Forward Kinematics of Cable-Driven Continuum Robot Using Optimization Method

Abstract

An elephant trunk robot is a continuum robot consisting of a flexible backbone actuated by two pairs of cables (or tendons) offset by a distance and along the circumference of the backbone. By pulling the cables, the continuum robot assumes the shape of an arc of a circle in 3D space. In the literature, forward kinematics of the robot has been developed using differential geometry of 3D curves. In this paper, we show that forward kinematics can also be obtained by discretizing along the length of the robot, with each discrete element modeled as a four-bar mechanism, and using a minimization approach. Each of the four-bar mechanism is assumed to be rigid with constant link length. It is shown that minimizing the angle made by the coupler link with the fixed link of the parallel linkage results in a profile which is numerically same as that derived from differential geometry for a segment of the cable-driven robot in 2D. The results obtained for actuation in 2D are extended to 3D, using two four-bar mechanisms actuated by the two sets of cables, and it is shown to match the analytical formulation available in the literature. The proposed method of using a sequence of four-bar mechanisms opens up a new perspective in modeling the forward kinematics of cable-driven continuum robots.