Balance and impedance optimization control for COmpliant huMANoid stepping

Abstract

The work presented herein, attempts to address the problem of designing stepping recovery controllers for compliantly actuated humanoid robots. Based on the decomposition of the stepping procedure into three distinct phases, which are characterized by unique combinations of configurations and impedance levels, the contrivance of a Linear Quadratic Regulator (LQR) optimization process allows for the production of a corresponding number of controllers. The penalties associated with the proposed cost functions, which account for compliant dynamics and balance-related parameters alike, are selected in a systematic manner that facilitates the generation of the appropriate impedance levels required for each particular phase of the stepping motion. Subsequently, the superimposition of gravity compensation control, onto the original LQR controllers, renders them nonlinear and theoretically capable of tracking referential stepping trajectories. The associated referential motor positions are then generated by exploiting a formula relating the Centre-of-Pressure (CoP) to the compliant ankle dynamics, thereby satisfying the balancing constraints whilst also accounting for the system's inherent under-actuation. Thus, the technique's novelty stems from its explicit consideration of flexible joint dynamics and deflection torques, for the design of the desired impedance levels and joint stepping trajectories. The Series Elastic Actuator (SEA) powered COmpliant huMANoid (COMAN), has served as an avatar of the stepping recovery methodology that is expounded in the paper.