scholarly journals Suboptimal approximations in repeatable inverse kinematics for robot manipulators

2017 ◽  
Vol 65 (2) ◽  
pp. 209-217
Author(s):  
I. Duleba ◽  
I. Karcz-Duleba
Keyword(s):  
Configuration Space ◽  
Simulation Study ◽  
Inverse Kinematics ◽  
Jacobian Matrix ◽  
Robot Manipulator ◽  
Inverse Kinematic ◽  
Forward Kinematics ◽  
Definition Of ◽  
Pseudo Inverse ◽  
Selection Of

Abstract In this paper a repeatable inverse kinematic task was solved via an approximation of a pseudo-inverse Jacobian matrix of a robot manipulator. An entry configuration to the task was optimized and a task-dependent definition of an approximation region, in a configuration space, was utilized. As a side effect, a relationship between manipulability and optimally augmented forward kinematics was established and independence of approximation task solutions on rotations in augmented components of kinematics was proved. A simulation study was performed on planar pendula manipulators. It was demonstrated that selection of an initial configuration to the repeatable inverse kinematic task heavily impacts solvability of the task and its quality. Some remarks on a formulation of the approximation task and its numerical aspects were also provided.

Proper Smart Method of the Inverse Kinematic Problem

2015 ◽  
Vol 772 ◽  
pp. 455-460 ◽  
Author(s):  
Adrian Olaru ◽  
Serban Olaru ◽  
Niculae Mihai
Keyword(s):  
Inverse Kinematics ◽  
Jacobian Matrix ◽  
Inverse Kinematic ◽  
Iterative Approximation ◽  
Inverse Kinematic Problem ◽  
Space Curves ◽  
Inverse Kinematics Problem ◽  
Artificial Intelligence Algorithm ◽  
Pseudo Inverse

One of the most precise method solving the inverse kinematics problem in the redundant cases of the robots is the coupled method. The proposed method use the Iterative Pseudo Inverse Jacobian Matrix Method (IPIJMM) coupled with the proper Sigmoid Bipolar Hyperbolic Tangent Neural Network with Time Delay and Recurrent Links (SBHTNN-TDRL). One precise solution of the inverse kinematics problem is very difficult to find, when the degree of freedom increase and in many cases this is impossible because the redundant solutions. In all these cases must be used the numerical iterative approximation, like the proposed method, with artificial intelligence algorithm. The paper describe all the steps in one case study to obtain the space circle curve in different planes by using one arm type robot and the proposed method. The errors of the space movement of the robot end-effecter, after applying the proposed method, was less than 0,01. The presented method is general and it can be used in all other robots types and for all other conventional and unconventional space curves.

Increase the Space Trajectory Precision by Using the Proper Assisted Research Method for Inverse Kinematics Problem

2015 ◽  
Vol 789-790 ◽  
pp. 711-716 ◽  
Author(s):  
Adrian Olaru ◽  
Serban Olaru ◽  
Niculae Mihai
Keyword(s):  
Inverse Kinematics ◽  
Numerical Approximation ◽  
Jacobian Matrix ◽  
Industrial Robot ◽  
Forward Kinematics ◽  
Hyperbolic Tangent ◽  
Space Curves ◽  
Inverse Kinematics Problem ◽  
Pseudo Inverse

Inverse kinematics model of the industrial robot is used in the control of the end-effecter trajectory. The solution of the inverse kinematics problem is very difficult to find, when the degree of freedom increase and in many cases this is impossible. In these cases is used the numerical approximation or other method with diffuse logic. The paper showed one new method for optimization of the inverse cinematic solution by applying the proper assisted Iterative Pseudo Inverse Jacobian Matrix Method coupled with proper Sigmoid Bipolar Hyperbolic Tangent Neural Network with Time Delay and Recurrent Links Method (IPIJMM-SBHTNN-TDRLM). In the paper was shown one case study to obtain one space circle curve by using one arm type robot and the proposed method. The errors of the space coordinates of the circle, after applying the proposed method, was less than 0.001. The study has contained the determining the internal coordinates corresponding to the external coordinates of the circle space curve, by solving the inverse kinematics with the proposed method and after that, by applying the forward kinematics to this coordinates, were obtained the external coordinates, what were compared with the theoretical one. The presented method is general and it can be used in all other robots types and for all other conventional and unconventional space curves.

scholarly journals Inverse kinematic solution of 6R robot manipulators based on screw theory and the Paden–Kahan subproblem

