GeoFIK: A Fast and Reliable Geometric Solver for the IK of the Franka Arm Based on Screw Theory Enabling Multiple Redundancy Parameters
Pablo Lopez-Custodio, Yuhe Gong, Luis Figueredo
AI summary
Problem
The Franka arm’s unconventional wrist and elbow offsets make its 7-DOF inverse kinematics highly complex, leaving existing solvers slow, fragile near singularities, and limited to a single redundancy parameter.
Approach
GeoFIK uses screw theory to compute the robot’s geometric screw axes first, enabling systematic joint angle calculation and Jacobian extraction while supporting flexible redundancy resolution via multiple free parameters.
Key results
- Outperforms HeLiu, IKFast, and IKGeo in speed, robustness, and reliability
- Maintains numerical stability and finds solutions at extreme singular poses
- Supports multiple free parameters (q7, q6, q4, swivel angle) to maximize valid configurations
- Computes the Jacobian matrix as a byproduct at zero extra cost
Why it matters
It equips robotics researchers and engineers with a dependable IK tool for the industry-standard Franka arm, enhancing real-world planning, safety, and deployment reliability.
Abstract
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 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, computing the Jacobian matrix prior to the joint angles. All singularities are 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 GeoFIK against three state-of-the-art solvers.