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.