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

TL;DR

The paper tackles robust bipedal locomotion under disturbances by developing a nonlinear model predictive controller that simultaneously leverages ZMP manipulation, step location adjustment, angular momentum adaptation, and CoM height variation. Grounded in the nonlinear inverted pendulum plus flywheel model (NIPFM), the approach yields a QCQP that is efficiently solved with SQP, enabling real-time gait generation. Extensive simulations show improved push-recovery and terrain adaptability, including stair climbing and narrow-space traversal, with quantified computation efficiency. This framework offers a unified, data-driven method to enhance real-world humanoid robustness by exploiting multiple balance strategies in a coherent optimization loop.

Abstract

Human beings can utilize multiple balance strategies, e.g. step location adjustment and angular momentum adaptation, to maintain balance when walking under dynamic disturbances. 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.

Figures (18)

• Figure 1: NIPFM for bipedal walking. (a) The ankle torque helps to manipulate the ZMP and the flywheel rotation models the effect of the change of angular momentum. Note that the vertical height is changeable. (b) The definition of step parameters when walking on uneven terrains.
• Figure 2: Bipedal gait generation for 3D walking across uneven terrains. (a) Generated horizontal CoM trajectory, ZMP trajectory and step locations. The green blocks represent the supporting foot area. (b) Generated sagittal CoM trajectory. Defining the constant height reference during each walking cycle, time-varying height trajectory is automatically generated.
• Figure 3: Generated body inclination angles (a) and hip torques (b) for 3D walking across uneven terrains. Since the CoM height variation is integrated, the generated body rotation angles and hip torques are very low.
• Figure 4: Forward CoM trajectories, ZMP trajectories and ZMP boundaries generated by four different strategies. The ZMP boundaries are determined by the adjusted step locations.
• Figure 5: Forward step location sequences (a), pitch angles (b), pitch torques (c) and CoM height trajectories (d) generated by four different strategies.