Dynamics and Indirect Control Walking of Combined Elastic Rimless Wheels

The dynamics modeling and control of semi-passive walking of the combined elastic rimless wheels along an inclined plane based on indirect control are investigated. Initially, the dynamics model of the semi-passive walking of the combined elastic rimless wheels is established by the first type of Lagrange equation, the constraints during the motion process have been fully considered. Subsequently, inspired by the visceral vibrations observed in biological running, an indirect controller system is designed. The stable periodic walking of combined elastic rimless wheels along an inclined plane is realized through the regulation of scalable lengths in both vertical and horizontal telescopic masses. Finally, numerical simulations are conducted based on the derived equations. Through these simulations, the gait of the combined elastic rimless wheels is analyzed, and the effectiveness of the indirect control strategy is verified under conditions of external disturbances, persistent periodic disturbances, and mass errors. Additionally, simulation animations are provided to visually demonstrate the walking state along the inclined plane. The experimental results demonstrate that stable walking along an inclined plane can be achieved by combined elastic rimless wheels through indirect control. External disturbance forces and persistent periodic disturbances are effectively mitigated, allowing for the rapid restoration of periodic walking states even in the presence of mass parameter errors.