Stable Wheel Gait Generation for Planar X-shaped Walker with Telescopic Legs Based on Asymmetric Impact Posture

This paper introduces a novel X-shaped walker with telescopic legs and investigates its control method with the aim of generating a stable wheel gait on a horizontal plane without including zero dynamics which is essentially unstable and difficult to stabilize. First, we outline a planar 6-DOF robot model with three control inputs, and describe the equations of motion and inelastic collision. Second, we design an output-following control system that smoothly controls the extension/contraction lengths of the legs and relative hip-joint angle to their target terminal values, and creates an asymmetric impact posture in the anteroposterior direction so that the robot can easily overcome the next potential barrier. The coefficients of the desired-time trajectory for each control output are updated with the position and velocity values immediately after each impact as the target initial values, so the generated leg motion and control inputs exhibit smooth time variation. The validity of the proposed gait generation method and the change trend of fundamental motion characteristics with respect to control parameters are investigated through numerical simulations.