Non-linear observer design with finite time convergence for estimation of unactuated angular variables of an underactuated biped robot

Abstract

This paper proposes a non-linear observer for estimation of the unactuated variables of a biped robot with point feet. By considering the underactuation problem, a time invariant feedback control is first presented for tracking the stable gait, defined as timescale trajectories, during different phases of motion. A triangular form is derived by only one diffeomorphism map from the original system for the single support phase. A non-linear observer is then designed based on a new form of biped equations, and thereafter finite time convergence of estimation error dynamics is proven. Moreover, the stability of biped motion is studied during different phases by a Poincaré map. The effectiveness of the proposed method is verified by numerical simulations. Simulation results show that the angular variables of the shank of the stance leg which is unactuated can be estimated properly by a measuring the angular variables of the actuated joints.