Inverse Kinematic Solution of 6-DOF Robot-Arm Based on Dual Quaternions and Axis Invariant Methods

Ahmed, Abubaker; Meng, Yonggang; Chen, Feifei

doi:10.1007/s13369-022-06794-6

Cited by 7 publications

(6 citation statements)

References 27 publications

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“…These symbols are not only for conciseness but also for describing the partial structure ordering and topological relation feature of the MASs. The choice for the notation comes in this works from the fact that we are interested in the geometric properties of the kinematic modeling tools in the 3D Cartesian space and Natural coordinate systems and axis vectors of kinematics systems [29]. The left superscript and the right subscript indicate the coordinate system and KC (k-th joints) order to which a particular vector is referred.…”

Section: The Kinematic and Mathematical Frameworkmentioning

confidence: 99%

“…The axis-vector n l represents the unit direction of the kinematic axis and is the natural reference axis, of which its members n l = n x , n y , n z T determine unit direction; and the angular position θ l determines the magnitude of fixed-axis rotation [19]. Therefore, the axis vector is also termed the Axis-Invariant in [29]. The axis invariant is a free vector, and it is always directed to the outside of the origin of the frame.…”

Section: Joint ( ) Kmentioning

confidence: 99%

“…Then the direct IK for joint (n − 2) and (n − 1) is obtained by Theorem 2. In contrast, the structure parameters are given or measured directly by the natural axis fixed frame theorem, which were proposed in references [29].…”

Section: Direction Ikmentioning

confidence: 99%

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An Improved Unit Quaternion for Attitude Alignment and Inverse Kinematic Solution of the Robot Arm Wrist

Ahmed

yang

et al. 2023

Machines

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This paper introduces a new method for kinematic modeling of the robot arm by deriving a new elegant mathematical formula based on the axis vector with the tangent of the rotation angle. For this purpose, an innovative analytical quaternion is introduced through integration between Axis-Invariants and unit quaternion features named Ju-Gibbs quaternion, which expresses the body rotation with non-redundant parameters compared with the quaternions in literature. Two theorems based on the new form of the quaternion are developed and proved for the kinematic modeling of the robot arm. The first is attitude alignment, which is essential in multiaxial rotation systems. The second theorem for the wrist inverse kinematic (IK) solution is utilized to obtain the joint variables for the last joints of the end effector. In order to verify the effectiveness and accuracy of the proposed method, a numerical example and simulation of different structural configurations of robot and human arms are intensively studied. The novel quaternion provides a new tool for kinematic analysis and reduces the computational complexity of the kinematic solutions of the Robot-Arms wrist. Furthermore, the method laid a new foundation for the IKs of multi-axis systems based on Axis-Invariant and tangent quaternion.

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Section: The Kinematic and Mathematical Frameworkmentioning

confidence: 99%

Section: Joint ( ) Kmentioning

confidence: 99%

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An Improved Unit Quaternion for Attitude Alignment and Inverse Kinematic Solution of the Robot Arm Wrist

Ahmed

yang

et al. 2023

Machines

Self Cite

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show abstract

“…Thus, the first and second rotations are done correctly, while the rotation around the axis X is impossible because the three rotations axis become coplanar. Dual quaternions algebra benefits have been argued in many works comprising dynamics modeling of a mobile manipulator [5], stabilization of a rigid body motion, multiple body interaction [6], inverse kinematic study of 6-DOF of robot arm and tracking control [7,8], etc. Valverde et al [9] presented a serial manipulator dynamics using the recursive Newton-Euler based on dual quaternions.…”

Section: Introductionmentioning

confidence: 99%

Kinematics and Dynamics Modeling of 7 Degrees of Freedom Human Lower Limb Using Dual Quaternions Algebra

Benhmidouch¹,

Moufid²,

Omar³

2023

Preprint

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Denavit and Hartenberg based methods as Cardan, Fick and Euler angles describe the position and orientation of an end-effector in Three Dimensional (3D) space. However, the generation of unrealistic human posture in joint space constitutes the weak point to these methods because they impose a well-defined rotations order. A method to handle the transformation homogeneous performance uses the dual quaternions. Quaternions have proven themselves in many fields as providing a computational efficient method to represent a rotation, and yet, they can not deal with the translations in 3D-space. The dual numbers can extend quaternions to dual quaternions. This paper exploits dual quaternions theory to provide a fast and accurate solution to the forward, inverse kinematics and recursive Newton-Euler dynamics algorithm for 7 Degree of Freedom (DOF) human lower limb in 3D-space.

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“…In paper [38], using AutoCAD and MATLAB as testing tools, Kinematics, path planning, and Jacobian velocities were evaluated in an AL5B Educational Robot. This study [39] combined two distinct approaches that are axis-invariant and dual quaternions for the location and orientation of the endeffector with the least amount of error to simulate the inverse kinematics for the 6 DOF manipulator. The paper [40] presented a 7-DOF humanoid robotic arm with a configuration like a human arm.…”

Section: Introductionmentioning

confidence: 99%

Design and Modeling of 9 Degrees of Freedom Redundant Robotic Manipulator

Anjum

Samo

Nighat

et al. 2022

Journal of Robotics and Control

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In disaster areas, robot manipulators are used to rescue and clearance of sites. Because of the damaged area, they encounter disturbances like obstacles, and limited workspace to explore the area and to achieve the location of the victims. Increasing the degrees of freedom is required to boost the adaptability of manipulators to avoid disturbances, and to obtain the fast desired position and precise movements of the end-effector. These robot manipulators offer a reliable way to handle the barrier challenges since they can search in places that humans can't reach. In this research paper, the 9-DOF robotic manipulator is designed, and an analytical model is developed to examine the system’s behavior in different scenarios. The kinematic and dynamic representation of the proposed model is analyzed to obtain the translation or rotation, and joint torques to achieve the expected position, velocity, and acceleration respectively. The number of degrees may be raised to avoid disturbances, and to obtain the fast desired position and precise movements of the end-effector. The simulation of developed models is performed to ensure the adaptable movement of the manipulators working in distinct configurations and controlling their motion thoroughly and effectively. In the proposed configuration the joints can easily be moved to achieve the desired position of the end-effector and the results are satisfactory. The simulation results show that the redundant manipulator achieves the victim location with various configurations of the manipulator. Results reveal the effectiveness and efficacy of the proposed system.

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Inverse Kinematic Solution of 6-DOF Robot-Arm Based on Dual Quaternions and Axis Invariant Methods

Cited by 7 publications

References 27 publications

An Improved Unit Quaternion for Attitude Alignment and Inverse Kinematic Solution of the Robot Arm Wrist

An Improved Unit Quaternion for Attitude Alignment and Inverse Kinematic Solution of the Robot Arm Wrist

Kinematics and Dynamics Modeling of 7 Degrees of Freedom Human Lower Limb Using Dual Quaternions Algebra

Design and Modeling of 9 Degrees of Freedom Redundant Robotic Manipulator

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