Kinematics Modeling and Analysis of Manipulator Using the Dual Quaternion

Ge, Weimin; Chen, Lei; Xing, Enhong; Zielińska, Teresa

doi:10.1109/icma.2019.8816603

Cited by 6 publications

(8 citation statements)

References 11 publications

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“…In the field of control this is for example controlling a rigid body, specifically orientation and position [29], controlling an omnidirectional moving mobile robot [30] or deriving an observer for velocities of a rigid body which is later used for control [31]. Dual Quaternions can also be used in robotics to model forward and inverse kinematics [32]. Other application scenarios are designing algorithms for strapdown inertial navigation systems [33] or interpolating poses of rigid bodies [5].…”

Section: A Related Workmentioning

confidence: 99%

“…This is the author's version which has not been fully edited and content may change prior to final publication. Machine learning LWPR / Kernel Density Estimation Real numbers Yes [22] Machine learning Gaussian process kernels Dual quaternions Yes [23] Machine learning RNN Dual quaternions Yes [24] Rigid body simulation -Dual quaternions No [25] Rigid body simulation -Real numbers / Quaternions No [26], [27] Rigid body simulation --No [28] Rigid body simulation -Real numbers No [29], [30], [31] Control theory -Dual quaternions No [32] Robotics -Dual quaternions No [33] Inertial navigation system -Dual quaternions No [5] Pose interpolation -Dual quaternions No [34], [37], [38] Machine learning CNN Real numbers Yes [35] Machine learning PhysNet Real numbers Yes [36] Machine learning Graph NN Real numbers Yes [39] Machine learning Hamiltonian Generative Network Real numbers Yes [40] Machine learning Hamiltonian NN Real numbers Yes [41] Machine learning MLP / Graph NN Real numbers Yes [42] Machine learning MLP Real numbers Yes [43] Machine learning MLP Quaternions Yes [44], [45] Machine learning CNN Quaternions Yes [46] Machine learning RNN Quaternions Yes…”

Section: A Quaternionsmentioning

confidence: 99%

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Predicting Rigid Body Dynamics Using Dual Quaternion Recurrent Neural Networks With Quaternion Attention

Pöppelbaum

Schwung

2022

IEEE Access

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We propose a novel neural network architecture based on dual quaternions which allow for a compact representation of information with a main focus on describing rigid body movements. After introducing the underlying dual quaternion math, we derive dual quaternion valued neural network layer which are generally applickable to all sorts of problems which can benefit from a mathematical description in dual quaternion space. To cover the dynamic behavior inherent to rigid body movements, we propose recurrent architectures in the neural network. To further model the rigid bodies interactions efficiently, we incorporate a novel attention mechanism employing dual quaternion algebra. The introduced architecture is trainable by means of gradient based algorithms. We apply our approach to a parcel prediction problem where a rigid body with an initial position, orientation, velocity and angular velocity moves through a fixed simulation environment which exhibits rich interactions between the parcel and the boundaries. There we can show that the dual quaternion valued models outperform their counterparts operation on the real numbers, confirming the successful introduction of an inductive bias through the usage of dual quaternion math. Furthermore, we used an advantageous custom data augmentation technique specifically tailored for the usage with our dual quaternion valued input data. INDEX TERMSdual quaternion attention, dual duaternion neural networks, hypercomplex neural networks, rigid body dynamics

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Section: A Related Workmentioning

confidence: 99%

Section: A Quaternionsmentioning

confidence: 99%

Predicting Rigid Body Dynamics Using Dual Quaternion Recurrent Neural Networks With Quaternion Attention

Pöppelbaum

Schwung

2022

IEEE Access

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“…Hence, in order to control the dynamics of the robot manipulator, inverse dynamics, and a fuzzy PD controller optimized via particle swarm optimization were used. Ge et al (2019) developed a kinematic modeling method based on dual quaternions. The method requires less calculation time comparing to the traditional approaches, e.g.…”

Section: Related Workmentioning

confidence: 99%

Development of forward kinematics and construction of the driving and command system of a robotic manipulator

Mendes

Oliveira

2020

jme

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The idea of working with a robotic manipulator came from the availability of doing a retrofit of the drive and command system for the RD5 robot, a manipulator that is part of the IFCE's Energy Processing Laboratory. The challenges of working with this robot is the fact this manipulator has not been used for some time, needing adjustments such as tightening its joints, redo connections and add potentiometers instead of damaged ones. The objectives of this work are the development of forward kinematics (FK) and the construction of its drive and command system. The expected positions are obtained from FK using the Denavit-Hatenberg (DH) method. The expected positioning of the manipulator in each situation was compared with that obtained through the drive and command system and thus it was possible to perform the acquisition of position error estimation data. The results were then discussed.

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“…Wang Y et al [3][4] used quaternions to describe attitudes and establish kinematics equations. Lin P F et al [5][6][7] improved quaternions and described kinematics with dual quaternions. Rotation and translation can be considered jointly by dual quaternions.…”

Section: Introductionmentioning

confidence: 99%

Inverse attitude solution of manipulator based on improved quaternion

Yin

Ju²,

Chen³

2023

J. Phys.: Conf. Ser.

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Typically, quaternions or rotational matrices are used to establish kinematic equations and produce inverse kinematic solutions for the attitude of 6R decoupled manipulators. These approaches have certain drawbacks, such as duplicate equations and manual solution processes that cannot be eliminated automatically. In this study, we introduce the Ju-Gibbs quaternion to establish the kinematic equations, which are isomorphic to the Euler quaternion and share the same mathematical characteristics. Using this modeling method, one can create non-redundant kinematic equations wherein the number of equations equals the number of unknowns. A novel Dixon elimination method is then used to resolve the multilinear problem. Since no division operations are involved in the solution process, the solution has the advantage of being free of computation singularity issues. The experiment verifies that the proposed method can accomplish the autonomous modeling and elimination solution process of 6R manipulators with low computation complexity and high precision.

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Kinematics Modeling and Analysis of Manipulator Using the Dual Quaternion

Cited by 6 publications

References 11 publications

Predicting Rigid Body Dynamics Using Dual Quaternion Recurrent Neural Networks With Quaternion Attention

Predicting Rigid Body Dynamics Using Dual Quaternion Recurrent Neural Networks With Quaternion Attention

Development of forward kinematics and construction of the driving and command system of a robotic manipulator

Inverse attitude solution of manipulator based on improved quaternion

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