Inverse Kinematics of Discretely-Actuated Manipulators Within a Bounded Grid Element

2006 ◽  
Author(s):  
Deanne C. Kemeny ◽  
Raymond J. Cipra
Keyword(s):  
Inverse Kinematics ◽  
Lower Cost ◽  
Robotic Manipulators ◽  
Forward Kinematics ◽  
End Effector ◽  
Grid Element ◽  
The Third ◽  
Inverse Kinematics Problem

Discretely-actuated manipulators are defined in this paper as serial planar chains of many links and are an alternative to traditional robotic manipulators, where continuously variable actuators are replaced with discrete, or digital actuators. Benefits include reduced weight and complexity, and predictable manipulation at lower cost. Challenges to using digital manipulators are the discrete end-effector positions which make the inverse kinematics problem difficult to solve. Furthermore, for a specific application position in the manipulator workspace, there may not be an actual end-effector position. This research has relaxed the inverse kinematics problem around this challenge making each application position an element of a grid in which the end effector must reach. There may be many possible end-effector positions that would reach the element goal, the solution uses the first one that is found. The inverse kinematics solution assumes the assembly configuration of the digital manipulator is already solved specifically for the application grid. The Jacobian function, normally used to solve joint velocities, can be used to identify the exact shift vectors that are used for the inverse kinematics. Three methods to solve this problem are discussed and the third method was implemented as a four-part solution that is a directed and manipulated search for the inverse kinematics solution where all four solutions may be needed. A discussion of forward kinematics and the Jacobian function in relation to digital manipulators is also presented.

Proper Assisted Research Method Solving of the Robots Inverse Kinematics Problem

2014 ◽  
Vol 555 ◽  
pp. 135-146 ◽  
Author(s):  
Adrian Olaru ◽  
Serban Olaru ◽  
Niculae Mihai
Keyword(s):  
Inverse Kinematics ◽  
Descent Method ◽  
Forward Kinematics ◽  
Hyperbolic Tangent ◽  
End Effector ◽  
Variable Parameters ◽  
Space Curves ◽  
Complete Study ◽  
Inverse Kinematics Problem ◽  
Study Case

Finding the better solution of the inverse kinematics problem, with the minimum of the trajectory errors, is very difficult because there are many variable parameters and many redundant solutions. The presented paper show the assisted solving of the inverse kinematics with the goal to minimize the final end-effector trajectory errors, by optimizing the distance between the and-effector final position and the target. All obtained results were been verified by applying the proper forward kinematics virtual LabVIEW instrumentation. The paper tries to answer at the inverse kinematics problem for one known mathematical trajectory and identifying the cinematic errors after the establishing and applying the proper assisted solving method using the Cycle Coordinate Descent Method coupled to the proper Neural Network Sigmoid Bipolar Hyperbolic Tangent (CCDM-SBHTNN). We were shown one complete study case to obtain one circle space trajectory using one arm type robot fixed on the ceiling. The presented method is general and can be used in all other robots types and in all other conventional and unconventional space curves.

A Generalized Solution to the Inverse Kinematics of Robotic Manipulators

1985 ◽  
Vol 107 (1) ◽  
pp. 103-106 ◽  
Author(s):  
A. A. Goldenberg ◽  
D. L. Lawrence
Keyword(s):  
Inverse Kinematics ◽  
Iterative Procedure ◽  
Generalized Inverse ◽  
Robotic Manipulators ◽  
Generalized Solution ◽  
Task Space ◽  
End Effector ◽  
Kinematic Control ◽  
Inverse Kinematics Problem ◽  
Position And Orientation

In the context of kinematic control of a robotic manipulator if a certain set of task space coordinates (end effector position and orientation) are commanded then the corresponding configuration space coordinates (joint variables) must be provided. The joint variables are obtained by solving the “inverse kinematics problem.” Typically a solution to the problem can be obtained in closed-form; however, such a solution is inherently manipulator-dependent. The paper presents an approach for providing a generalized inverse kinematics solution which is manipulator-independent. The solution is based on an iterative procedure. An algorithm was developed and demonstrated using the PUMA-560 and Stanford manipulator models.

Kinematics of a Fully-Decoupled Remote Center-of-Motion Parallel Manipulator for Minimally Invasive Surgery

2012 ◽  
Vol 6 (2) ◽  
Author(s):  
Chin-Hsing Kuo ◽  
Jian S. Dai
Keyword(s):  
Minimally Invasive Surgery ◽  
Minimally Invasive ◽  
Invasive Surgery ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Surgical Instruments ◽  
End Effector ◽  
Minimally Invasive Surgical ◽  
Inverse Kinematics Problem

A crucial design challenge in minimally invasive surgical (MIS) robots is the provision of a fully decoupled four degrees-of-freedom (4-DOF) remote center-of-motion (RCM) for surgical instruments. In this paper, we present a new parallel manipulator that can generate a 4-DOF RCM over its end-effector and these four DOFs are fully decoupled, i.e., each of them can be independently controlled by one corresponding actuated joint. First, we revisit the remote center-of-motion for MIS robots and introduce a projective displacement representation for coping with this special kinematics. Next, we present the proposed new parallel manipulator structure and study its geometry and motion decouplebility. Accordingly, we solve the inverse kinematics problem by taking the advantage of motion decouplebility. Then, via the screw system approach, we carry out the Jacobian analysis for the manipulator, by which the singular configurations are identified. Finally, we analyze the reachable and collision-free workspaces of the proposed manipulator and conclude the feasibility of this manipulator for the application in minimally invasive surgery.

