Continuum robots have gained widespread popularity due to their inherent
compliance and flexibility, particularly their adjustable levels of stiffness
for various application scenarios. Despite efforts to dynamic modeling and
control synthesis over the past decade, few studies have focused on
incorporating stiffness regulation in their feedback control design; however,
this is one of the initial motivations to develop continuum robots. This paper
aims to address the crucial challenge of controlling both the position and
stiffness of a class of highly underactuated continuum robots that are actuated
by antagonistic tendons. To this end, the first step involves presenting a
high-dimensional rigid-link dynamical model that can analyze the open-loop
stiffening of tendon-driven continuum robots. Based on this model, we propose a
novel passivity-based position-and-stiffness controller adheres to the
non-negative tension constraint. To demonstrate the effectiveness of our
approach, we tested the theoretical results on our continuum robot, and the
experimental results show the efficacy and precise performance of the proposed
methodology