Bias Propagation and Estimation in Homogeneous Differentiators for a Class of Mechanical Systems

Motivated by non-anthropomorphic dynamic stabilization of a walking robot, we consider the bias propagation problem for a homogeneous nonlinear model-based differentiator applied to a reaction wheel pendulum with a biased position sensor. We show that the bias propagates through the velocity observer and compromises the vertical stabilization. To cancel the impact of the bias, we propose to augment the differentiator with a reduced-order bias observer. Local asymptotic stability of the augmented nonlinear observer is shown, where the observer gain can be tuned using matrix inequalities. Experimental results illustrate the applicability of the proposed solution.