Nonlinear Model Predictive Control for Robust Bipedal Locomotion: Exploring Angular Momentum and CoM Height Changes

-- Human beings can utilize multiple balance strategies, e.g. In this work, we propose a novel Nonlinear Model Predictive Control (NMPC) framework for robust locomotion, with the capabilities of step location adjustment, Center of Mass (CoM) height variation, and angular momentum adaptation. These features are realized by constraining the Zero Moment Point within the support polygon. By using the nonlinear inverted pendulum plus flywheel model, the effects of upper-body rotation and vertical height motion are considered. As a result, the NMPC is formulated as a quadratically constrained quadratic program problem, which is solved fast by sequential quadratic programming. Using this unified framework, robust walking patterns that exploit reactive stepping, body inclination, and CoM height variation are generated based on the state estimation. The adaptability for bipedal walking in multiple scenarios has been demonstrated through simulation studies. Humanoid robots have attracted much attention for their capabilities in accomplishing challenging tasks in real-world environments. With several decades passed, state-of-the-art robot platforms such as ASIMO [1], Atlas [2], W ALK-MAN [3], and CogIMon [4] have been developed for this purpose. However, due to the complex nonlinear dynamics of bipedal locomotion over the walking process, enhancing walking stability, which is among the prerequisites in making humanoids practical, still needs further studies. In this paper, inspired by the fact that human beings can make use of the redundant Degree of Freedom (DoF) and adopt various strategies, such as the ankle, hip, and stepping strategies, to realize balance recovery [5]-[7], we aim to develop a versatile and robust walking pattern generator which can integrate multiple balance strategies in a unified way. To generate the walking pattern in a time-efficient manner, simplified dynamic models have been proposed, among which the Linear Inverted Pendulum Model (LIPM) is widely used [8]. Using the LIPM, Kajita et al. proposed the preview control for Zero Moment Point (ZMP) tracking [9]. By adopting a Linear Quadratic Regulator (LQR) scheme, the ankle torque was adjusted to modulate the ZMP trajectory and Center of Mass (CoM) trajectory. Nevertheless, this strategy can neither modulate the step parameters nor take into consideration the feasibility constraints arisen from actuation limitations and environmental constraints. To overcome this drawback, Wieber et al. proposed a Model Predictive Control (MPC) algorithm to utilize the ankle strategy [10] and then extended it for adjusting step location [11].