2018 ◽  
Vol 15 (6) ◽  
pp. 172988141881829 ◽  
Author(s):  
Rongbo Zhao ◽  
Zhiping Shi ◽  
Yong Guan ◽  
Zhenzhou Shao ◽  
Qianying Zhang ◽  
...  
Keyword(s):  
Inverse Kinematics ◽  
Matrix Theory ◽  
Screw Theory ◽  
Robot Manipulator ◽  
Inverse Kinematic ◽  
Kinematic Calibration ◽  
Kinematic Parameters ◽  
Kinematics Modeling ◽  
High Level ◽  
Kinematic Solution

The traditional Denavit–Hatenberg method is a relatively mature method for modeling the kinematics of robots. However, it has an obvious drawback, in that the parameters of the Denavit–Hatenberg model are discontinuous, resulting in singularity when the adjacent joint axes are parallel or close to parallel. As a result, this model is not suitable for kinematic calibration. In this article, to avoid the problem of singularity, the product of exponentials method based on screw theory is employed for kinematics modeling. In addition, the inverse kinematics of the 6R robot manipulator is solved by adopting analytical, geometric, and algebraic methods combined with the Paden–Kahan subproblem as well as matrix theory. Moreover, the kinematic parameters of the Denavit–Hatenberg and the product of exponentials-based models are analyzed, and the singularity of the two models is illustrated. Finally, eight solutions of inverse kinematics are obtained, and the correctness and high level of accuracy of the algorithm proposed in this article are verified. This algorithm provides a reference for the inverse kinematics of robots with three adjacent parallel joints.

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.

scholarly journals A Fast Evaluation of Initial Configurations in Repeatable Inverse Kinematics for Redundant Manipulators

2018 ◽  
Vol 28 (3) ◽  
pp. 483-492
Author(s):  
Ignacy Duleba ◽  
Iwona Karcz-Duleba ◽  
Arkadiusz Mielczarek
Keyword(s):  
Configuration Space ◽  
Inverse Kinematics ◽  
Indirect Method ◽  
Inverse Kinematic ◽  
Initial Configuration ◽  
Redundant Manipulators ◽  
Task Space ◽  
Original Function ◽  
Fast Evaluation ◽  
Computationally Expensive

Abstract A repeatable inverse kinematic task in robot manipulators consists in finding a loop (cyclic trajectory) in a configuration space, which corresponds to a given loop in a task space. In the robotic literature, an entry configuration to the trajectory is fixed and given by a user. In this paper the assumption is released and a new, indirect method is introduced to find entry configurations generating short trajectories. The method avoids a computationally expensive evaluation of (infinite) many entry configurations for redundant manipulators (for each of them, repeatable inverse kinematics should be run). Some fast-to-compute functions are proposed to evaluate entry configurations and their correlations with resulting lengths of trajectories are computed. It appears that only an original function, based on characteristics of a manipulability subellipsoid, properly distinguishes entry configurations that generate short trajectories. This function can be used either to choose one from a few possible entry configurations or as an optimized function to compute the best initial configuration.

Fundamental Exercises in Mechanical Systems Engineering Using Robot Manipulator

2011 ◽  
Author(s):  
Hideaki Takanobu
Keyword(s):  
Mechanical System ◽  
Linear Algebra ◽  
Systems Engineering ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Engineering Students ◽  
Robot Manipulator ◽  
Mechanical Systems ◽  
Forward Kinematics ◽  
Basic Learning

A five degrees-of-freedom (5-DOF) robot manipulator is used for the basic learning of mechanical system engineering. Students learned the forward kinematics as concrete applications of the mathematics, especially linear algebra. After making a manipulator, baton relay contest was done to understand the inverse kinematics by controlling the manipulator using a manual controller having five levers.

Kinematics Analysis for a 4-DOF Palletizing Robot Manipulator

2013 ◽  
Vol 313-314 ◽  
pp. 937-940 ◽  
Author(s):  
Yong Guo Zhao ◽  
Yong Fei Xiao ◽  
Tie Chen
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Robot Manipulator ◽  
Forward Kinematics ◽  
Kinematics Analysis

In order to meet theneeds of high-speedpalletizing inlogistics automation industry, a 4 d4-DOF palletizingrobot manipulatorwas designed. Inthis paper,focusing on kinematic analysis, forward kinematics modeland inverse kinematics were introduced in detail.

