GeoFIK: A Fast and Reliable Geometric Solver for the IK of the Franka Arm based on Screw Theory Enabling Multiple Redundancy Parameters

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Bibliographic Details
Main Authors:	Lopez-Custodio, Pablo C., Gong, Yuhe, Figueredo, Luis F. C.
Format:	Preprint
Published:	2025
Subjects:	Robotics
Online Access:	Acceder al recurso
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author	Lopez-Custodio, Pablo C. Gong, Yuhe Figueredo, Luis F. C.
author_facet	Lopez-Custodio, Pablo C. Gong, Yuhe Figueredo, Luis F. C.
contents	Modern robotics applications require an inverse kinematics (IK) solver that is fast, robust and consistent, and that provides all possible solutions. Currently, the Franka robot arm is the most widely used manipulator in robotics research. With 7 DOFs, the IK of this robot is not only complex due to its 1-DOF redundancy, but also due to the link offsets at the wrist and elbow. Due to this complexity, none of the Franka IK solvers available in the literature provide satisfactory results when used in real-world applications. Therefore, in this paper we introduce GeoFIK (Geometric Franka IK), an analytical IK solver that allows the use of different joint variables to resolve the redundancy. The approach uses screw theory to describe the entire geometry of the robot, allowing the computation of the Jacobian matrix prior to computation of joint angles. All singularities are identified and handled. As an example of how the geometric elements obtained by the IK can be exploited, a solver with the swivel angle as the free variable is provided. Several experiments are carried out to validate the speed, robustness and reliability of the GeoFIK against two state-of-the-art solvers.
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publishDate	2025
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spellingShingle	GeoFIK: A Fast and Reliable Geometric Solver for the IK of the Franka Arm based on Screw Theory Enabling Multiple Redundancy Parameters Lopez-Custodio, Pablo C. Gong, Yuhe Figueredo, Luis F. C. Robotics Modern robotics applications require an inverse kinematics (IK) solver that is fast, robust and consistent, and that provides all possible solutions. Currently, the Franka robot arm is the most widely used manipulator in robotics research. With 7 DOFs, the IK of this robot is not only complex due to its 1-DOF redundancy, but also due to the link offsets at the wrist and elbow. Due to this complexity, none of the Franka IK solvers available in the literature provide satisfactory results when used in real-world applications. Therefore, in this paper we introduce GeoFIK (Geometric Franka IK), an analytical IK solver that allows the use of different joint variables to resolve the redundancy. The approach uses screw theory to describe the entire geometry of the robot, allowing the computation of the Jacobian matrix prior to computation of joint angles. All singularities are identified and handled. As an example of how the geometric elements obtained by the IK can be exploited, a solver with the swivel angle as the free variable is provided. Several experiments are carried out to validate the speed, robustness and reliability of the GeoFIK against two state-of-the-art solvers.
title	GeoFIK: A Fast and Reliable Geometric Solver for the IK of the Franka Arm based on Screw Theory Enabling Multiple Redundancy Parameters
topic	Robotics
url	https://arxiv.org/abs/2503.03992

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