Profile Estimation of Multi-segmented Cable-Driven Continuum Robots Using Optimization Method

Cable-driven continuum robot (CCR) is a class of flexible robots in which the robot is deformed by pulling a set of inextensible cables. To improve the dexterity of this robot, multiple robotic segments are stacked serially on top of each other to form a multi-segmented CCR. One method to solve the forward kinematics of a single-segmented robot is to use the optimization-based method, which is derived from the principle of minimization of strain energy density. In this paper, the optimization-based method is extended to predict the profile of a multi-segmented continuum robot. For a multi-segmented robot, the distance between the backbone and the cable pairs of each segment is different. Hence, the mathematical model is modified to account for the same. In order to validate the model, a series of experiments was conducted on a 300 mm long robot prototype which uses Nitinol (NiTi) rod as its backbone and nylon threads for actuation cables. The optimization-based model is solved using the fmincon routine in MATLAB, and the solution is superimposed on actual deformation profiles. The mathematical model predicts the profile of a multi-segmented CCR for in-plane bending as well as out-of-plane bending with RMS errors of 1.3% of CCR length and 4.2% of CCR length, respectively. It was found that the proposed model could also predict the deformed profile of a multi-segmented CCR in contact with the obstacle, with an RMS error of 1.1% of the CCR length.