I. Introduction
The advancement of bio-inspired soft continuum robots, featuring high compliance and inherent safety of operation in contrast to traditional rigid-bodied, precise but often dangerous robots, opens up novel research paradigms [1]–[3]. Continuum robotics is an umbrella term that herein is used to cover all types of active and physically reactive compliant systems. In this paper, we mainly focus on continuum robotic systems that can be bent, twisted and elongated, actively or passively, during operation. Continuum robots in this sense have often been made of elastomeric material or superelastic alloys, allowing them to change their shape with a few degrees of freedom (DoF) to form complex organic shapes (in contrast to fixed geometric shapes of rigid-bodied robots) and to be theoretically able to regulate stiffness over a broad range. Because of the passive deformation these robots undergo in the face of external forces, they can be considered as infinite DoF systems that are highly under-actuated. Continuum robotics has been a highly active area of research in the past few years. An impressive number of prototypes has been proposed over the years [4]–[7]. Yet control of continuum robots has not received as much attention, and therefore much of the control of continuum robots is limited to open loop control. Due to the presence of infinitely many DoF associated with inherent compliance, it became clear that controlling continuum robots are challenging. Kinematic control has been implemented on continuum robots wherein the robots are moved slowly in order not to invoke the compliance related oscillatory behaviors [8]. As a result, despite their enormous potential as human-friendly manipulators, continuum arms are primarily restricted to lab spaces, with their full potential remained to be realized.
(A) Pneumatically actuated multisection continuum arm designed at italian institute of technology handling and object, (B) the same arm bending on a plane [9], and (C) schematic of the prototype arm showing the coordinate convention and the output signal points (tip coordinates) used to record system response in this paper.