Rapid Vibration Suppression and Trajectory Tracking of a Serial Manipulator with Multi-Flexible Links

2026-05-17

AI Summary

This study addresses the challenges of excessive vibration, degraded tracking performance, and speed limitations in multi-link flexible robotic arms caused by structural flexibility. The authors formulate a hyperbolic partial differential equation (PDE) system by coupling Timoshenko beam dynamics with ordinary differential equations (ODEs) and develop a backstepping-based boundary output feedback controller that relies solely on boundary measurements. A key innovation lies in the first-time incorporation of the DeepONet neural operator to approximate the backstepping kernel function, substantially reducing computational overhead and enhancing the controller’s real-time performance and scalability under varying operating conditions. Experimental validation on a two-link flexible manipulator demonstrates that the proposed approach achieves faster vibration suppression and higher-precision end-point trajectory tracking compared to a conventional LQR with feedforward control scheme.

Abstract

Flexible robotic manipulators (FRMs) offer advantages in lightweight design and large workspace, but their structural flexibility induces vibrations, accelerates fatigue, degrades tracking performance, and limits operational speed. These challenges are further amplified in multi-link serial manipulators, where increased overall length leads to greater structural flexibility. This article presents a backstepping output-feedback framework for fast vibration suppression and tip tracking of an n-degree-of-freedom serial flexible manipulator robot (nDSFMR), with a DeepONet-based approximation for practical deployment. Each link-joint is modeled as a Timoshenko beam coupled with an ODE and transformed into a canonical hyperbolic PDE with boundary dynamics. A backstepping-based boundary controller at the joint is developed to equivalently inject distributed damping along the beam, enabling rapid vibration suppression and trajectory tracking, only using available boundary measurements. To enable real-time implementation and scalability, a DeepONet neural operator is introduced to approximate the backstepping kernels, significantly reducing computational cost and facilitating fast controller updates under varying operating conditions. Experiments on a two-link flexible manipulator demonstrate faster vibration suppression and convergence of the end-effector to the desired trajectory, compared with a linear quadratic regulator (LQR) with feedforward control.

Problem

• flexible robotic manipulators
• vibration suppression
• trajectory tracking
• multi-link serial manipulator
• structural flexibility

Innovation

• backstepping control
• flexible manipulator
• DeepONet
• vibration suppression
• boundary feedback