Artificial Invariant Subspace for Humanoid Robot Balancing in Locomotion

Legged robots that make use of compliant actuators have demonstrated greater robustness of locomotion than their rigid counterparts. Stiffness and damping are key parameters that characterize the adaptation to perturbations. In this work, by drawing inspirations from controllable compliance and damping in existing soft and bio-inspired legged robots, we propose an approach to design a nonlinear controller for the balancing of humanoid robots with rigid bodies. Existing literature has proposed simplified dynamical models of biped robots in order to predict the timing and placement of swing foot for walking without falling. We further employ the properties of invariance to perturbations in damped harmonic oscillators and formulate continuous feedback control in combination with predictive foot stepping in order to achieve continuous adaptive recoveries of the nominal walking cycle from unexpected physical disturbances. Our method allows asymptotic convergence of the rigid body dynamics to a subspace with the desired energy level. We demonstrate the robustness of the proposed algorithm base on extensive push recovery experiments on a NAO robot on flat terrains.