Limit cycles generation for energy-efficient bipedal walking via nonlinear model predictive control

Abstract This paper proposes an energy-efficient walking generation method utilizing limit cycles generated by nonlinear model predictive control (NMPC). Conventional limit cycle walking methods rely on strong feedback, such as output zeroing control, to attract the robot’s state toward a predefined periodic trajectory. However, we hypothesize that employing feedback control that better leverages the robot’s dynamics can improve energy efficiency during walking. Our previous work confirmed that using limit cycles generated by NMPC can produce energy-efficient walking patterns. This study builds upon this foundation and proposes a new method for generating walking in a general five-link bipedal robot. Through extensive numerical simulations, we demonstrate that the proposed method achieves highly energy-efficient walking while exhibiting excellent convergence to periodic trajectories.