Observer-based control of a walking biped robot without orientation measurement

Two observers based on high order sliding mode approach are proposed to determine the absolute orientation of a walking biped robot without feet. Contrary to velocities observers which have been often designed for robot control, very few works have been proposed for the orientation estimation: in this paper, the estimation of all state variables are derived from only the actuated joint variables. Then the technology problem of the absolute measurement is avoided. This latter point is an original contribution of this paper. The observers and the control law converge in finite-time and are well adapted for analysis of the cyclic walking gait. Then, a second original contribution consists in adapting an existing “simplified” Poincaré's sections-based analysis of the stability of the walking to nonlinear systems with not fully available state variables.