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Comparison of curvilinear parametrization methods and avoidance of orthogonal singularities in the path following task

Dyba Filip, Mazur Alicja

Journal of Automation Mobile Robotics and Intelligent Systems

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2023

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Vol. 17, No. 3

46--64

EN

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.

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Adaptive and robust following of 3D paths by holonomic manipulator

Mazur Alicja, Kaczmarek Mirela

Journal of Automation Mobile Robotics and Intelligent Systems

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2023

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Vol. 17, No. 3

65--77

EN

This paper addresses the problem of the following three-dimensional path by holonomic manipulator with parametric or structural uncertainty in the dynamics. Description of the manipulator relative to a desired three-dimensional path was presented. The path is parameterized orthogonally to the Serret-Frenet frame, which is moving along the curve. The adaptive and robust control laws for a stationary manipulator which ensures realization of the task were specified. Theoretical considerations are supported by the results of computer simulations conducted for an RTR manipulator.

3

The non-orthogonal Serret-Frenet parametrization applied to the path following problem of a manipulator with partially known dynamics

Mazur Alicja, Dyba Filip

Archives of Control Sciences

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2023

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Vol. 33, No. 2

339--370

EN

In this paper an application of the Serret-Frenet parametrization of a curve to the path following task is presented. This curvilinear parametrization method is used to obtain a control object description relative to the desired curve defined in the three-dimensional space. In order to derive proper equations, the innovative approach of the non-orthogonal projection of a control object on the given path is investigated. The non-orthogonal projection allows to design a global control algorithm. The proposed solution results in a cascade structure of the control system. Thus, the backstepping integrator algorithm was applied to create a control law. Due to the partial knowledge of control object dynamic parameters, an adaptive algorithm is taken into account. Theoretical considerations are confirmed with simulation study. Conducted simulations illustrated following paths at different levels of complexity by a holonomic non-redundant manipulator with a fixed base.

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Following 3D paths by a manipulator

Mazur A., Płaskonka J., Kaczmarek M.

Archives of Control Sciences

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2015

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Vol. 25, no. 1

117--133

EN

In the paper a description of a manipulator relative to a desired three-dimensional path was presented. The path is parameterized orthogonally to the Serret-Frenet frame which is moving along the curve. For the path two different time parameterizations were chosen. The control law for the RTR manipulator which ensures realization of the task was specified. Theoretical considerations were illustrated by simulation results.