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Paper details
Number 2 - June 2025
Volume 35 - 2025
A robust path following algorithm based on the orthogonal Bishop parametrization for a non–holonomic mobile manipulator
Alicja Mazur, Filip Dyba
Abstract
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.
Keywords
backstepping integrator control, non-holonomic mobile manipulator, orthogonal Bishop parametrization, singularity avoidance, path following algorithm, sliding mode controller