Modeling and control of a 3D under-actuated bipedal robot using partial feedback linearization

Abstract

This article presents a dynamic modeling and control framework for a 3D underactuated five-link bipedal robot with 14 degrees of freedom (DoF) and eight actuators. The robot exhibits highly nonlinear, strongly coupled, and hybrid dynamics, posing challenges for conventional control approaches. To address these issues and introduce our research contribution, a partial feedback linearization (PFL)-based tracking framework is proposed, which analytically decouples the system into actuated and unactuated subsystems, enabling efficient real-time control. Unlike hybrid zero dynamics (HZD) methods that enforce virtual constraints online and require offline gait optimization, or model predictive control (MPC) schemes that are online optimization based dependent and computationally demanding, the proposed PFL approach achieves computational simplicity and fast implementation through closed-form control laws. In contrast to zero-moment point (ZMP)-based controllers, PFL enables dynamic underactuated walking with PD feedback for accurate trajectory tracking and disturbance attenuation, though robustness to large uncertainties and disturbances may require additional mechanisms, such as adaptive control, sliding-mode, or fuzzy logic. Simulation results of the applied control method demonstrate the periodic nature and stability of generated walking gaits, which proves the effectiveness and reliability of the proposed control approach.