Algorithm for controlling an inertioid robot with a flywheel and an unbalance in conditions of restrictions on the angular acceleration of the unbalance

Abstract

The plane-parallel motion of a vibrating robot containing one unbalanced rotor and one flywheel is considered. The robot body is supported by two points on a rough supporting plane. The friction is modeled with Coulomb's law. The motion is controlled by the angular acceleration of the unbalanced rotor and the flywheel. The control strategy implies the alternation of two modes. In one mode, the unbalanced rotor gains the required angular momentum using the friction of the body against the surface. In the second mode, the body is lifted off the surface and moved in the desired direction. The first integrals of the unbalanced rotor rotation equations are found for both modes. It is shown that if no restrictions are imposed on the angular acceleration of the rotor then the angular velocity of the rotor tends to infinity. An algorithm for controlling the motion of the robot's body in a given direction is proposed that takes into account the constraint on the angular acceleration of the unbalanced rotor. Motion modes are added with constant control and control stabilizing the angular velocity of the unbalanced rotor. The numerical simulation of the robot motion with the proposed control was performed in a wide range of values of the friction coefficient. It is shown that, in some cases, several revolutions of the unbalanced rotor are required in order to gain the required angular momentum.