We consider scissored pair gyroscopes as an auxiliary stabilization system for legged robots. A standard state-feedback control can stabilize the system if all states are available; thus, the velocity estimation becomes the key element for the stabilization. To this end, we implement and experimentally compare a model-free linear differentiator, a model-based full-state linear observer with time-varying gains, and a model-based homogeneous nonlinear differentiator. Moreover, we also show that the considered system cannot be partially linearized via a change of coordinates, and thus is not suitable for a recently reported class of nonlinear observers. The proposed designs are tested on an experimental scissored pair control moment gyroscope setup constructed for a walking robot stabilization.

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.

A simple fixed-time converging estimation algorithm is presented for a linear regression using the dynamic regressor extension and mixing (DREM) method within a discrete-time setting, with a persistently excited regressor and bounded measurement noises. The solution is based on Kreisselmeier's filters, and it is computationally simpler than the existing analogs.

This paper investigates estimating unknown constant parameters in linear regression with measurement noise. It introduces two concepts to analyze different types of excitation of the regressor: partial and feeble. The former indicates the absence of persistent or interval excitation, while the latter characterizes the presence of excitation that is inadequate for efficient estimation in a noisy environment. Furthermore, the paper proposes integrating regularization techniques to improve the estimation performance of the dynamic regressor extension and mixing (DREM) method. This enhancement is scrutinized analytically to gauge the extent of improvement achieved. The efficacy of theoretical findings is illustrated in the simulations.

The constant parameter identification problem is considered for a linear regression model assuming that the noise is sufficiently small comparing to the regressor. Introducing a nonlinear transformation, the estimation is performed for an extended regression dependent on the powers of the unknown parameters and the disturbance, where the influence of the latter is attenuated. It is shown that such a transformation preserves the excitation of regressor under reasonable assumptions. The quality improvement is demonstrated in numerical experiments.