Inverse kinematics of modular Cable-driven Snake-like Robots with flexible backbones

A Cable-driven Snake-like Robot (CSR) with a flexible backbone possesses a number of promising advantages over the conventional rigid-link manipulators, such as lightweight mechanical structure, large reachable workspace, high dexterity, and high maneuverability. In general, a CSR is a hyper-redundant manipulator that consists of a large number of identical or similar segments. A modular design approach is employed in this paper in order to simplify the CSR design, analysis, and control to a manageable level. As the basic building block of CSRs, a 2-DOF cable-driven joint module with a flexible backbone is proposed. Based on the motion characteristics of the 2-DOF joint module, the concept of instantaneous rotation axis in conjunction with the Product-Of-Exponentials (POE) formula is proposed to formulate its kinematic model. However, as the instantaneous rotation axis is unfixed, the Lie Bracket method from the Group theory is employed to derive the instantaneous kinematic model of the joint module. With the joint´s kinematics model, a configuration-independent numerical inverse kinematics (NIK) algorithm is formulated for the modular CSRs. The effectiveness of the proposed NIK algorithm is validated through simulation examples.