Synergetic Control of the Mobile Self-Balanced Robot

This article is devoted to an automatic motion control of the mobile self-balanced robot installed on a two-wheeled gyroscopic platform. The traditional solution of this task is to generate the control action for the engines of the wheels that would combine the stabilization process of horizontal position of the platform and its movement along the preset trajectory. Generally, when the frequency division or phase separation of these processes is impossible, then the position control and control of robot's motion interfere and exert the mutual perturbating effect. This influence is caused by kinematic and dynamic interrelations of coordinates of the mechanical system which is balancing freely on the mobile axis: any attempt to start movement or to deviate from the uniform rectilinear motion is accompanied inevitably with the deviation of the robot's longitudinal axis whereas any inclination of the platform leads to the emergence of the torques which move the platform on the surface of rolling. Any intention to suppress the internal interdependence of the coordinates of the system leads to further complication of control algorithms which requires considerable energy resources, viz., the overestimated power of engines and the capacities of storage batteries. To eliminate these fundamental shortcomings the synergetic approach is offered realizing the control of the considered system, i.e. to enter an additional minor operating influence - the position of the center of mass of a system. Working off this influence is carried out by the intrinsic kinematic and dynamic interrelations of the coordinates of a platform. As a result the system movement arises providing the matched solution for both the stabilization of the platform position and its coplanar motion. The two-member return pendulum kinematic scheme with the slowed-down hinge between the links was used for simulation and implementation of this control mode. The motion of the system's center of mass is realized in the form of angular deviation of the top link of a pendulum to the required angle. The mathematical model was built on the basis of the Lagrange's equations for kinetic energy of a system in the generalized coordinates in the form of two nonlinear differential equations of the second order. The center of masses position is entered to these equations in the form of a parameter. Indistinct regulators for each channel of regulation are synthesized and the operability test results of the offered automatic motion control are presented.