Hierarchical sliding mode control for a two-dimensional ball segway that is a class of a second-order underactuated system

Ball segway, a ballbot-type personal carrier robot, is an actual under-actuated system with second-order nonholonomic velocity constraints and input coupling case. The two-dimensional ball segway system has two outputs consisting of ball position and body tilt angle, which needs to be controlled but has only one torque driving the ball. Actuators directly drive the ball and the body has no direct control. The main objective of this study is to design a robust controller for the ball segway so that the ball is transferred in a point-to-point motion while the body is maintained in the vertical position. The proposed controller is designed on the basis of hierarchical sliding mode control technique. Both simulations and experiments were conducted to verify the quality and stability of the control system.