scholarly journals Guaranteed Manipulator Precision via Interval Analysis of Inverse Kinematics

2013 ◽  
Author(s):  
Muhammed R. Pac ◽  
Micky Rakotondrabe ◽  
Sofiane Khadraoui ◽  
Dan O. Popa ◽  
Philippe Lutz
Keyword(s):  
Interval Analysis ◽  
Inverse Kinematics ◽  
Computational Analysis ◽  
Inverse Kinematic ◽  
Forward Kinematics ◽  
Uncertainty Modelling ◽  
Uncertainty Interval ◽  
Design Problems ◽  
End Effector ◽  
Precision Design

The paper presents a new methodology for solving the inverse problem of manipulator precision design. Such design problems are often encountered when the end-effector uncertainty bounds are given, but it is not clear how to allocate precision bounds on individual robot axes. The approach presented in this paper uses interval analysis as a tool for uncertainty modelling and computational analysis. In prior work, the exponential formulation of the forward kinematics map was extended to intervals. Here, we use this result as an inclusion function in the computation of solutions to set-valued inverse kinematic problems. Simulation results are presented in two case studies to illustrate how we can go from an uncertainty interval at the end-effector to a design domain of allowable uncertainties at individual joints and links. The proposed method can be used to determine the level of precision needed in the design of a manipulator such that a predefined end-effector precision can be guaranteed. Also, the approach is general as such it can be easily extended to any degree-of-freedom and kinematic configuration.

scholarly journals Computational Analysis of Kinematics of 3 – Links Articulated Robotic Manipulator

2019 ◽  
Vol 9 (2) ◽  
pp. 3640-3643
Keyword(s):  
Inverse Kinematics ◽  
Computational Analysis ◽  
Robot Manipulators ◽  
Robotic Manipulator ◽  
Robotic Arm ◽  
Forward Kinematics ◽  
End Effector ◽  
Computational Estimation ◽  
Arm Motion ◽  
Free Body

The Computational Analysis of Kinematics of 3 – Links Articulated Robotic Manipulator has been presented in this. The design of robot manipulators requires accurate computational analysis, involving the geometric position of the linking arms. The method of Forward Kinematics and Inverse Kinematics were employed in estimating the robotic arm’s position with respect to link lengths and angle, in which the angle required to move the end effector to a desired position is estimated and determined. A three link robotic arm with a rigid rotational base was also illustrated using free body diagrams, and computational estimation of the required parameters. The outcomes of the forward kinematics reveals that the robot end effector position can be estimated using the values of x, y, and z coordinates thereby providing a better means of controlling or adapting robot’s arm/motion to its environment.

scholarly journals Design and Implementation of 6 DOF ROTARIC Robot Using Inverse Kinematics Method

2021 ◽  
Vol 13 (2) ◽  
pp. 125-134
Author(s):  
Fransisko Limanuel ◽  
Calvin Susanto ◽  
Ferry Rippun Gideon Manalu
Keyword(s):  
Inverse Kinematics ◽  
Inverse Kinematic ◽  
Intersection Point ◽  
Forward Kinematics ◽  
End Effector ◽  
Work Area ◽  
Kinematic Method ◽  
Point Equation ◽  
Articulated Robot ◽  
Forward Kinematic

This paper will discuss the calculation of inverse kinematic which will be used to control the 6-DOF articulated robot. This robot consists of 6 Dynamixel MX-28 smart servo with OpenCM 9.04 microcontroller. The articulated robot has been simplified to 4-DOF because there are no obstacles in the work area and no special movements are required. The calculation method uses the intersection point equation between the ball and the line, so that it can make it easier to determine the point in calculating the kinematic inverse. The experiment is carried out using the desired position as input for the kinematic inverse to produce the angle of each joint. From the angle of each joint obtained, it will be entered into forward kinematic so that the end-effector position will be obtained. The desired position will be compared with the end-effector position, and then how much difference will be calculated. From the experimental results, it was found that the inverse kinematic method which has been inverted by the forward kinematic produces the same final position. Keywords: 6-DOF manipulator, Articulated robot, inverse kinematics and forward kinematics, Dynamixel MX-28, OpenCM 9

Inverse Kinematic Solution of Robot Manipulators Using Interval Analysis

1998 ◽  
Vol 120 (1) ◽  
pp. 147-150 ◽  
Author(s):  
R. S. Rao ◽  
A. Asaithambi ◽  
S. K. Agrawal
Keyword(s):  
Computational Complexity ◽  
Numerical Algorithm ◽  
Interval Analysis ◽  
Inverse Kinematics ◽  
Inverse Kinematic ◽  
Real Numbers ◽  
Computational Mathematics ◽  
All Solutions ◽  
Inverse Kinematics Problem ◽  
Kinematic Solution

Interval analysis is a growing branch of computational mathematics where operations are carried out on intervals instead of real numbers. This paper presents the first application of this method to robotic mechanisms for the solution of inverse kinematics. As shown in this paper, it is possible to potentially compute all solutions of the inverse kinematics problem using this method. This paper describes the preliminaries of interval analysis, the numerical algorithm, the computational complexity, and illustrations with examples.

