Closed-Form Solution of Inverse Kinematics for a Minimally Invasive Surgical Robot Slave Manipulator Similar to Da Vinci Robot System

2020 ◽  
Vol 3 (2) ◽  
Author(s):  
Wenjie Wang ◽  
Yuting Cao ◽  
Xiaohua Wang ◽  
Lingtao Yu
Keyword(s):  
Minimally Invasive ◽  
Closed Form ◽  
Inverse Kinematics ◽  
Robot Control ◽  
Da Vinci ◽  
Closed Form Solution ◽  
Form Solution ◽  
Surgical Robot ◽  
New Method ◽  
Minimally Invasive Surgical

Abstract Closed-form solution inverse kinematics has a unique advantage in robot control; it is quite difficult to be obtained through traditional methods as no effective analytic method has been identified so far, when the robot's joint configuration does not conform to the “Pieper Criterion.” In this paper, a new modeling method named extended Denavit-Hartenberg (DH) method was presented for solving this problem. And the conditions of robots' configuration that conform to the method have been given for different joints combinations. The precise closed-form solution to a minimally invasive surgical robot slave manipulator was obtained through this new method. The correctness of the new method was verified through simulation analyses; this study enriched robot kinematic modeling and the closed-form solution to inverse kinematics of Da Vinci surgical robot, and will help to obtain a fast, accurate, and general method of closed-form solution for the same kind of robots and provide the precondition for robot control and trajectory planning.

3D Modeling and Closed-Form Inverse Kinematics Solution for 6dof Surgical Robot

2013 ◽  
Vol 455 ◽  
pp. 533-538
Author(s):  
Edris Farah ◽  
Shao Gang Liu
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Closed Form Solution ◽  
Inverse Kinematic ◽  
Form Solution ◽  
Surgical Robot ◽  
Decoupling Method ◽  
Six Degrees Of Freedom ◽  
Inverse Kinematics Problem

Since robots began to inter the medical fields, more research efforts and more attention have been given to this kind of robots. In this paper six degrees of freedom surgical robot was studied. The Denavit-Hartenberg parameters of the robot have been computed and 3D model has been built by using open source robotics toolbox. The paper also discussed a closed form solution for the inverse kinematics problem by using inverse kinematic decoupling method.

Structure design and kinematics of a robot manipulator

Robotica ◽  
1988 ◽  
Vol 6 (4) ◽  
pp. 299-309 ◽  
Author(s):  
Kesheng Wang ◽  
Terje K. Lien
Keyword(s):  
Numerical Solution ◽  
Closed Form ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Robot Manipulator ◽  
Closed Form Solution ◽  
Form Solution ◽  
Structure Design ◽  
General Algorithm ◽  
6 Degrees Of Freedom

SUMMARYIn this paper we show that a robot manipulator with 6 degrees of freedom can be separated into two parts: arm with the first three joints for major positioning and wrist with the last three joints for major orienting. We propose 5 arms and 2 wrists as basic construction for commercially robot manipulators. This kind of simplification can lead to a general algorithm of inverse kinematics for the corresponding configuration of different combinations of arm and wrist. The approaches for numerical solution and closed form solution presented in this paper are very efficient and easy for calculating the inverse kinematics of robot manipulator.

scholarly journals Existence Conditions and General Solutions of Closed-form Inverse Kinematics for Revolute Serial Robots

2019 ◽  
Vol 9 (20) ◽  
pp. 4365 ◽  
Author(s):  
Wang Shanda ◽  
Luo Xiao ◽  
Luo Qingsheng ◽  
Han Baoling
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Closed Form Solution ◽  
Form Solution ◽  
Algebraic Equations ◽  
Closed Form Solutions ◽  
Serial Robots ◽  
Existence Conditions ◽  
Low Degrees

This study proposes a method for judging the existence of closed-form inverse kinematics solutions based on the Denavit–Hartenberg (DH) model. In this method, serial robots with closed-form solutions are described using three types of sub-problems from the viewpoint of solving algebraic equations. If a serial robot can be described using these three types of sub-problems, i.e., if the inverse kinematics problems can be solved by several basic problems, then there is a closed-form solution. Based on the above method, we design a set of universal closed-form inverse kinematics solving algorithms. Since there is a definite formula solution for the three types of sub-problems, the joint angles can be rapidly determined. In addition, because the DH parameters can directly reflect the linkage of the robot, the judgment of the sub-problems is also quick and accurate. More importantly, the algorithm can be applied to serial robots with low degrees of freedom. This enables the algorithm to not only quickly and accurately solve inverse kinematics problems but also to exhibit high universality. This proposed theory improves the existence conditions for closed-form reverse solutions and further promotes the development of motion control techniques for serial robots.

scholarly journals Complete follow-the-leader kinematics using concentric tube robots

2017 ◽  
Vol 37 (1) ◽  
pp. 197-222 ◽  
Author(s):  
Arnau Garriga-Casanovas ◽  
Ferdinando Rodriguez y Baena
Keyword(s):  
Minimally Invasive Surgery ◽  
Minimally Invasive ◽  
Closed Form ◽  
Invasive Surgery ◽  
Closed Form Solution ◽  
Form Solution ◽  
Illustrative Case ◽  
Full Potential ◽  
Constant Stiffness ◽  
Concentric Tube Robots

Concentric tube robots offer the capability of follow-the-leader motion, which is desirable when navigating in cluttered environments, such as in minimally invasive surgery or in-situ inspections. The follow-the-leader capabilities identified in the existing literature, however, are limited to trajectories with piecewise constant-curvature segments or piecewise helical segments. A complete study of follow-the-leader kinematics is, therefore, relevant to determine the full potential of these robots, and clarify an open question. In this paper, a general analysis of follow-the-leader motion is presented, and a closed-form solution to the complete set of trajectories where follow-the-leader is possible under the assumption of no axial torsion of the tubes composing the robot is derived. For designs with constant-stiffness tubes, the precurvatures required are found to be either circumference arcs, helices, or deformed helices with exponentially varying curvature magnitude. The analysis developed also elucidates additional motions of interest, such as the combination of follow-the-leader motion in a robot segment with general maneuvers in another part. To determine the applicability of the assumption regarding the tubes’ torsion, the general equilibrium of the robot designs of interest is considered, and a closed-form solution to torsion in two-tube robots with helical precurvatures is derived. Criteria to select a desired torsional behavior are then extracted. This enables one to identify stable trajectories where follow-the-leader is possible, for potential application to minimally invasive surgery. An illustrative case study involving simulation and experiment is conceived using one of these trajectories, and the results are reported, showcasing the research.

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