Effective position–posture control strategy based on switching control for planar three-link underactuated mechanical system

ABSTRACT

A planar three-link passive–active–active (PAA) underactuated mechanical system is a kind of nonlinear system with a passive first joint. The position–posture control objective for the planar PAA system is to move the end effector from an initial position to a target position with a specified posture. This paper presents a switch control strategy to solve the position–posture control problem. First, a Lyapunov function is constructed based on the system control objective. Then, a set of main controllers based on this Lyapunov function are designed. However, the main controllers may make the system stabilise at one of equilibrium points, which is not the system target position. To avoid the above phenomenon, when the system is about to stabilise at one non-target position, the main controllers are switched to a set of sub-controllers, which are designed according to another Lyapunov function constructed based on the control objective of the active links. When the sub-controllers are running, their design parameters are adjusted to try to keep the derivative of the first Lyapunov function being a non-positive function. Therefore, the switch control between the main controllers and the sub-controllers realises the position–posture control objective of the system. Finally, the simulation results demonstrate the effectiveness of the switch control strategy.

KEYWORDS:

• Planar underactuated mechanical system
• position–posture control
• inverse kinematics calculate
• switch control
• Lyapunov function

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 61374106]; Hubei Provincial Natural Science Foundation of China [grant number 2015CFA010]; 111 Project [grant number B17040].

Notes on contributors

Pan Zhang

Pan Zhang received her B.S. degree in engineering from China University of Geosciences, Wuhan, China, in 2015. She is currently working towards the Ph.D. degree at the School of Automation, China University of Geosciences, Wuhan, China. Her current research interests include nonlinear system control and intelligent control.

Xuzhi Lai

Xuzhi Lai received her 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 Engineering, University of Toronto, Toronto, ON, Canada, and with the School of Engineering, University of Guelph, Guelph, ON, Canada. In 2014, she joined the China University of Geosciences, Wuhan, China, where she is currently a professor in the School of Automation. Her research interests include intelligent control, robot control and nonlinear system control.

Yawu Wang

Yawu Wang received his B.S. and M.S. degrees in engineering from the Hubei University of Technology, Wuhan, China, in 2012 and 2015, respectively. He is currently working towards the Ph.D. degree at the School of Automation, China University of Geosciences, Wuhan, China. His current research interests include robot control and nonlinear system control.

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 the Ph.D. degree in engineering from the Tokyo Institute of Technology, Tokyo, Japan, in 1999. From 1986 to 2014, he was a faculty member of the School of Information Science and Engineering, Central South University, as a full professor. From 1989 to 1990, he was a visiting scholar with the Department of Electrical Engineering, Tohoku University, Sendai, Japan, and from 1996 to 1999, a visiting research scholar with the Department of Control and Systems Engineering, Tokyo Institute of Technology. From 2001 to 2002, he was a visiting professor with the School of Mechanical, Materials, Manufacturing Engineering and Management, University of Nottingham, Nottingham, UK. In 2014, he joined the China University of Geosciences, Wuhan, China, where he is currently a professor in the School of Automation. His research interests include robust control and its applications, process control and intelligent control. Prof. Wu is a member 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).