the reference one. Results of numerical experiments demonstrate the effectiveness of the proposed approach.