A New Algorithm for a Spatial Serial Robot

2010 ◽  
Vol 29-32 ◽  
pp. 952-955
Author(s):  
Xi Guang Huang ◽  
Guang Pin He ◽  
Duan Ling Li
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Greatest Common Divisor ◽  
Closed Form Solutions ◽  
Numerical Example ◽  
Serial Robot ◽  
Univariate Polynomial

In this paper a new algorithm to compute all the closed-form inverse kinematics solutions of a spatial serial robot. Based on the method, A 16th degree univariate polynomial of the spatial serial robot is obtained without factoring out or deriving the greatest common divisor. We also obtain all the closed-form solutions for the inverse kinematics of the robot. Finally a numerical example is given to demonstrate the algorithm process.

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.

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.

A Computational Algorithm for a Spatial Serial Robot

2011 ◽  
Vol 217-218 ◽  
pp. 233-237
Author(s):  
Xi Guang Huang
Keyword(s):  
Automatic Control ◽  
Inverse Kinematics ◽  
Computational Algorithm ◽  
Polynomial Equation ◽  
Central Problem ◽  
Serial Robots ◽  
Symbolic Calculations ◽  
Inverse Kinematics Problem ◽  
Serial Robot ◽  
Univariate Polynomial

The inverse kinematics of serial robots is a central problem in the automatic control of robot manipulators. The aim of this paper is to obtain a computational algorithm to compute the inverse kinematics problem of a spatial serial robot. We use a series of algebraic and numeric transformations to reduce the problem to a univariate polynomial equation. The results can be directly applied to symbolic calculations and decreased considerably the calculation time.

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.

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.

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.

Kinematics of Continuum Robots With Constant Curvature Bending and Extension Capabilities

2018 ◽  
Vol 11 (1) ◽  
Author(s):  
Arnau Garriga-Casanovas ◽  
Ferdinando Rodriguez y Baena
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Rapid Development ◽  
Closed Form Expression ◽  
Great Promise ◽  
Continuum Robots ◽  
Cluttered Environments ◽  
Closed Form Solutions ◽  
Significant Attention

Continuum robots are becoming increasingly popular due to the capabilities they offer, especially when operating in cluttered environments, where their dexterity, maneuverability, and compliance represent a significant advantage. The subset of continuum robots that also belong to the soft robots category has seen rapid development in recent years, showing great promise. However, despite the significant attention received by these devices, various aspects of their kinematics remain unresolved, limiting their adoption and obscuring their potential. In this paper, the kinematics of continuum robots with the ability to bend and extend are studied, and analytical, closed-form solutions to both the direct and inverse kinematics are presented. The results obtained expose the redundancies of these devices, which are subsequently explored. The solution to the inverse kinematics derived here is shown to provide an analytical, closed-form expression describing the curve associated with these redundancies, which is also presented and analyzed. A condition on the reachable end-effector poses for robots with six actuation degrees-of-freedom (DOFs) is then distilled. The kinematics of robot layouts with over six actuation DOFs are subsequently considered. Finally, simulated results of the inverse kinematics are provided, verifying the study.

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.

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