An immersion and invariance based speed and rotation angle observer for a class of revolute/prismatic manipulators with two degrees of freedom

This contribution presents a nonlinear observer for a class of revolute/prismatic (RP) manipulators with two degrees of freedom. It is based upon the Immersion and Invariance (I&I) methodology and uses measurements of the revolute joint´s relative angle and the prismatic joint´s absolute position. The estimated quantities consist of the absolute rotation angle as well as the linear and angular velocities. The practical relevance of this contribution is given by the processing of the relative rotation angle measurement, provided by most commercially available encoders. For the considered system class the observability is studied and a nonlinear observer is designed using the (reduced-order) observer theorem of the I&I technique. Employing Lyapunov arguments, the asymptotical convergence of the observation error is proven.