A Method of Inverse Kinematics Solution for a Class of Robotic Manipulators

1997 ◽  
Author(s):  
Tuna Balkan ◽  
M. Kemal Özgören ◽  
M. A. Sahir Arikan ◽  
H. Murat Baykurt
Keyword(s):  
Nonlinear Equation ◽  
Analytical Method ◽  
Multiple Solutions ◽  
Inverse Kinematics ◽  
Industrial Robot ◽  
Robotic Manipulators ◽  
Inverse Kinematic ◽  
Singular Configurations ◽  
Inverse Kinematics Problem ◽  
Joint Variable

Abstract A semi-analytical method and a computer program are developed for inverse kinematics solution of a class of robotic manipulators, in which four joint variables are contained in wrist point equations. For this case, it becomes possible to express all the joint variables in terms of a joint variable, and this reduces the inverse kinematics problem to solving a nonlinear equation in terms of that joint variable. The solution can be obtained by iterative methods and the remaining joint variables can easily be computed by using the solved joint variable. Since the method is manipulator dependent, the equations will be different for kinematically different classes of manipulators, and should be derived analytically. A significant benefit of the method is that, the singular configurations and the multiple solutions indicated by sign ambiguities can be determined while deriving the inverse kinematic expressions. The developed method is applied to a six-revolute-joint industrial robot, FANUC Arc Mate Sr.

Analyses of Error and Precision of 6-DOF Platform

2012 ◽  
Vol 591-593 ◽  
pp. 2081-2086 ◽  
Author(s):  
Rui Ren ◽  
Chang Chun Ye ◽  
Guo Bin Fan
Keyword(s):  
Inverse Kinematics ◽  
Newton Iteration ◽  
Forward Kinematics ◽  
Parallel Mechanisms ◽  
End Effector ◽  
C Programming Language ◽  
C Programming ◽  
Manufacturing Tolerances ◽  
Parallel Robotics ◽  
Forward Kinematic

A particular subset of 6-DOF parallel mechanisms is known as Stewart platforms (or hexapod). Stewart platform characteristic analyzed in this paper is the effect of small errors within its elements (strut lengths, joint placement) which can be caused by manufacturing tolerances or setting up errors or other even unknown sources to end effector. The biggest kinematics problem is parallel robotics which is the forward kinematics. On the basis of forward kinematic of 6-DOF platform, the algorithm model was built by Newton iteration, several computer programs were written in the MATLAB and Visual C++ programming language. The model is effective and real-time approved by forwards kinematics, inverse kinematics iteration and practical experiment. Analyzing the resource of error, get some related spectra map, top plat position and posture error corresponding every error resource respectively. By researching and comparing the error spectra map, some general results is concluded.

scholarly journals Hybrid Mutation Fruit Fly Optimization Algorithm for Solving the Inverse Kinematics of a Redundant Robot Manipulator

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Jianping Shi ◽  
Yuting Mao ◽  
Peishen Li ◽  
Guoping Liu ◽  
Peng Liu ◽  
...  
Keyword(s):  
Optimization Algorithm ◽  
Inverse Kinematics ◽  
Robot Manipulator ◽  
Fruit Fly ◽  
Fruit Fly Optimization Algorithm ◽  
Redundant Manipulators ◽  
End Effector ◽  
Redundant Robot ◽  
Fruit Fly Optimization ◽  
Inverse Kinematics Problem

The inverse kinematics of redundant manipulators is one of the most important and complicated problems in robotics. Simultaneously, it is also the basis for motion control, trajectory planning, and dynamics analysis of redundant manipulators. Taking the minimum pose error of the end-effector as the optimization objective, a fitness function was constructed. Thus, the inverse kinematics problem of the redundant manipulator can be transformed into an equivalent optimization problem, and it can be solved using a swarm intelligence optimization algorithm. Therefore, an improved fruit fly optimization algorithm, namely, the hybrid mutation fruit fly optimization algorithm (HMFOA), was presented in this work for solving the inverse kinematics of a redundant robot manipulator. An olfactory search based on multiple mutation strategies and a visual search based on the dynamic real-time updates were adopted in HMFOA. The former has a good balance between exploration and exploitation, which can effectively solve the premature convergence problem of the fruit fly optimization algorithm (FOA). The latter makes full use of the successful search experience of each fruit fly and can improve the convergence speed of the algorithm. The feasibility and effectiveness of HMFOA were verified by using 8 benchmark functions. Finally, the HMFOA was tested on a 7-degree-of-freedom (7-DOF) manipulator. Then the results were compared with other algorithms such as FOA, LGMS-FOA, AE-LGMS-FOA, IFOA, and SFOA. The pose error of end-effector corresponding to the optimal inverse solution of HMFOA is 10−14 mm, while the pose errors obtained by FOA, LGMS-FOA, AE-LGMS-FOA, IFOA, and SFOA are 102 mm, 10−1 mm, 10−2 mm, 102 mm, and 102 mm, respectively. The experimental results show that HMFOA can be used to solve the inverse kinematics problem of redundant manipulators effectively.

