Efficient singularity-robust inverse kinematics and redundancy management for robotic systems
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Authors
Elias, Alexander, Jacob
Issue Date
2025-08
Type
Electronic thesis
Thesis
Thesis
Language
en_US
Keywords
Electrical engineering
Alternative Title
Abstract
A robot must control the position of its hand or end effector, but this requires understanding the complex relationship between the end effector pose and the joint angles. This thesis seeks to provide a unified, computationally efficient, and singularity-robust framework for the inverse kinematics (IK) and redundancy management of robotic systems. IK is the problem of finding which joint angles correspond to an end effector pose. There is a need for an IK solver which is efficient, robust, and precise, and which finds all solutions including singular solutions. We present new IK methods using geometric subproblem decomposition which apply to 6-DOF arms, 7-DOF arms, and parallel manipulators (also solving forward kinematics for parallel manipulators). Depending on intersecting or parallel joint axes, the methods are closed-form or use 1D or 2D search. Search methods may be converted to high-order polynomials. The open-source implementation, IK-Geo, is the fastest general IK solver in our testing, with >40x faster IK for the UR5 than IKFast. 7-DOF manipulators avoid singularities and obstacles better than 6-DOF manipulators because they have an extra internal degree of freedom. However, redundancy parameterizations create new algorithmic singularities. We propose a new parameterization called the Stereographic SEW angle that reduces the presence of algorithmic singularities in the workspace. We prove algorithmic singularities are unavoidable, but the stereographic SEW angle is ideal in that the robot pose is singular only when the wrist is on a half-line from the shoulder. We apply our 7-DOF analysis to the ABB YuMi and provide the first complete and validated definition of the SEW angle used by the ABB controllers. Cuspidal robots are a surprising and increasingly common class of manipulator. Classical path planners may fail for these robots because they can travel between IK solutions without encountering a singularity. We are the first to show the ABB GoFa and some 3-parallel-axis robots are cuspidal. We also propose a graph-based planner to find optimal joint paths for a given end effector path and an optimizer to adjust the workpiece placement. For the first time, we apply cuspidality analysis to 7-DOF arms. While redundant arms can usually travel between self-motion manifolds without encountering a singularity, certain 7-DOF arms may or may not be cuspidal once the redundancy is parameterized. We find the ABB YuMi is cuspidal after parameterization, while the KUKA iiwa is not.
Description
August2025
School of Engineering
School of Engineering
Full Citation
Publisher
Rensselaer Polytechnic Institute, Troy, NY