Modelling and identification of the asymmetric hysteresis in the viscoelastic response of the fingertip under indentation: A multistate friction model with switching parameters

This paper presents a dynamic model for the identification of asymmetric hysteresis in the force response of the fingertip under cyclic local deformation of the fingertip soft tissues. Viscoelastic effects, marked anisotropy and nonlinearity contribute to the hysteretic behaviour of the force of the fingertip undergoing indentation. The fingertip force in response to an indentation stimulus varies along the loading and unloading cycles; the resulting hysteresis loops are asymmetric. The asymmetry arises from the simultaneous convexity of the branches of the hysteresis loop. The proposed model belongs to the class of multistate friction models that can effectively describe the hysteresis in the presliding regime of motion of general mechanisms with friction, by exploiting a mechanical analogy obtained through the concatenation of multiple elasto-plastic elements. The multistate model, which provides the mechanical representation of the fingertip response through a set of newly-conceived switching elements and viscoelastic blocks, can reproduce the convex and asymmetric hysteresis loops of the fingertip mechanical response, including the viscoelastic effects of stress relaxation and the influence of time interval between consecutive cycles of indentation. The model has been validated through the experimental identification of fingertip indentation tests performed on an optomechanical test-rig. This model potentially opens the way for efficient model-based control strategies of servomechanisms involved in tactile and haptic displays and interfaces.