Estimating Loads Along Elastic Rods

Abstract

Mechanics-based models of thin elastic structures are prevalent in robotics research, both in soft/continuum robot modeling, and in robotic manipulation of strings, sutures, needles, and endoscopes. In all these applications, distributed loads along the device's length can affect its shape in space. Estimation of the distributed loading based on observation of the object's shape constitutes a classical mechanics inverse problem that would be useful in many applications, but this problem has received relatively little attention to date. In this paper, we propose methods to estimate distributed loads on an elastic rod using a large-deflection Cosserat-rod model and constrained nonlinear optimization. We perform experiments that illustrate the feasibility of using these methods to locate regions of high contact force along the rod, and to estimate magnitudes of the forces that are applied. Results show that overall force magnitudes and locations can be estimated with average error of 0.29 N (6.7% of average resultant magnitude) and 4 mm (2% of rod length) for complex double-bend shapes, and the shape approximation has near-zero error.