Kinematic Model and Real-Time Path Generator for a Wire-Driven Surgical Robot Arm with Articulated Joint Structure

This paper presents a forward kinematic model of a wire-driven surgical robot arm with an articulated joint structure and path generation algorithms with solutions of inverse kinematics. The proposed methods were applied to a wire-driven surgical robot for single-port surgery. This robot has a snake-like robotic arm with double segments to fit the working space in a single port and a joint structure to secure stiffness. The accuracy of the model is highly important because small surgical robot arms are usually controlled by open-loop control. A curvature model is widely used to describe and control a continuum robotic body. However, the model is quite different from a continuum robotic arm with a joint structure and can lead to slack of the driving wires or decreased stiffness of the joints. An accurate forward kinematic model was derived to fit the actual hardware structure via the frame transformation method. An inverse kinematic model from the joint space to the wire-length space was determined from an asymmetric model for the joint structure as opposed to a symmetric curvature model. The path generation algorithm has to generate a command to send to each actuator in open-loop control. Two real-time path generation algorithms that solve for inverse kinematics from the task space to the joint space were designed and compared using simulations and experiments. One of the algorithms is an optimization method with sequential quadratic programming (SQP), and the other uses differential kinematics with a PID (Proportional-Integral-Derivative) control algorithm. The strengths and weaknesses of each algorithm are discussed.