Vision-based sensing of forces in elastic objects

Abstract

A minimally intrusive, vision-based, computational force sensor for elastically deformable objects is proposed in this paper. Estimating forces from the visually measured displacements is straightforward in the case of the linear problem of small displacements, but not in the case of the large displacements where geometric non-linearities must be taken into account. From the images of the object taken before and after the deformation, we compute the deformation gradients and logarithmic strains. Using the stress–strain relationships for the material, we compute the Cauchy’s stresses and from this we estimate the locations and magnitudes of the external forces that caused the deformation. A sensitivity analysis is performed to examine the effect of small deviations in the experimentally captured displacements on the estimated external forces. This analysis showed that the small-strain case is more sensitive and prone to numerical errors than the large-strain case. Additionally, a related method that is indirect and iterative is also presented in which we assume that we know the locations of the external forces. Numerical and experimental studies are presented for both micro- and macro-scale objects. The main conclusion of this work is that the vision-based force estimation is viable if the displacements of the deforming object can be captured accurately.