Online impedance parameter tuning for compliant biped balancing

This paper describes a technique aimed at the online active impedance regulation of compliant humanoid robots, for the purpose of maintaining balance. The presence of passive elastic elements in their drives leads to under-actuation, thereby rendering the control of compliant robots a rather intricate task. Consequently, the impedance regulation procedure proposed in this paper accounts for these elastic elements. In order to acquire an indication of the robot´s state of balance in an online fashion, an energy (Lyapunov) function is introduced, whose sign then allows one to determine whether the robot is converging to or diverging from, a desired equilibrium position. This function´s derivative reveals the energy-injecting nature of the active stiffness regulation, while it attests to the fact that active damping regulation has no effect on the system´s stability properties. Furthermore, the notion of the velocity margin is described as a velocity beyond which the system might lose its balance, or below which it will be guaranteed to remain stable. As a result, the impedance optimization procedure´s functionality relies upon the use of bounds that have been defined based on the energy function´s derivative, in addition to the velocity margin. A series of experiments carried out using the COmpliant huMANoid (COMAN), demonstrates the superior balancing results acquired when using the proposed scheme, as compared to utilizing controllers possessing constant impedance parameters.