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Sensors 2026 , 26 , 829 20 of 21 References 1. Chandu, H.S. A Survey of Semiconductor W afer Fabrication T echnologies: Advances and Futur e T rends. Int. J. Res. Anal. Rev . 2023 , 10 , 344–349. 2. W ang, H.; Kang, R.; …

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sion trajectory optimization problem is signiﬁcantly enhanced, beneﬁting from improved

population diversity and global search capability.

To further evaluate the robustness of the proposed method, random external torque

disturbances are introduced into the system. Under such disturbances, the tracking re-

sponses remain highly consistent with the planned trajectories, and no signiﬁcant overshoot

or residual oscillation is observed during acceleration, constant-velocity, or deceleration

phases. In particular, the angular velocity ﬂuctuation is effectively constrained within a

small range, indicating that high-frequency vibration components are signiﬁcantly sup-

pressed. These results conﬁrm that minimizing the jerk-based vibration energy index leads

to improved dynamic smoothness and enhanced vibration suppression capability of the

wafer-handling robotic arm.

7. Conclusions

This paper addresses the micro-vibration problem of wafer transfer robotic arms and

proposes and validates a vibration suppression trajectory optimization method based on the

Graylag Goose Optimization (GGO) algorithm. After theoretical derivation and simulation

tests, the following conclusions are drawn:

(1) This study established and analyzed the dynamic model of the wafer transfer

robotic arm based on the Lagrange method, providing a theoretical foundation for vi-

bration suppression trajectory planning. The model fully considers the ﬂexible dynamic

characteristics of the robotic arm and accurately describes the system’s dynamic behavior.

(2) By combining a multi-segment polynomial trajectory planning method with a

residual vibration energy dissipation equation, a multi-objective optimization function

targeting both time-optimal performance and vibration energy was constructed. By rea-

sonably setting weight coefﬁcients according to working conditions, a multi-objective

coordinated optimization was achieved to ensure trajectory smoothness and minimal

residual vibration energy.

(3) Simulation results show that when solving the dual-objective vibration suppression

trajectory optimization, introducing the proposed improved multi-objective Gray Goose

Optimization (MOGGO) algorithm effectively solves the dual-objective problem. The

results indicate that the derived trajectory, when subjected to random external disturbances,

maintains speed ﬂuctuations basically within 0.01 deg/s, demonstrating good vibration

suppression performance.

However, this study only performed Pareto optimization for two objectives and has not

been extended to higher-dimensional, multi-objective optimization problems. Moreover, it

is limited to SIMULINK and MATLAB simulation environments. Future work will expand

to validation on a PLC platform and further explore the algorithm’s applicability under

more complex operating conditions and with additional optimization objectives.

Author Contributions: Conceptualization, Y.J.; Software, P.H.; Formal analysis, P.H.; Writing—

original draft, P.H.; Writing—review & editing, P.H.; Supervision, Y.J. All authors have read and

agreed to the published version of the manuscript.

Funding: This research was funded by the Basic Scientiﬁc Research Project of Higher EducationInsti-

tutions of Liaoning Province (grant number JYTQN2023064).

Institutional Review Board Statement: Not applicable.

Informed Consent Statement: Not applicable.

Data Availability Statement: The original contributions presented in this study are included in the

article. Further inquiries can be directed to the corresponding author.

Conﬂicts of Interest: The authors declare no conﬂicts of interest.

https://doi.org/10.3390/s26030829

Sensors 2026, 26, 829

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