Analysis of the Kinematics of an Eight-Wheeled Mobile Platform

2013 ◽  
Vol 198 ◽  
pp. 67-72
Author(s):  
Marek Stania
Keyword(s):  
Inverse Kinematics ◽  
Object Motion ◽  
Forward Kinematics ◽  
Contact Phenomenon ◽  
Kinematics Model ◽  
Inverse Kinematics Problem ◽  
Transport Vehicle ◽  
Forward And Inverse Kinematics ◽  
Motion Parameters ◽  
Simulation Results

This paper presents the modeling problem connected with the autonomous transport vehicle designed at Hochschule Ravensburg-Weingarten. The forward and inverse kinematics problem of eight-wheeled autonomous transport vehicle have been formulated and solved, additionally examples of simulation results representing the changes of individual motion parameters have been presented. Contact phenomenon between foundation and drive wheel has been taken into account in the kinematics model. Motion trajectory and velocity of the selected point belonging to the platform have been intended while the inverse kinematics problem has been solved. The forward kinematics problem has been worked out in order to verify correctness of the studied kinematics model. The presented simulation results point out compatibility of the worked out kinematics model of investigated object. The worked out models allow carrying out analysis of object motion through simulation investigations on the basis of proposed computational model.

Kinematics Analysis of a Hot-Line Live Working Manipulator

2014 ◽  
Vol 610 ◽  
pp. 28-34 ◽  
Author(s):  
Xiao Lin Ma ◽  
Hui Chai ◽  
Yun Jiang Li
Keyword(s):  
Analytical Solutions ◽  
Inverse Kinematics ◽  
Transformation Method ◽  
Forward Kinematics ◽  
Euler Angles ◽  
Kinematics Analysis ◽  
Hydraulic Actuator ◽  
End Effector

This paper introduces the development of hot-line live working manipulators and gives a new configuration manipulator driven by hydraulic actuator firstly. Then, its forward kinematics equations are derived with homogenous transformation method. Finally, the analytical solutions of its inverse kinematics are solved under the condition that the posture of the end-effector is known and given with z-y-z Euler angles.

A Simple Method for Inverse Kinematic Analysis of the General 6R Serial Robot

2006 ◽  
Vol 129 (8) ◽  
pp. 793-798 ◽  
Author(s):  
Shi Zhi Xin ◽  
Luo Yu Feng ◽  
Hang Lu Bing ◽  
Yang Ting Li
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Inverse Kinematic ◽  
New Method ◽  
One Dimension ◽  
Forward Kinematics ◽  
The Real ◽  
Inverse Kinematics Problem ◽  
Serial Robot ◽  
Inverse Kinematic Analysis

The inverse kinematic analysis of the general 6R serial robot has been a very significant and important problem in the theory of the spatial mechanisms. Because the solution to inverse kinematics problem of the general 5R serial robot is unique and its assembly condition has been derived, a simple effective method for inverse kinematics problem of general 6R serial robot or forward kinematics problem of general 7R single-loop mechanism is presented based on a one-dimension searching algorithm. All the real solutions to inverse kinematics problems of the general 6R serial robot or forward kinematics problems of the general 7R single-loop mechanism can be obtained. The new method has the following features: (1) using one-dimension searching algorithm, all the real inverse kinematic solutions are obtained and it has higher computing efficiency; and (2) compared with the algebraic method, it has evidently reduced the difficulty of deducing formulas. The principle of the new method can be generalized to kinematic analysis of parallel mechanisms.

A complete analytical solution to the inverse kinematics of the Pioneer 2 robotic arm

Robotica ◽  
2005 ◽  
Vol 23 (1) ◽  
pp. 123-129 ◽  
Author(s):  
John Q. Gan ◽  
Eimei Oyama ◽  
Eric M. Rosales ◽  
Huosheng Hu
Keyword(s):  
Analytical Solution ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Robotic Manipulators ◽  
Robotic Arm ◽  
Effective Solution ◽  
Robotic Arms ◽  
Unstructured Environment ◽  
Inverse Kinematics Problem

For robotic manipulators that are redundant or with high degrees of freedom (dof), an analytical solution to the inverse kinematics is very difficult or impossible. Pioneer 2 robotic arm (P2Arm) is a recently developed and widely used 5-dof manipulator. There is no effective solution to its inverse kinematics to date. This paper presents a first complete analytical solution to the inverse kinematics of the P2Arm, which makes it possible to control the arm to any reachable position in an unstructured environment. The strategies developed in this paper could also be useful for solving the inverse kinematics problem of other types of robotic arms.

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