Selective-Compliance-Based Lagrange Model and Multilevel Noncollocated Feedback Control of a Humanoid Robot

This paper presents unified control schemes for compliant humanoid robots that are aimed at ensuring successful execution of both balancing tasks and walking trajectories for this class of bipeds, given the complexity of under-actuation. A set of controllers corresponding to the single-support (SS) and double-support (DS) walking phases has been designed based on the flexible sagittal joint dynamics of the system, accounting for both the motor and link states. The first controller uses partial state feedback (proportional–derivative–derivative (PDD)), whereas the second considers the full state of the robot (proportional–proportional–derivative–derivative (PPDD)), while both are mathematically proven to stabilize the closed-loop systems for regulation and trajectory tracking tasks. It is demonstrated mathematically that the PDD controller possesses better stability properties than the PPDD scheme for regulation tasks, even though the latter has the advantage of allowing for its associated gain-set to be generated by means of standard techniques, such as linear quadratic regulator (LQR) control. A switching condition relating the center-of-pressure (CoP) to the energy functions corresponding to the DS and SS models has also been established. The theoretical results are corroborated by means of balancing and walking experiments using the COmpliant huMANoid (COMAN), while a practical comparison between the designed controller and a classical PD controller for compliant robots has also been performed. Overall, and a key conclusion of this paper, the PPDD scheme has produced a significantly improved trajectory tracking performance, with 9%, 15%, and 20% lower joint space error for the hip, knee, and ankle, respectively.