A guaranteed approach for kinematic analysis of continuum robot based catheter

Controlling a continuum robot in a constrained environment constitutes a real challenge due to the nature of this robot and its bending properties. The navigation in un-structured environments, such as surgical operations, presents a potential application of the use of such robots. In this paper, a new formulation of a continuum robot forward kinematics is presented firstly. In a second step, an analytical inverse kinematics of the continuum robot is developed. It computes the continuum robot bellows length as a function of the robot end-tool position and orientation in the task space. Then a resolution of the inverse kinematics is shown based on the use of interval analysis. This technique has the advantage of dealing with uncertainties that may occur in the system modeling, parameter identification and could be used as well for robot control. System redundancies when computing the inverse kinematics are solved by a branch and bound based algorithm that minimizes a given quadratic criterion.