On Planar Discrete Elastic Rod Models for the Locomotion of Soft Robots

Modeling soft robots that move on surfaces is challenging from a variety of perspectives. A recent formulation by Bergou et al. of a rod theory that exploits new developments in discrete differential geometry offers an attractive, numerically efficient avenue to help overcome some of these challenges. Their formulation is an example of a discrete elastic rod theory. In this article, we consider a planar version of Bergou et al.'s theory and, with the help of recent works on Lagrange's equations of motion for constrained systems of particles, show how it can be used to model soft robots that are composed of segments of soft material folded and bonded together. We then use our formulation to examine the dynamics of a caterpillar-inspired soft robot that is actuated using shape memory alloys and exploits stick-slip friction to achieve locomotion. After developing and implementing procedures to prescribe the parameters for components of the soft robot, we compare our calibrated model to the experimental behavior of the caterpillar-inspired soft robot.