Kinematic modeling of a class of n-tendon continuum manipulators

Flexible manipulators become widely used in industrial and medical fields due to their high dexterity compared with traditional discrete manipulators. However, in existing kinematics models of flexible manipulators without extension ability, the inverse kinematic (IK) analytical solution including the end-effector position and pose cannot be obtained. In this paper, a design example of a class of n-tendon continuum manipulators is presented. Based on the constant curvature hypothesis, a unified solution for solving the coupling relationship among tendons is derived. Combined with the Denavit-Hartenberg (D-H) method, the Taylor Series and the quaternion, the forward and inverse models are established, and an approximate analytical solution to the IK is derived. Simulations show the proposed IK solution has a good performance in accuracy and efficiency. A two-dimensional plane experiment and a three-dimensional space experiment are implemented. The average position errors of the two validation experiments respectively account for less than 2.0% and 3.5% of the total manipulator length, and the average pose errors are respectively no more than 0.8° and 2.5°. GRAPHICAL ABSTRACT

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