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

TL;DR

The paper tackles forward kinematics estimation for a wearable neck-traction robot built from three identical five-DoF chains in a 3-RRUR parallel configuration. An analytic inverse kinematics model is used to generate data that train two forward models: a Koopman operator with EDMDc and a recurrent neural network (RNN). In simulation and on a physical prototype, the RNN achieves higher trajectory accuracy (translation error around $0.0062\ \mathrm{mm}$ and orientation error around $0.0035^\ ext{\circ}$, with $R^2=0.9974$) than the Koopman approach, which trains quickly (about $28.1$ s) but yields larger errors (translation $\approx 3.24\ \mathrm{mm}$, orientation $\approx 0.06^ ext{\circ}$). The work demonstrates the feasibility of data-driven forward kinematics for parallel robotic orthotics, highlighting a trade-off between accuracy and computation and pointing to future online Koopman learning as a path to real-time control.

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.

Figures (8)

• Figure 1: Diagram of the developed 3-RRUR parallel robot.
• Figure 2: Chain structure diagram of 3-RRUR parallel robot
• Figure 3: Description of three orientations of the head-neck aligned with the fixed base frame shown in Figure \ref{['fig:diagram_3RRUR']}: (i) axial rotation, (ii) lateral bending, (iii) flexion and extension.
• Figure 4: The RNN-based architecture considered herein.
• Figure 5: Predicted end-effector position (left) and orientation (right) in simulation using the Koopman operator-based estimator.