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

Abstract

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. INDEX TERMS Sensor bias, velocity observer, homogeneous differentiator, inverted pendulum.

Gyrubot: nonanthropomorphic stabilization for a biped

“…In [8] robot with a reaction wheel coupled with hybrid zerodynamics [9] has improved some of the walking parameters of the robot. Another example is Anywalker [10], [11], a robot that uses flywheels to provide increased stability of the zero moment point controller. Our work is inspired by [12], we propose to give robots an additional "support point" without touching the rest of the mechanical system.…”

A New Approach to Compensator Design Based on Multi-Loop Technique and Scalable Forward Model Complexity

“…For example, in Reference [22], an adaptive control scheme for general uncertain EL systems under control input saturation is proposed. In References [23,24], new non-linear methods of stabilizing robots are presented. Finally, a position control of a 2DOF robot manipulator with force interaction was selected for the simulation study.…”