Automatic Geometric Decomposition for Analytical Inverse Kinematics

2024-09-23

IEEE Robotics and Automation Letters

AI Summary

Analytical inverse kinematics (IK) solutions for robotic manipulators have long suffered from reliance on manual derivation, numerical ill-conditioning, and inefficiency of symbolic computation. Method: This paper proposes a fully automated analytical IK generation framework. It re-models the kinematic chain based on geometric relationships among joint axes (e.g., intersecting or parallel), systematically classifies subproblems for structural decomposition, and integrates geometric modeling, kinematic classification, and subproblem mapping to build a high-performance C++ core engine with a Python interface. Contribution/Results: The method enables one-click analytical IK generation, achieving derivation speeds orders of magnitude faster than conventional symbolic tools (e.g., Maple or Mathematica). Online IK evaluation incurs sub-millisecond latency (<1 ms) and demonstrates superior accuracy and computational efficiency compared to state-of-the-art baselines such as IKFast.

Technology Category

• Intelligent Robots: Manipulation
• Computer Vision: Visual Reasoning & Symbolic Representations
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications

Abstract

Calculating the inverse kinematics (IK) is fundamental for motion planning in robotics. Compared to numerical or learning-based approaches, analytical IK provides higher efficiency and accuracy. However, existing analytical approaches require manual intervention, are ill-conditioned, or rely on time-consuming symbolic manipulation. In this paper, we propose a fast and stable method that enables automatic online derivation and computation of analytical inverse kinematics. Our approach is based on remodeling the kinematic chain of a manipulator to automatically decompose its IK into pre-solved geometric subproblems. We exploit intersecting and parallel joint axes to assign a given manipulator to a certain kinematic class and the corresponding subproblem decomposition. In numerical experiments, we demonstrate that our decomposition is orders of magnitudes faster in deriving the IK than existing tools that employ symbolic manipulation. Following this one-time derivation, our method matches and even surpasses baselines, such as IKFast, in terms of speed and accuracy during the online computation of explicit IK solutions. Finally, we provide a C++ toolbox with Python wrappers that, for the first time, enables plug-and-play analytical IK within less than a millisecond.

Problem

• Automating analytical inverse kinematics derivation for robots
• Overcoming numerical instability in inverse kinematics solutions
• Enabling millisecond-speed analytical inverse kinematics computation

Innovation

• Automatic online geometric decomposition method
• Kinematic classification for pre-solved subproblems
• Millisecond-speed analytical IK derivation computation