Non-Orthogonal Serret–Frenet Parametrization Applied to Path Following of B-Spline Curves by a Mobile Manipulator

A tool for path following for a mobile manipulator is herein presented. The control algorithm is obtained by projecting a local frame associated with the robot onto the desired path, thus obtaining a non-orthogonal moving frame. The Serret–Frenet frame moving along the curve is considered as a refer...

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Bibliographic Details
Published inRobotics (Basel) Vol. 13; no. 9; p. 139
Main Authors Dyba, Filip, Frego, Marco
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.09.2024
Subjects
Algorithms
B spline functions
B-spline curve
Control algorithms
Control theory
Design
Kinematics
Manipulators
mobile manipulator
non-holonomic constraints
Parameterization
path following
Robot arms
Robot control
Robotics
Robots
Serret–Frenet parametrization
Trajectory planning
Velocity
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Summary:A tool for path following for a mobile manipulator is herein presented. The control algorithm is obtained by projecting a local frame associated with the robot onto the desired path, thus obtaining a non-orthogonal moving frame. The Serret–Frenet frame moving along the curve is considered as a reference. A curve resulting from the control points of a B-spline in 2D or 3D is investigated as the desired path. It is used to show how the geometric continuity of the path has an impact on the performance of the robot in terms of undesired force spikes. This can be understood by looking at the curvature and, in 3D, at the torsion of the path. These unwanted effects vanish and better performance is achieved thanks to the change of the B-spline order. The theoretical results are confirmed by the simulation study for a mobile manipulator consisting of a non-holonomic wheeled base coupled with a holonomic robotic arm with three degrees of freedom (rotational and prismatic).
ISSN:2218-6581
2218-6581
DOI:10.3390/robotics13090139