Online impedance regulation techniques for compliant humanoid balancing

This paper presents three distinct techniques, aimed at the online active impedance regulation of compliant humanoid robots, which endeavours to induce a state of balance to the system once it has been perturbed. The presence of passive elastic elements in the drives powering this class of robots leads to under-actuation, thereby rendering the control of compliant robots an intricate task. Consequently, the impedance regulation procedures proposed in this paper directly account 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 ascertain whether the robot is converging to or diverging from, a desired equilibrium position. Computing this function's time derivative unequivocally gives the energy-injecting nature of the active stiffness regulation, and reveals that active damping regulation has no bearing on the system's state of stability. Furthermore, the velocity margin notion is interpreted as a velocity value beyond which the system's balance might be jeopardized, or below which the robot will be guaranteed to remain stable. As a result, the unidirectional and bidirectional impedance optimization methods rely upon the use of bounds that have been defined based on the energy function's derivative, in addition to the velocity margin. Contrarily, the third technique's functionality revolves solely around the use of Lyapunov Stability Margins (LSMs). A series of experiments carried out using the COmpliant huMANoid (COMAN), demonstrates the superior balancing results acquired when using the bidirectional scheme, as compared to utilizing the two alternative techniques.