Generation of Steady Wheel Gait for Planar X-shaped Walker with Reaction Wheel

Abstract

This paper addresses the problem of realizing a novel robotic bipedal locomotion called wheel gait, which is achieved by rotating the stance and swing legs in the same direction. First, a model of a planar 3-DOF X-shaped walker with a reaction wheel is introduced, and the mathematical equations are described. Second, the condition for stabilizing zero dynamics is formulated as the time integral value of control input to the reaction wheel for one step becomes zero, and the control system for achieving this is designed based on the method of continuous-time output deadbeat control. Third, a typical steady wheel gait of the linearized model is numerically generated, and its extension to the nonlinear model is discussed. Although the nonlinear model has only one nonlinear term in the gravity term, numerical simulations show that there is a big gap between this and the linearized model. Through analysis of the typical nonlinear wheel gaits, the difficulty of achieving the same walking speed as the linearized model is discussed.