Variable impedance walking using Time-Varying Lyapunov Stability Margins

This paper introduces novel methods for a humanoid robot's online balance monitoring, as well as for the tuning of its impedance parameters, based on Time-Varying Lyapunov Stability Margins (TVLSMs). It distinguishes itself from previous works by considering TVLSMs whose values evolve in real-time, in accordance with the references supplied to a trajectory tracking controller, as opposed to the previously-considered static LSMs that revolve around the use of set-point regulators. As a result, an analytical relationship between the system's energy and its Centre-of-Pressure (CoP) is derived, providing a means of predicting the robot's balancing behaviour based on the evolution of the closed-loop system's actual and critical, energy values. An appropriate manipulation of this expression facilitates a real-time tuning of the active stiffness gains, which may be viewed as a process of constraining the robot's energy to residing within a `safe region' of operation. Walking experiments performed using the COmpliant huMANoid (COMAN), reveal the proposed technique's accuracy in terms of predicting stable states, in addition to its capability of enabling an automated real-time tuning of a robot's impedance levels. The proposed strategy has permitted the stable replication of a wide range of joint impedance values, which is imperative for ground interaction during walking.