Lyapunov Stability Margins for humanoid robot balancing

This work introduces a novel balance monitoring strategy for humanoid robots. The proposed method addresses the problem of ensuring the balance maintenance of a humanoid robot, through the online monitoring of its state of balance by means of a Lyapunov (energy) function. The proposed method involves the use of dynamical models accounting for both the link and motor states. Energy limits corresponding to the front and rear edges of the support polygon are computed using a closed-loop Lyapunov function. Therefore, this method focuses on the resolution of two issues through a single control scheme, namely, guaranteeing asymptotical stability of the robot at the joint level, in addition to ensuring that it maintains its dynamical balance. A mathematical proof of the previous claims, as well as of the method's validity, is provided in the paper, whereby a direct relationship between the CoP and the system's energy has been established for the first time. Experimental results of step recovery and walking tests performed on the COmpliant huMANoid (COMAN) corroborate the method's applicability and performance as a balance monitor.