Optimal conditions for inverse kinematics of a robot manipulator with redundancy

Robotica ◽  
1995 ◽  
Vol 13 (1) ◽  
pp. 95-101 ◽  
Author(s):  
Dong Kwon Cho ◽  
Byoung Wook Choi ◽  
Myung Jin Chung
Keyword(s):  
Inverse Kinematics ◽  
Robot Manipulator ◽  
Sufficient Conditions ◽  
Optimal Solution ◽  
Simple Algorithm ◽  
Inverse Kinematic ◽  
Performance Measure ◽  
Configuration Change ◽  
Necessary Conditions For Optimality ◽  
Kinematic Solution

SummaryThe algorithms of inverse kinematics based on optimality constraints have some problems because those are based only on necessary conditions for optimality. One of the problems is a switching problem, i.e., an undesirable configuration change from a maximum value of a performance measure to a minimum value may occur and cause an inverse kinematic solution to be unstable. In this paper, we derive sufficient conditions for the optimal solution of the kinematic control of a redundant manipulator. In particular, we obtain the explicit forms of the switching condition for the optimality constraintsbased methods. We also show that the configuration at which switching occurs is equivalent to an algorithmic singularity in the extended Jacobian method. Through a numerical example of a cyclic task, we show the problems of the optimality constraints-based methods. To obtain good configurations without switching and kinematical singularities, we propose a simple algorithm of inverse kinematics.

scholarly journals Inverse kinematic analysis of 4 DOF pick and place arm robot manipulator using fuzzy logic controller

2020 ◽  
Vol 10 (2) ◽  
pp. 1376
Author(s):  
Tresna Dewi ◽  
Siti Nurmaini ◽  
Pola Risma ◽  
Yurni Oktarina ◽  
Muhammad Roriz
Keyword(s):  
Fuzzy Logic ◽  
Inverse Kinematics ◽  
Fuzzy Logic Controller ◽  
Robot Manipulator ◽  
Inverse Kinematic ◽  
Experimental Results ◽  
Position Errors ◽  
Motion System ◽  
Pick And Place ◽  
The Right

The arm robot manipulator is suitable for substituting humans working in tomato plantation to ensure tomatoes are handled efficiently. The best design for this robot is four links with robust flexibility in x, y, and z-coordinates axis. Inverse kinematics and fuzzy logic controller (FLC) application are for precise and smooth motion. Inverse kinematics designs the most efficient position and motion of the arm robot by adjusting mechanical parameters. The FLC utilizes data input from the sensors to set the right position and motion of the end-effector. The predicted parameters are compared with experimental results to show the effectiveness of the proposed design and method. The position errors (in x, y, and z-axis) are 0.1%, 0.1%, and 0.04%. The rotation errors of each robot links (θ1, θ2, and θ3) are 0%, 0.7% and 0.3%. The FLC provides the suitable angle of the servo motor (θ4) responsible in gripper motion, and the experimental results correspond to FLC’s rules-based as the input to the gripper motion system. This setup is essential to avoid excessive force or miss-placed position that can damage tomatoes. The arm robot manipulator discussed in this study is a pick and place robot to move the harvested tomatoes to a packing system.

scholarly journals Inverse kinematics of mobile manipulators based on differential evolution

2018 ◽  
Vol 15 (1) ◽  
pp. 172988141775273 ◽  
Author(s):  
Carlos López-Franco ◽  
Jesús Hernández-Barragán ◽  
Alma Y. Alanis ◽  
Nancy Arana-Daniel ◽  
Michel López-Franco
Keyword(s):  
Differential Evolution ◽  
Inverse Kinematics ◽  
Jacobian Matrix ◽  
Inverse Kinematic ◽  
Mobile Manipulator ◽  
Robot Kinematics ◽  
Mobile Manipulators ◽  
Inverse Kinematic Problem ◽  
Simulation Results ◽  
Traditional Approaches

The solution of the inverse kinematics of mobile manipulators is a fundamental capability to solve problems such as path planning, visual-guided motion, object grasping, and so on. In this article, we present a metaheuristic approach to solve the inverse kinematic problem of mobile manipulators. In this approach, we represent the robot kinematics using the Denavit–Hartenberg model. The algorithm is able to solve the inverse kinematic problem taking into account the mobile platform. The proposed approach is able to avoid singularities configurations, since it does not require the inversion of a Jacobian matrix. Those are two of the main drawbacks to solve inverse kinematics through traditional approaches. Applicability of the proposed approach is illustrated using simulation results as well as experimental ones using an omnidirectional mobile manipulator.

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