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

In this paper applications of curvilinear parametrizations (Serret–Frenet, Bishop) in the path following task have been considered. The parametrizations allow one to derive manipulator’s equations with respect to a path. The full mathematical model of the path following task involves two groups of equations, i.e., the dynamics of the manipulator and the equations obtained from the parametrization method, connected in the cascaded system.
Based on those relations two path following algorithms have been designed according to the backstepping integrator method (dedicated to the cascaded systems). Depending on the chosen parametrization method the algorithms differ in requirements and performance. In the paper an in-depth analysis comparing features of both considered methods has been presented.
The parametric description of a path requires projection of a robot on the path. In this article the orthogonal projection has been taken into account. It introduces a singularity in the robot description. We have proposed a new form of the orthogonal projection constraint which allows a robot to not only approach the path, but also move along it. This novelty design is an important enhancement of the algorithms used so far.
The problem of partially known dynamic parameters of a robot has also been addressed. In this paper, we have shown how to apply an adaptive controller to the path following task.
Theoretical considerations have been verified with a simulation study conducted for a holonomic stationary manipulator. Achieved results emphasized why it is strongly recommended to use the algorithm version with the orthogonal singularity outside the path. Moreover, the comparative analysis results may be used to select the best curvilinear parametrization method according to the considered task requirements.
</abstract>

In this paper applications of curvilinear parametrizations (Serret–Frenet, Bishop) in the path following task have been considered. The parametrizations allow one to derive manipulator’s equations with respect to a path. The full mathematical model of the path following task involves two groups of equations, i.e., the dynamics of the manipulator and the equations obtained from the parametrization method, connected in the cascaded system.
Based on those relations two path following algorithms have been designed according to the backstepping integrator method (dedicated to the cascaded systems). Depending on the chosen parametrization method the algorithms differ in requirements and performance. In the paper an in-depth analysis comparing features of both considered methods has been presented.
The parametric description of a path requires projection of a robot on the path. In this article the orthogonal projection has been taken into account. It introduces a singularity in the robot description. We have proposed a new form of the orthogonal projection constraint which allows a robot to not only approach the path, but also move along it. This novelty design is an important enhancement of the algorithms used so far.
The problem of partially known dynamic parameters of a robot has also been addressed. In this paper, we have shown how to apply an adaptive controller to the path following task.
Theoretical considerations have been verified with a simulation study conducted for a holonomic stationary manipulator. Achieved results emphasized why it is strongly recommended to use the algorithm version with the orthogonal singularity outside the path. Moreover, the comparative analysis results may be used to select the best curvilinear parametrization method according to the considered task requirements.

Comparison of Curvilinear Parametrization Methods and Avoidance of Orthogonal Singularities in the Path Following Task

Department of Cybernetics and Robotics, Faculty of Electronics, Photonics and Microsystems

Wrocław University of Science and Technology

Journal of Automation, Mobile Robotics and Intelligent Systems

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

In this paper applications of curvilinear parametrizations (Serret–Frenet, Bishop) in the path following task have been considered. The parametrizations allow...

Comparison of Curvilinear Parametrization Methods and Avoidance of Orthogonal Singularities in the Path Following Task

Publié en ligne: 04 mars 2024

Pages: 46 - 64

Reçu: 08 janv. 2023

Accepté: 06 juin 2023

DOI: https://doi.org/10.14313/jamris/3-2023/22

Mots clés
Path following, Serret–Frenet parametrization, Bishop parametrization, Orthogonal projection, Backstepping algorithm, Holonomic manipulator, Singularity

© 2023 Filip Dyba et al., published by Sciendo

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

Comparison of Curvilinear Parametrization Methods and Avoidance of Orthogonal Singularities in the Path Following Task

Publié en ligne: 04 mars 2024

Pages: 46 - 64

Reçu: 08 janv. 2023

Accepté: 06 juin 2023

DOI: https://doi.org/10.14313/jamris/3-2023/22

Mots clésPath following, Serret–Frenet parametrization, Bishop parametrization, Orthogonal projection, Backstepping algorithm, Holonomic manipulator, Singularity

© 2023 Filip Dyba et al., published by Sciendo

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

Mots clés
Path following, Serret–Frenet parametrization, Bishop parametrization, Orthogonal projection, Backstepping algorithm, Holonomic manipulator, Singularity