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 Analytical inverse kinematics for 5-DOF humanoid manipulator under arbitrarily specified unconstrained orientation of end-effector

Robotica ◽  
2014 ◽  
Vol 33 (4) ◽  
pp. 747-767 ◽  
Author(s):  
Masayuki Shimizu
Keyword(s):  
Analytical Method ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Singularity Analysis ◽  
Inverse Kinematic ◽  
Inverse Kinematic Problem ◽  
Target Orientation ◽  
End Effector ◽  
Position And Orientation

SUMMARYThis paper proposes an analytical method of solving the inverse kinematic problem for a humanoid manipulator with five degrees-of-freedom (DOF) under the condition that the target orientation of the manipulator's end-effector is not constrained around an axis fixed with respect to the environment. Since the number of the joints is less than six, the inverse kinematic problem cannot be solved for arbitrarily specified position and orientation of the end-effector. To cope with the problem, a generalized unconstrained orientation is introduced in this paper. In addition, this paper conducts the singularity analysis to identify all singular conditions.

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.

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.

Design and Analysis of a Biomimetic Wire-Driven Robot Arm

2011 ◽  
Author(s):  
Zheng Li ◽  
Ruxu Du ◽  
Man Cheong Lei ◽  
Song Mei Yuan
Keyword(s):  
Inverse Kinematics ◽  
Geometric Analysis ◽  
Forward Kinematics ◽  
Positioning Error ◽  
Robot Arm ◽  
End Effector ◽  
Fixed Node

Inspired by the octopus and snakes, we designed and built a wire-driven serpentine robot arm. The robot arm is made of a number of rigid nodes connected by two sets of wires. The rigid nodes act as the backbone while the wires work as the muscle, which enables the 2 DOF bending. The forward kinematics is derived using D-H method, while the inverse kinematics and its workspace can be solved by geometric analysis. To validate the design, a prototype is built. It is found that the positioning error of the robot arm is generally less than 2%. The advantage of this robot arm is that with several nodes fixed the rest nodes are still controllable. The positioning error is smaller when the fixed node is closer to the end effector.

Kinematic and Kinetostatic Analysis of Parallel Manipulators with Emphasis on Position, Motion, and Actuation Singularities

Robotica ◽  
2018 ◽  
Vol 37 (4) ◽  
pp. 599-625 ◽  
Author(s):  
M. Kemal Ozgoren
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
The Other ◽  
Forward Kinematics ◽  
Velocity Mapping ◽  
Active Joint ◽  
End Effector ◽  
Jacobian Matrices ◽  
Other Hand

SummaryThis paper provides a contribution to the singularity analysis of the parallel manipulators by introducing the position singularities in addition to the motion and actuation singularities. The motion singularities are associated with the linear velocity mapping between the task and joint spaces. So, they are the singularities of the relevant Jacobian matrices. On the other hand, the position singularities are associated with the nonlinear position mapping between the task and joint spaces. So, they are encountered in the position-level solutions of the forward and inverse kinematics problems. In other words, they come out irrespective of the velocity mapping and the Jacobian matrices. Considering these distinctions, a kinematic singularity is denoted here by one of the four acronyms, which are PSFK (position singularity of forward kinematics), PSIK (position singularity of inverse kinematics), MSFK (motion singularity of forward kinematics), and MSIK (motion singularity of inverse kinematics). There may also occur an actuation singularity (ACTS) concerning the kinetostatic relationships that involve forces and moments. However, it is verified that an ACTS is the same as an MSFK. Each singularity induces different consequences in the joint and task spaces. A PSFK imposes a constraint on the active joint variables and makes the end-effector position indefinite and uncontrollable. Therefore, it must be avoided. An MSFK imposes a constraint on the rates of the active joint variables and makes the end-effector motion indefinite and easily perturbable. Besides, since it is also an ACTS, it causes the actuator torques or forces to grow without bound. Therefore, it must also be avoided. On the other hand, a PSIK imposes a constraint on the end-effector position but provides freedom for the active joint variables. Similarly, an MSIK imposes a constraint on the end-effector motion but provides freedom for the rates of the active joint variables. A PSIK or MSIK need not be avoided if the constraint it imposes on the position or motion of the end-effector is acceptable or if the task can be planned to be compatible with that constraint. Besides, with such a compatible task, a PSIK or MSIK may even be advantageous, because the freedom it provides for the active joint variables can sometimes be used for a secondary purpose. This paper is also concerned with the multiplicities of forward kinematics in the assembly modes of the manipulator and the multiplicities of inverse kinematics in the posture modes of the legs. It is shown that the assembly mode changing poses of the manipulator are the same as the MSFK poses, and the posture mode changing poses of the legs are the same as the MSIK poses.

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