LQR Based Cooperative Vibration Suppression in Dual Flexible Robotic Manipulators with Unequal Load Sharing

Abstract

This paper examines cooperative vibration suppression in two flexible robotic manipulators lifting a common load under unequal load sharing scenarios. Flexible motions and imbalanced force distribution tend to unwanted oscillations, compromising manipulation precision and payload stability. To overcome this challenge, a simulation environment is established in MATLAB, simulating two UR5 robotic manipulators lifting a common load. Time and frequency domain vibration responses of the payload are examined, and a control technique, Linear Quadratic Regulator (LQR) to reduce the vibrations. It shows reduced payload oscillations and enhancement in the load sharing index, identifying the capability of the proposed method. Unlike existing studies that treat load imbalance as a disturbance, this work explicitly models unequal load sharing and demonstrates how cooperative control redistributes damping responsibility to suppress vibrations effectively.

Introduction

The text focuses on cooperative vibration control in dual flexible robotic manipulators handling a common payload, particularly under unequal load-sharing conditions. In collaborative tasks, variations in grasp points, actuator capabilities, or structural stiffness can create imbalances, causing oscillations and vibrations that reduce positional accuracy, payload stability, and manipulator safety. Traditional rigid-body models fail to account for these flexible dynamics, making advanced control strategies necessary.

Key points include:

1. Problem Context:

   • Flexible dual-arm manipulators face vibrations due to link flexibility, asymmetrical forces, and dynamic payload interaction.

   • Unequal load sharing exacerbates instability, a scenario common in realistic cooperative manipulation but often neglected in existing research.

2. Existing Research:

   • Classical controllers (PID), modern techniques (LQR, sliding mode, input shaping, fuzzy logic, adaptive control) have been used for vibration suppression.

   • Most studies assume symmetric load sharing or use high-order models, making controller design complex.

   • Few studies address reduced-order models for unequal load distribution in dual manipulators.

3. Proposed Approach:

   • Reduced-order modeling: Dominant low-frequency payload vibrations are represented as a second-order mass-spring-damper system, ignoring high-frequency link dynamics for computational efficiency.

   • LQR control: Applied to minimize vibration amplitudes and maintain smooth, stable cooperative motion. Linearization around an operating point allows the use of linear control techniques.

   • Joint-payload dynamics modeling: Simplified yet effective for simulating and controlling vibrations in MATLAB.

4. Methodology:

   • Two UR5 robotic manipulators share a payload with uneven load distribution.

   • The system models joint torques, Coriolis effects, gravity, and damping.

   • Linearization and reduced-order modeling facilitate LQR synthesis, ensuring vibration suppression and synchronized end-effector movement.

   • Simulation compares open-loop, PID, and LQR performance, showing substantial vibration reduction and improved cooperative stability.

5. Significance:

   • First attempt to systematically address unequal load sharing in reduced-order cooperative vibration models.

   • Provides a framework for efficient, low-complexity vibration suppression in dual flexible manipulators, enhancing precision and reliability in collaborative robotic applications.

Conclusion

The experiment was successful in realistically capturing the key advantage of the LQR Controller for regulating vibrations and force in Flexible dual-arm manipulation of a payload. The Open-loop case was a crucial reference point, showing drastic, high-amplitude, and long-lasting Payload velocity oscillations, Flexible link deflection oscillations, and Joint angle response oscillations, validating the system\'s instability. In contrast, the LQR system offered improved dynamic performance by robust vibration attenuation while maintaining high Joint Angle fidelity. Moreover, the controller demonstrated its advanced level by employing a scheduled unequal load sharing, dynamically allocating force responsibility in the Load share index plot to strategically deploy the higher damping gain arm for improved stability. The high Sensitivity to Payload mass for light payloads of the system was also validated, emphasizing the need for such an adaptive control strategy. In general, the LQR controller is validated to be a very effective solution for coordinated, high-precision, and vibration-free motion in dual-arm systems manipulating flexible payloads.

References

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Copyright

Copyright © 2025 Vijitha K, Sarvesh R, Dr. Anbarasi M P. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.