Application of Dual-Number Matrices to the Inverse Kinematics Problem of Robot Manipulators

1985 ◽  
Vol 107 (2) ◽  
pp. 201-208 ◽  
Author(s):  
G. R. Pennock ◽  
A. T. Yang
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Robot Manipulators ◽  
Closed Form Solutions ◽  
Dual Number ◽  
Special Geometry ◽  
Inverse Kinematics Problem ◽  
Concise Representation ◽  
Joint Parameters ◽  
General Geometry

This paper presents the application of dual-number matrices to the formulation of displacement equations of robot manipulators with completely general geometry. Dual-number matrices make possible a concise representation of link proportions and joint parameters; together with the orthogonality properties of the matrices we are able to derive, in a systematic manner, closed-form solutions for the joint displacements of robot manipulators with special geometry as illustrated by three examples. It is hoped that the method presented here will provide a meaningful alternative to existing methods for formulating the inverse kinematics problem of robot manipulators.

From Origami to a New Class of Centralized 3-DOF Parallel Mechanisms

2007 ◽  
Author(s):  
Ernesto Rodriguez Leal ◽  
Jian S. Dai
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Geometric Constraints ◽  
Parallel Mechanisms ◽  
Closed Form Solutions ◽  
New Class ◽  
Workspace Analysis ◽  
Inverse Kinematics Problem

This paper applies the ‘technomimetics’ concept to generate a new class of parallel mechanisms inspired by origami folds. This new class of 3-DOF (Degree of Freedom) parallel mechanisms is constructed with 3-RPRP architecture. When the geometric constraints mentioned in this paper are applied, the mechanisms will be allowed to rotate around the x and y axes and translate vertically along the z axis, while the centre of the platform remains concentric to the centre of its base. This paper investigates both position and geometry of these mechanisms and identifies the closed form solutions for the inverse kinematics problem. The differential kinematical analysis is developed by deriving the Jacobian matrix through screw theory and the singularities are identified with workspace analysis. The paper ends with isotropic configuration analysis and illustrates the characteristics of the new mechanisms.

Inverse Kinematics Analysis of 5-DOF Robot Manipulators Based on Virtual Joint Method

2011 ◽  
Vol 143-144 ◽  
pp. 265-268
Author(s):  
Zhi Zhong Liu ◽  
Hong Yi Liu ◽  
Zhong Luo
Keyword(s):  
Iterative Method ◽  
Closed Form ◽  
Inverse Kinematics ◽  
Robot Manipulator ◽  
Kinematics Analysis ◽  
One Dimensional ◽  
Closed Form Solutions ◽  
Inverse Kinematics Problem ◽  
Serial Robot ◽  
Joint Method

To solve the inverse kinematics problem of a robot manipulator without closed form solutions, one-dimensional iterative method is very useful. However, for a 5-DOF robot manipulator, because of the uncontrolable and uncertain orientation vectors, it's difficult to analytically express all joint variables by one of them, therefore one-dimensional iterative method can not be directedly used. By adding an appropriate virtual joint to it, a 5-DOF manipulator can be changed into a 6-DOF one so that the uncertain orientation vectors can be pre-given, and the difficulty is solved. To illustrate this virtual joint method a 5-DOF serial robot manipulator with prismatic arm joint and offset wrist is discussed in this paper as an example.

scholarly journals IKBT: Solving Symbolic Inverse Kinematics with Behavior Tree (Extended Abstract)

2020 ◽  
Author(s):  
Dianmu Zhang ◽  
Blake Hannaford
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Intelligent System ◽  
Logical Reasoning ◽  
Robot Arm ◽  
Kinematics Analysis ◽  
Closed Form Solutions ◽  
Behavior Tree ◽  
Behavior Trees ◽  
High Level

Inverse kinematics solves the problem of how to control robot arm joints to achieve desired end effector positions, which is critical to any robot arm design and implementations of control algorithms. It is a common misunderstanding that closed-form inverse kinematics analysis is solved. Popular software and algorithms, such as gradient descent or any multi-variant equations solving algorithm, claims solving inverse kinematics but only on the numerical level. While the numerical inverse kinematics solutions are relatively straightforward to obtain, these methods often fail, even when the inverse kinematics solutions exist. Therefore, closed-form inverse kinematics analysis is superior, but there is no generalized automated algorithm. Up till now, the high-level logical reasoning involved in solving closed-form inverse kinematics made it hard to automate, so it's handled by human experts. We developed IKBT, a knowledge-based intelligent system that can mimic human experts' behaviors in solving closed-from inverse kinematics using Behavior Tree. Knowledge and rules used by engineers when solving closed-from inverse kinematics are encoded as actions in Behavior Tree. The order of applying these rules is governed by higher level composite nodes, which resembles the logical reasoning process of engineers. It is also the first time that the dependency of joint variables, an important issue in inverse kinematics analysis, is automatically tracked in graph form. Besides generating closed-form solutions, IKBT also explains its solving strategies in human (engineers) interpretable form. This is a proof-of-concept of using Behavior Trees to solve high-cognitive problems.

