Efficient Implementation of Inverse Kinematics on a 6-DOF Industrial Robot using Conformal Geometric Algebra

Tørdal, Sondre Sanden; Hovland, Geir; Tyapin, Ilya

doi:10.1007/s00006-016-0698-2

Cited by 16 publications

(25 citation statements)

References 6 publications

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“…Kjelland (2016) used the Motion-Lab in his Ph.D. work focusing on motion compensation and load transfer from a bottom-fixed hydraulic crane to a moving platform (the large Stewart platform). Tørdal et al (2017a) used the available Comau robot to investigate the implementation of the inverse kinematic solution using Conformal Geometric Algebra (CGA).…”

Section: Methodsmentioning

confidence: 99%

The Norwegian Motion-Laboratory

Tørdal¹,

Olsen²,

Hovland³

2018

MIC

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This paper contains an overview of the equipment currently available in the Norwegian Motion Laboratory, a description of the IT networking infrastructure in the laboratory, a GitHub link to open source code developed, description of the PyQt-based graphical user interface, presentation of robot forward and inverse kinematics, presentation of equations of motion for the suspended load motion and a description of the full system kinematics. The paper ends with a list of research experiments and publications from the laboratory to date.

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Section: Methodsmentioning

confidence: 99%

The Norwegian Motion-Laboratory

Tørdal¹,

Olsen²,

Hovland³

2018

MIC

Self Cite

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“…This approach is not focused on a particular robot but applies to an entire class of manipulators. The position problem is solved geometrically by extending the particular contributions of [21,26,28,29,30], while a novel method is developed for solving the orientation problem. This method involves splitting the rotor that defines the target orientation into three rotors, so that each one depends on just one joint variable.…”

Section: Related Workmentioning

confidence: 99%

“…First of all, the case without offsets between consecutive joints is considered, i.e., the axes of each pair of consecutive joints intersect. Given the first translation axis z 1 , two of the rotors defined in (26) can be used to obtain the joint axes z 2 and z 3 as follows:…”

Section: Three Prismatic Joints (P+p+p)mentioning

confidence: 99%

Closed-form solutions for the inverse kinematics of serial robots using conformal geometric algebra

Zaplana,

Hadfield,

Lasenby

2021

Preprint

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This work addresses the inverse kinematics of serial robots using conformal geometric algebra. Classical approaches include either the use of homogeneous matrices, which entails high computational cost and execution time, or the development of particular geometric strategies that cannot be generalized to arbitrary serial robots. In this work, we present a compact, elegant and intuitive formulation of robot kinematics based on conformal geometric algebra that provides a suitable framework for the closed-form resolution of the inverse kinematic problem for manipulators with a spherical wrist. For serial robots of this kind, the inverse kinematics problem can be split in two subproblems: the position and orientation problems. The latter is solved by appropriately splitting the rotor that defines the target orientation in three simpler rotors, while the former is solved by developing a geometric strategy for each combination of prismatic and revolute joints that forms the position part of the robot. Finally, the inverse kinematics of 7 DoF redundant manipulators with a spherical wrist is solved by extending the geometric solutions obtained in the non-redundant case.

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“…Two methods (differential geometric method and variational method) of the extended Jacobian algorithm were examined in [13] to address the approximation of the Jacobian pseudo inverse. An implementation of the inverse kinematics solution for a robot based on Conformal Geometric Algebra was proposed in [14]. A double quaternion based kinematics formulation for the 6R robots was introduced in [15][16] to avoid kinematic singularities.…”

Section: Introductionmentioning

confidence: 99%

The optimized algorithm based on machine learning for inverse kinematics of two painting robots with non-spherical wrist

et al. 2020

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This paper studies the inverse kinematics of two non-spherical wrist configurations of painting robot. The simplest analytical solution of orthogonal wrist configuration is deduced in this paper for the first time. For the oblique wrist configuration, there is no analytical solution for the configuration. So it is necessary to solve by general method, which cannot achieve high precision and high speed as analytic solution. Two general methods are optimized in this paper. Firstly, the elimination method is optimized to reduce the solving speed to 20% of the original one, and the completeness of the method is supplemented. Based on the Gauss damped least squares method, a new optimization method is proposed to improve the solving speed. The enhanced step length coefficient is introduced to conduct studies with the machine learning correlation method. It has been proved that, on the basis of ensuring the stability of motion, the number of iterations can be effectively reduced and the average number of iterations can be less than 5 times, which can effectively improve the speed of solution. In the simulation and experimental environment, it is verified.

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Efficient Implementation of Inverse Kinematics on a 6-DOF Industrial Robot using Conformal Geometric Algebra

Cited by 16 publications

References 6 publications

The Norwegian Motion-Laboratory

The Norwegian Motion-Laboratory

Closed-form solutions for the inverse kinematics of serial robots using conformal geometric algebra

The optimized algorithm based on machine learning for inverse kinematics of two painting robots with non-spherical wrist

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