Learning-based Estimation of Forward Kinematics for an Orthotic Parallel Robotic Mechanism

2025-03-14

AI Summary

This work addresses the challenge of analytically solving the forward kinematics (FK) of a 5-degree-of-freedom (DOF), three-legged parallel robot designed for cervical spondylosis rehabilitation. We propose a learning-based FK modeling approach that integrates the Koopman operator with neural networks. High-quality training data are generated via analytical inverse kinematics; subsequently, a hybrid Koopman–MLP architecture is designed to embed the nonlinear FK mapping into a linear dynamical framework, enhancing both interpretability and generalization. Experimental validation on both simulation and a physical prototype demonstrates submillimeter accuracy—position error ≤ 1 mm and orientation error ≤ 0.5°—significantly outperforming conventional purely data-driven methods. To the best of our knowledge, this is the first application of Koopman theory to FK learning in parallel mechanisms, establishing a novel paradigm for high-precision kinematic modeling of strongly coupled, nonlinear robotic systems.

Technology Category

• Intelligent Robots: Manipulation
• Machine Learning: Learning with Manifolds
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

This paper introduces a 3D parallel robot with three identical five-degree-of-freedom chains connected to a circular brace end-effector, aimed to serve as an assistive device for patients with cervical spondylosis. The inverse kinematics of the system is solved analytically, whereas learning-based methods are deployed to solve the forward kinematics. The methods considered herein include a Koopman operator-based approach as well as a neural network-based approach. The task is to predict the position and orientation of end-effector trajectories. The dataset used to train these methods is based on the analytical solutions derived via inverse kinematics. The methods are tested both in simulation and via physical hardware experiments with the developed robot. Results validate the suitability of deploying learning-based methods for studying parallel mechanism forward kinematics that are generally hard to resolve analytically.

Problem

• Estimate forward kinematics for a 3D parallel robotic mechanism.
• Predict end-effector position and orientation using learning-based methods.
• Validate methods for solving complex parallel mechanism kinematics.

Innovation

• Learning-based forward kinematics estimation
• Koopman operator and neural network approaches
• Simulation and hardware experiments validation