Continuum Robot Stiffness Under External Loads and Prescribed Tendon Displacements

Soft and continuum robots driven by tendons or cables have wide-ranging applications, and many mechanics-based models for their behavior have been proposed. In this paper, we address the unsolved problem of predicting robot deflection and stiffness with respect to environmental loads where the axial displacements of the tendon ends are held constant. We first solve this problem analytically for a tendon-embedded Euler-Bernoulli beam. Nondimensionalized equations and plots describe how tendon stretch and routing path affect the robot's output stiffness at any point. These analytical results enable stiffness analysis of candidate robot designs without extensive computational simulations. Insights gained through this analysis include the ability to increase robot stiffness by using converging tendon paths. Generalizing to large deflections in three dimensions (3-D), we extend a previous nonlinear Cosserat-rod-based model for tendon-driven robots to handle prescribed tendon displacements, tendon stretch, pretension, and slack. We then provide additional dimensionless plots in the actuated case for loads in 3-D. The analytical formulas and numerically computed model are experimentally validated on a prototype robot with good agreement.