A new control method for planar four-link underactuated manipulator based on intelligence optimization

  • Ya-Wu Wang
  • Xu-Zhi LaiEmail author
  • Pan Zhang
  • Chun-Yi Su
  • Min Wu
Original Paper


This paper presents a continuous control strategy based on the differential evolution (DE) algorithm for a planar four-link underactuated manipulator with a passive first joint to realize its position-posture control objective. First, we obtain the coupling equation in integral form between the angle of the passive link and the states (angles and angular velocities) of three active links according to the angular velocity constraint of the system. Then, according to this coupling equation, we construct a Lyapunov function only based on the control targets of three active links, and use the Lyapunov function to design the PD controllers. In addition, these general PD controllers are modified to be the step PD controllers to overcome the sudden change in the initial torques. Next, we use the DE algorithm to optimize the target angles of all links and the design parameters of the step PD controllers, which ensures that the angle of the passive link converges to its target angle when the angles of three active links converge to their target angles. Finally, simulation results demonstrate the effectiveness of the proposed control strategy.


Planar four-link underactuated manipulator Position-posture control Nonholonomic system Continuous control strategy Differential evolution algorithm 



This work was supported by the National Natural Science Foundation of China under Grant 61773353, the Hubei Provincial Natural Science Foundation of China under Grant 2015CFA010, and the 111 Project under Grant B17040.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of AutomationChina University of GeosciencesWuhanChina
  2. 2.Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex SystemsWuhanChina
  3. 3.Faculty of Engineering and Computer ScienceConcordia UniversityMontrealCanada

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