Optimization of Output Functions with Nonholonomic Virtual Constraints in Underactuated Bipedal Walking Control

Abstract

Underactuation is a challenging issue to deal with in bipedal walking control. Because of the highly nonlinear behaviors of bipedal robotic walking, nonlinear control theories, especially state feedback control based on input-output feedback linearization, has been applied to achieve stable walking. For underactuated bipeds, control design based on input-output linearization can result in internal dynamics whose stability and convergence rate to the desired gait affect the closed-loop stability and the overall convergence rate. Because the stability and the convergence rate of the internal dynamics can only be affected by the output function design, this paper proposes a general output function design to allow for greater freedom in output function optimization and better control performance as compared with previous studies. The proposed output function design and optimization, as well as the input-output linearizing controller, are simulated on a planar bipedal robot to validate the fast convergence rate to desired gait and the high robustness to external disturbances of the proposed method.