Abstract
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.
Highlights
Invasive surgery has been a continuing medical trend because it can reduce the pain and the recovery time of patients
This paper proposes two algorithms to solve the inverse kinematics from the forward kinematic model
The inverse kinematic solution from the task space to the joint space is used in the inverse kinematic model from the joint space to the wire-length space, which means the path of each linear actuator for driving the wires can be generated in real-time
Summary
Invasive surgery has been a continuing medical trend because it can reduce the pain and the recovery time of patients. A more accurate kinematic model was derived to fit an articulated robot arm with a joint structure, and effective path generation algorithms are proposed to solve the inverse kinematics. The two inverse kinematics were connected by substituting the calculated values, which could effectively generate an accurate actuation path corresponding to each wire-driving length in real-time In this project, tungsten wire was considered to be a rigid structure, and the friction and elongation of the wire were negligible. The constraint logic for the mechanical limits of the robot arm works well in real-time, even when a human operator mistakenly manipulates the master device to an excessive value Compared to another method, the numerical method can respond to changes in robot structure, since only the forward kinematic model needs to be replaced without Jacobian or gain tuning. The last section gives a conclusion and discusses future work
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