  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 incorporated stiffness
regulation into their feedback control design; however, this is one of the
initial motivations to develop continuum robots. This paper addresses the
crucial challenge of controlling both the position and stiffness of
underactuated continuum robots actuated by antagonistic tendons. We begin by
presenting a 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 that adheres to the
non-negative tension constraint. Comprehensive experiments on our continuum
robot validate the theoretical results and demonstrate the efficacy and
precision of this approach.
