A Biarc Method for Kinematics and Configuration Planning of Concentric Wire-Driven Manipulators

Concentric wire-driven mechanism (CWM) contains two nested tendon/cable-driven mechanisms (TMs). In the CWM, the lengths of the bending sections are controlled by the insertion of the TMs. This greatly expands the workspace and improved the trajectory following performance. However, its inverse kinematics and configuration planning are very challenging. Conventionally, only end position (excluding equally important end direction and task configuration) is considered to solve inverse kinematics and configurations of this type of manipulator. In this paper, a biarc method is proposed to resolve end position, end direction, and task configuration simultaneously for the concentric wire-driven manipulator. Firstly, configuration of the concentric wire-driven manipulator is parameterized by typical biarc parameters, such as total bending angle of outer nodes, total bending angle of inner nodes and desired direction vector. Then, task configuration optimization based on basic module parameters, end direction, and bending angle is detailed. Corresponding to a minimally invasive surgery, configurations can easily be designed and re-planned by adjusting above biarc parameters. Finally, trajectory tracking on large intestine examination through typical `S' configuration are simulated and experimented on the designed concentric wire-driven manipulator. Results demonstrate that the proposed method can provide reasonable solutions of kinematics and configuration planning. In addition, results also demonstrate that the concentric wire-driven manipulator can track desired trajectory in extremely confined space.