Kinematics of a n–bay triangle–triangle variable geometry truss manipulator

Robotica ◽  
1992 ◽  
Vol 10 (3) ◽  
pp. 263-267
Author(s):  
L. Beiner
Keyword(s):  
Iterative Method ◽  
Closed Form ◽  
Inverse Kinematics ◽  
Variable Length ◽  
Variable Geometry ◽  
Closed Form Solutions ◽  
Numerical Example ◽  
Forward And Inverse Kinematics ◽  
Variable Geometry Truss Manipulator ◽  
Variable Geometry Truss

SUMMARYVariable geometry truss manipulators (VGTM) are static trusses where the lengths of some members can be varied, allowing one to control the position of the free end relative to the fixed one. This paper deals with a planar VGTM consisting of a n–bay triangle-triangle truss with one variable length link (i.e. one DOF) per bay. Closed-form solutions to the forward, inverse, and velocity kinematics of a 3-DOF version of this VGTM are presented, while the forward and inverse kinematics of an n–DOF (redundant) one are solved by a recursive and an iterative method, respectively. A numerical example is presented.

The Kinematics of Wheeled Mobile Robots With Dual-Wheel Transmission Units

2007 ◽  
Vol 130 (1) ◽  
Author(s):  
Chao Chen ◽  
Svetlana Ostrovskaya ◽  
Jorge Angeles
Keyword(s):  
Mobile Robots ◽  
Closed Form ◽  
Trajectory Tracking ◽  
Inverse Kinematics ◽  
Driving Mechanism ◽  
Ground Contact ◽  
Wheeled Mobile Robots ◽  
Closed Form Solutions ◽  
Novel Technique ◽  
Curve Method

The dual-wheel transmission unit, an innovative driving mechanism for wheeled mobile robots, was introduced elsewhere. In this paper, we discuss wheeled mobile robots with such units, supplied with a novel suspension to keep the wheel-ground contact in spite of the irregularities of the floor. We derive closed-form solutions and constraints pertaining to the direct and inverse-kinematics problems of these robots; the constraints reveal the mobility of the robots at hand. Furthermore, we provide an algorithm for the trajectory tracking of the same robots that relies on a novel technique, which is termed the companion-curve method.

scholarly journals Solution of Inverse Kinematics for 6R Robot Manipulators With Offset Wrist Based on Geometric Algebra

2013 ◽  
Vol 5 (3) ◽  
Author(s):  
Zhongtao Fu ◽  
Wenyu Yang ◽  
Zhen Yang
Keyword(s):  
Real Time ◽  
Geometric Algebra ◽  
Multiple Solutions ◽  
Inverse Kinematics ◽  
Robot Manipulators ◽  
Kinematic Modeling ◽  
Highly Nonlinear ◽  
Inverse Kinematics Problem ◽  
Painting Robot ◽  
Serial Robot

In this paper, we present an efficient method based on geometric algebra for computing the solutions to the inverse kinematics problem (IKP) of the 6R robot manipulators with offset wrist. Due to the fact that there exist some difficulties to solve the inverse kinematics problem when the kinematics equations are complex, highly nonlinear, coupled and multiple solutions in terms of these robot manipulators stated mathematically, we apply the theory of Geometric Algebra to the kinematic modeling of 6R robot manipulators simply and generate closed-form kinematics equations, reformulate the problem as a generalized eigenvalue problem with symbolic elimination technique, and then yield 16 solutions. Finally, a spray painting robot, which conforms to the type of robot manipulators, is used as an example of implementation for the effectiveness and real-time of this method. The experimental results show that this method has a large advantage over the classical methods on geometric intuition, computation and real-time, and can be directly extended to all serial robot manipulators and completely automatized, which provides a new tool on the analysis and application of general robot manipulators.

Inverse Kinematics of Serial-Chain Manipulators

1996 ◽  
Vol 118 (3) ◽  
pp. 396-404 ◽  
Author(s):  
Hong-You Lee ◽  
Charles F. Reinholtz
Keyword(s):  
Inverse Kinematics ◽  
Minimum Degree ◽  
Complete Solution ◽  
Linear Equations ◽  
End Effector ◽  
Serial Chain ◽  
Inverse Kinematics Problem ◽  
Univariate Polynomials ◽  
General Geometry

This paper proposes a unified method for the complete solution of the inverse kinematics problem of serial-chain manipulators. This method reduces the inverse kinematics problem for any 6 degree-of-freedom serial-chain manipulator to a single univariate polynomial of minimum degree from the fewest possible closure equations. It is shown that the univariate polynomials of 16th degree for the 6R, 5R-P and 4R-C manipulators with general geometry can be derived from 14, 10 and 6 closure equations, respectively, while the 8th and 4th degree polynomials for all the 4R-2P, 3R-P-C, 2R-2C, 3R-E and 3R-S manipulators can be derived from only 2 closure equations. All the remaining joint variables follow from linear equations once the roots of the univariate polynomials are found. This method works equally well for manipulators with special geometry. The minimal properties may provide a basis for a deeper understanding of manipulator geometry, and at the same time, facilitate the determination of all possible configurations of a manipulator with respect to a given end-effector position, the determination of the workspace and its subspaces with the different number of configurations, and the identification of singularity positions of the end-effector. This paper also clarifies the relationship between the three known solutions of the general 6R manipulator as originating from a single set of 14 equations by the first author.

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