Model Predictive Control for Biped Robot Running based on Dual Linear Inverted Pendulum Model

Abstract

Due to the fact that the legs of the bipedal robot are not fixed to the ground, a bipedal robot is significantly influenced by uncertainties, such as unobserved alter- ations and variations in the terrain. As a result, achieving dynamic locomotion of bipedal robots across diverse terrains continues to pose challenges, requiring con- tinuous research efforts. To address these challenges, it is imperative to implement online motion control that generates stable motion with adaptability to the environ- ment by considering the current state of the robot and its surroundings. This paper proposes an online motion control method based on linear model predictive control (MPC) to generate stable running motions. Bipedal running is a nonlinear dynamic process, and thus, generating this nonlin- ear motion using linear MPC presents difficulties. In this paper, to generate a motion for the dynamic nonlinear motion based on linear MPC, a dual linear inverted pen- dulum model (D-LIPM) is formulated for the biped robot’s horizontal and vertical motion, respectively. These linear models are then used in a two-step hierarchical control approach with an MPC to generate an online running trajectory for the robot. In the first stage, a linear MPC, incorporating stability constraints based on a friction cone, is utilized to produce the trajectory of the center of mass (COM). And then, in the second step, an optimization based motion control method with an extended model, considering the motions of each joint of the robot, is employed to make the robot track the generated COM trajectory. To validate the proposed methodology, simulations of a biped robot running in various environments were conducted. In the simulations of running on flat terrain, it was shown that the robot can run at various target speeds up to 6.30 m/s. To demonstrate the robot’s ability to run in diverse terrains, simulations were performed for environments with observable obstacles. In these simulations, the robot was able to run over small-sized obstacles or come to a stop before a large obstacle. Additionally, simulations were conducted ABSTRACT viii for running on a terrain of unknown characteristics, such as unknown slipperiness and ground levels. In these simulations, the robot ran successfully, reaching the target speed of 6 m/s despite the uncertainty. Through these simulations, it was confirmed that the proposed method made the robot maintain its stability while running on a track with diverse uncertainties.