A Robust Path Following Algorithm Based on the Orthogonal Bishop Parametrization for A non–Holonomic Mobile Manipulator

We deal with the fundamental problem of path following applied to control mobile manipulators. A parametric-based path following algorithm is proposed. Such an approach results in a cascaded structure of the control system, so that the control algorithm is designed using the backstepping integrator...

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Vydáno v:International journal of applied mathematics and computer science Ročník 35; číslo 2; s. 209 - 224
Hlavní autoři: Mazur, Alicja, Dyba, Filip
Médium: Journal Article
Jazyk:angličtina
Vydáno: Zielona Góra Sciendo 01.06.2025
De Gruyter Brill Sp. z o.o., Paradigm Publishing Services
Témata:
Algorithms
backstepping integrator control
Control algorithms
Control theory
Manipulators
non-holonomic mobile manipulator
orthogonal Bishop parametrization
Parameterization
path following algorithm
Robustness (mathematics)
Simulation
singularity avoidance
Sliding mode control
sliding mode controller
Trajectory planning
ISSN:1641-876X, 2083-8492
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Shrnutí:We deal with the fundamental problem of path following applied to control mobile manipulators. A parametric-based path following algorithm is proposed. Such an approach results in a cascaded structure of the control system, so that the control algorithm is designed using the backstepping integrator method. The proposed solution is robust due to the following features. Firstly, it is based on the Bishop parametrization, which is well-defined at every point of the curve. Moreover, we present a novel approach to the orthogonal projection method onto the path so that the motion precisely along the path is possible. Finally, the robustness to structural and parametric uncertainties of the dynamics model is guaranteed thanks to the sliding mode controller applied at the dynamic level of the control cascade. The problem is analyzed theoretically. The achieved results are verified with an exemplary simulation study. The proposed algorithm assures asymptotic convergence of errors to zero for less strict requirements imposed on the desired path and in the case of partial knowledge of the dynamics model.
Bibliografie:ObjectType-Article-1
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ISSN:1641-876X
2083-8492
DOI:10.61822/amcs-2025-0015