<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The use of robots is continuously growing, from heavy-duty industries to nanotechnology. Exact multilink robot end effector control is required to withstand this tendency in modern robotics. Mapping between joint variables in joint-space coordinate and end effector configuration in task-space coordinate are provided by serial manipulator kinematics. A computation of higher-order Jacobian matrix derivatives is required for accurate trajectory tracking. With conventional numerical derivation, only approximate results can be obtained. Still, the computation of high-order derivatives of multi-DoF manipulators with high accuracy requires long time intervals and it is difficult. This paper investigates a novel derivation method for a multilink robot Jacobian. According to this method, an exact value of higher-order acceleration can be obtained using a multidual differentiation transform. Multidual functions for sine and cosine will be used to get the exact value of acceleration, jerk, and hyper-jerk (jounce) expressions, commonly used for accurate trajectory-tracking.</p>
</abstract>

The use of robots is continuously growing, from heavy-duty industries to nanotechnology. Exact multilink robot end effector control is required to withstand this tendency in modern robotics. Mapping between joint variables in joint-space coordinate and end effector configuration in task-space coordinate are provided by serial manipulator kinematics. A computation of higher-order Jacobian matrix derivatives is required for accurate trajectory tracking. With conventional numerical derivation, only approximate results can be obtained. Still, the computation of high-order derivatives of multi-DoF manipulators with high accuracy requires long time intervals and it is difficult. This paper investigates a novel derivation method for a multilink robot Jacobian. According to this method, an exact value of higher-order acceleration can be obtained using a multidual differentiation transform. Multidual functions for sine and cosine will be used to get the exact value of acceleration, jerk, and hyper-jerk (jounce) expressions, commonly used for accurate trajectory-tracking.

High-Order Derivatives of Serial Manipulator Jacobians Using Multidual Differentiation Transform

“Gheorghe Asachi” Technical University of Iași

BULETINUL INSTITUTULUI POLITEHNIC DIN IAȘI. Secția Matematica. Mecanică Teoretică. Fizică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

The use of robots is continuously growing, from heavy-duty industries to nanotechnology. Exact multilink robot end effector control is required to withstand...

High-Order Derivatives of Serial Manipulator Jacobians Using Multidual Differentiation Transform

Published Online: Dec 29, 2023

Page range: 7 - 20

Received: Sep 01, 2023

Accepted: Oct 25, 2023

DOI: https://doi.org/10.2478/bipmf-2023-0001

Keywords
high-order derivatives, serial manipulator Jacobians, multidual differentiation transform, higher-order acceleration, Jacobian matrix

© 2023 Mihail Cojocari et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

High-Order Derivatives of Serial Manipulator Jacobians Using Multidual Differentiation Transform

Published Online: Dec 29, 2023

Page range: 7 - 20

Received: Sep 01, 2023

Accepted: Oct 25, 2023

DOI: https://doi.org/10.2478/bipmf-2023-0001

Keywordshigh-order derivatives, serial manipulator Jacobians, multidual differentiation transform, higher-order acceleration, Jacobian matrix

© 2023 Mihail Cojocari et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
high-order derivatives, serial manipulator Jacobians, multidual differentiation transform, higher-order acceleration, Jacobian matrix