Design, kinematic modeling and trajectory tracking of a variable-length planar continuum robot

Continuum robots present high flexibility, complex environmental adaptability, and safe human-robot interaction. Hence, it exhibits broad application prospects in many fields. Nevertheless, their application is still largely limited due to challenges such as low dexterity and complex modeling. This paper presents a design of a variable-length planar continuum robot (PCR) and a trajectory tracking method based on the modal kinematics model. First, a novel continuum robot with both telescopic and bending capabilities is designed, which greatly increases its dexterity. The robot is driven by six cables and three pneumatic compartments, which are composed of three segments. The backbone of the segment consists of pneumatic compartments and a spring, where the pneumatic compartment is primarily responsible for providing axial stiffness, and the spring is mainly used to provide radial stiffness. Then, a multi-level kinematic model is established based on the piecewise constant curvature model and the homogeneous transformation method, which can accurately describe the bending and stretching motions of the robot simultaneously. To solve the singularity issues induced by the piecewise constant curvature model, a modal kinematic model is established by using the Taylor series. Furthermore, a distributed algorithm is introduced to realize the trajectory tracking of the multi-segment PCR. Finally, a series of numerical simulations is performed. It can be seen from the results that the proposed modal kinematic model and distributed trajectory tracking algorithm are effective for the PCR with variable-length capability.