PSO-based nonlinear model predictive planning and discrete-time sliding tracking control for uncertain planar underactuated manipulators

Abstract

Control of planar underactuated manipulators (PUM) with unknown parameter perturbations and external disturbances is still a challenging task due to their complex and peculiar characteristics. The research on it is significant in the view of wide applications in practice. In this paper, taking an uncertain 3-degree of freedom PUM with a free first joint as a benchmark example, we discuss its position control issue. Specifically, an integrated control method is developed, including the nonlinear model prediction control (NMPC) based on an improved particle swarm optimisation (PSO) algorithm and the discrete-time fast terminal sliding mode (FTSM) control. The PSO-based NMPC is proposed for planning discrete trajectories of the active joint angles in real time, along which the manipulator end-point can reach the desired position. Then the discrete-time FTSM controllers are designed to keep the active joints tracking the discrete trajectories, where the uncertainties related to the active links/joints are estimated by time delay estimation method. Besides, the influence of the uncertainties related to the free link/joint on the system can be made up by the NMPC in real time. It is confirmed via simulations that the above method can achieve the accurate positioning of such an uncertain manipulator.

Keywords:

• Uncertain planar underactuated manipulators
• position control
• nonlinear model predictive control
• discrete-time fast terminal sliding mode control
• particle swarm optimisation (PSO)

Data availability statement

The data related to this paper are available from the corresponding author upon reasonable request.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 61773353], the Hubei Provincial Natural Science Foundation of China [grant number 2015CFA010], the 111 project [grant number B17040], the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) [grant number CUG2106110].

Notes on contributors

Pan Zhang

Pan Zhang received the B.S. degree in automation and the Ph.D. degree in control science and engineering from China University of Geosciences, Wuhan, China, in 2015 and 2020, respectively. She was a research intern with Gina Cody School of Engineering and Computer Science, Concordia University, Montreal, QC, Canada from 2017 to 2020. In 2021, she joined School of Automation, China University of Geosciences, where she is currently an Associate Professor. Her current research interests include nonlinear system control and intelligent control.

Xuzhi Lai

Xuzhi Lai received the B.S., M.S., and Ph.D. degrees in engineering from Central South University, Changsha, China, in 1988, 1991, and 2001, respectively. From 1991 to 2014, she was a Faculty Member of the School of Information Science and Engineering, Central South University, as a Full Professor. From 1998 to 1999, she was a Visiting Scholar with the Department of Mechatronics, School of Engineering, Tokyo University of Technology, Tokyo, Japan. From 2004 to 2006, she was a Visiting Scholar with the Department of Mechanical and Engineering, University of Toronto, Toronto, ON, Canada, and with the School of Engineering, University of Guelph, Guelph, ON, Canada. In 2014, she moved to the China University of Geosciences, Wuhan, China, where she is currently a Professor with the School of Automation. Her current research interests include intelligent control, robot control, and nonlinear system control.

Yawu Wang

Yawu Wang received the B.S. and M.S. degrees in engineering from Hubei University of Technology, Wuhan, China, in 2011 and 2015, respectively, the Ph.D. degree in control science and engineering from China University of Geosciences, Wuhan, in 2018. He was a joint doctoral student with Gina Cody School of Engineering and Computer Science, Concordia University, Montreal, QC, Canada, from 2017 to 2018. In 2019, he joined School of Automation, China University of Geosciences, where he is currently an Associate Professor. His research interests include robot control and nonlinear system control.

Chun-Yi Su

Chun-Yi Su received the Ph.D. degree in control engineering from the South China University of Technology, Guangzhou, China, in 1990. After a seven-year stint with the University of Victoria, Victoria, BC, Canada, he joined Concordia University, Montreal, QC, Canada, in 1998, where he is currently a Professor with the Gina Cody School of Engineering and Computer Science and holds the Concordia University Research Chair of Control. He has also held several short-time visiting positions, including the Chang Jiang Chair Professorship by the China’s Ministry of Education and JSPS Invitation Fellowship from Japan. He has authored or coauthored more than 400 publications, which have appeared in journals, as book chapters and in conference proceedings. His research interests include control theory and its applications to various mechanical systems, with a recent focus on the control of systems involving hysteresis nonlinearities. Prof. Su has served as an Associate Editor for the IEEE TRANSACTIONS ON AUTOMATIC CONTROL and the IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY. He has been on the Editorial Board of several journals including Mechatronics (IFAC). He is a Distinguished Lecturer with the IEEE Robotics and Automation Society and has served for many conferences as an Organizing Committee Member, including the General Chair and the Program Chair.

Min Wu

Min Wu received his B.S. and M.S. degrees in engineering from Central South University, Changsha, China, in 1983 and 1986, respectively, and his Ph.D. degree in engineering from the Tokyo Institute of Technology, Tokyo, Japan, in 1999. He was a faculty member of the School of Information Science and Engineering at Central South University from 1986 to 2014, and was promoted to Professor in 1994. In 2014, he moved to China University of Geosciences, Wuhan, China, where he is currently a professor in the School of Automation. He was a visiting scholar with the Department of Electrical Engineering, Tohoku University, Sendai, Japan, from 1989 to 1990, and a visiting research scholar with the Department of Control and Systems Engineering, Tokyo Institute of Technology, from 1996 to 1999. He was a visiting professor at the School of Mechanical, Materials, Manufacturing Engineering and Management, University of Nottingham, Nottingham, UK, from 2001 to 2002. His current research interests include process control, robust control, and intelligent systems. Dr. Wu is a Fellow of the IEEE and a Fellow of the Chinese Association of Automation. He received the IFAC Control Engineering Practice Prize Paper Award in 1999 (together with M. Nakano and J. She).