Estimation of Mechanical Impedance of a Flexible Transmission using Partial Knowledge of Elastic Characteristic and its Validation

Abstract

Use of flexible joints in robotic system is the recent trend in applications involving physical human robot interaction. A compliant transmission introduces the flexibility for intrinsically safe robots, whereas the ability to vary Impedance recovers some of the lost performance due to presence of compliance. Stiffness/impedance variability needs presence of nonlinearity in the passive elastic and/or damping characteristic. In controlling robot joint impedance knowledge of stiffness/impedance of transmission becomes necessary. Obtaining a predetermined model of the transmission always introduces inaccuracies and uncertainties with varying characteristics of the transmission with time and ambiance. It proves almost indispensable to estimate the joint stiffness/ impedance during operation for reliable control of variable impedance. It also proves to be a difficult task to estimate impedance/stiffness online on the basis of sensory information of differential motion and differential force. In this article, in order to estimate stiffness of the transmission, a favourable characteristic of the transmission has been exploited. The flexible transmission is designed with a first principle obtained from property of biological muscle so that it maintains an affine relationship between the stiffness and the force being transmitted. This article implements an Extended Kalman Filter algorithm for on-the-fly estimation of stiffness (along with impedance) exploiting the linearity property for applicability of EKF and to reduce complexity of the procedure. The effectiveness of the proposed estimator is examined through experiments on the mechanical transmission designed from the above biological principle. The results are further validated by comparing with the results of estimation using full parameter identification of specified model of the transmission.