Design and impedance estimation of a biologically inspired flexible mechanical transmission with exponential elastic characteristic

Nonlinear elasticity of transmission is indispensable in any passively variable stiffness mechanism. However, it remains obscure how to decide a desired nonlinear force-displacement function. On the other hand biological muscular actions are associated with stiffness/impedance variation in a wide range as demanded by everyday tasks. This paper addresses the issue of designing a nonlinear elastic transmission, where the elastic behaviour is obtained from the passive properties of biological muscle, which happens to be an exponential one, leading to existence of linearity between stiffness and force. In general, with passive damping, the transmission behaves as a mechanical impedance element, to be used in variable impedance actuation. Knowledge of the varying impedance is required to operate the transmission reliably. An off-line calibrated model can only be approximate and erroneous with noisy sensors and changing characteristics of the passive elements with time and environmental condition. This article implements an Extended Kalman Filter algorithm for on-line estimation of stiffness and impedance of such a damped series-elastic transmission. The underlined principle in stiffness-force affine relation is exploited favourably in stiffness estimation with reduced complexity. The effectiveness of the proposed estimator is examined through experiments on the mechanical transmission designed using the biological principle.