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Volume 14
Issue 10
10.3390/act14100505
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Velocity Trajectory Planning and Tracking Control Based on Basis Function Superposition and Metaheuristic Algorithms for Planar Underactuated Manipulators

by
Ba Zeng
1,
Yang Li
1,
Xiangyu Gong
1,
Hongwei Wang
2,
Zixin Huang
1,2,3,4 and
Hongjian Zhou
1,5,*
1
School of Electrical and Information Engineering, Wuhan Institute of Technology, Wuhan 430205, China
2
Fujian Provincial Key Laboratory of Data-Intensive Computing, Quanzhou Normal University, Quanzhou 362000, China
3
Anhui Province Key Laboratory of Special Heavy Load Robot, Maanshan 243032, China
4
Fujian Provincial University Applied Technology Engineering Center for Textile and Garment Science and Technology and Culture, Quanzhou Vocational and Technical University, Jinjiang 362268, China
5
School of Mechanical & Electrical Engineering, Wuhan Institute of Technology, Wuhan 430205, China
*
Author to whom correspondence should be addressed.
Actuators 2025, 14(10), 505; https://doi.org/10.3390/act14100505 (registering DOI)
Submission received: 2 September 2025 / Revised: 9 October 2025 / Accepted: 16 October 2025 / Published: 18 October 2025
(This article belongs to the Section Actuators for Robotics)
Versions Notes

Abstract

Planar underactuated manipulators are widely used in aerospace and deep-sea exploration. Due to their passive joints without actuation, it is difficult to perform trajectory planning and direct control. In this paper, an angular velocity trajectory planning method is proposed, aiming to calculate the velocity trajectory by using a superposition of basis functions and transforming the planning problem into an optimization problem by using a metaheuristic algorithm. According to the underactuated constraint relationship, the planning trajectory of the passive joint is obtained, which ensures that the passive joint can be indirectly controlled to reach the target angle while tracking the trajectory of the active joint. For the tracking control problem, a sliding mode controller with an exponential convergence rate is used to track the trajectory. Lastly, three sets of simulations are run to demonstrate the efficacy of the suggested approach.
Keywords: nonlinearsystems; underactuated manipulator; metaheuristic algorithms; velocity trajectory planning; sliding mode controller nonlinearsystems; underactuated manipulator; metaheuristic algorithms; velocity trajectory planning; sliding mode controller

Share and Cite

MDPI and ACS Style

Zeng, B.; Li, Y.; Gong, X.; Wang, H.; Huang, Z.; Zhou, H. Velocity Trajectory Planning and Tracking Control Based on Basis Function Superposition and Metaheuristic Algorithms for Planar Underactuated Manipulators. Actuators 2025, 14, 505. https://doi.org/10.3390/act14100505

AMA Style

Zeng B, Li Y, Gong X, Wang H, Huang Z, Zhou H. Velocity Trajectory Planning and Tracking Control Based on Basis Function Superposition and Metaheuristic Algorithms for Planar Underactuated Manipulators. Actuators. 2025; 14(10):505. https://doi.org/10.3390/act14100505

Chicago/Turabian Style

Zeng, Ba, Yang Li, Xiangyu Gong, Hongwei Wang, Zixin Huang, and Hongjian Zhou. 2025. "Velocity Trajectory Planning and Tracking Control Based on Basis Function Superposition and Metaheuristic Algorithms for Planar Underactuated Manipulators" Actuators 14, no. 10: 505. https://doi.org/10.3390/act14100505

APA Style

Zeng, B., Li, Y., Gong, X., Wang, H., Huang, Z., & Zhou, H. (2025). Velocity Trajectory Planning and Tracking Control Based on Basis Function Superposition and Metaheuristic Algorithms for Planar Underactuated Manipulators. Actuators, 14(10), 505. https://doi.org/10.3390/act14100505

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