Nonlinear Control for Underactuated Mechanical Systems: Swing-up Control for n-link Planar Robot with Passive Joint

Lecture / Panel
For NYU Community

Speaker: Professor Xin Xin

Faculty Host: Professor  Zhong-Ping Jiang


The last two decades have witnessed considerable progress in studying underactuated robots, which possess fewer actuators than degrees of freedom. A robot may be underactuated as a result of intentional design to reduce weight and cost, or as a result of an actuator failure. Since underactuated robots usually have second-order nonholonomic constraints, their control problems are challenging.

This talk concerns the swing-up control of an n-link revolute robot moving in the vertical plane with the first joint being passive and the others being active. The goal of this study is to design and analyze a swing-up controller that can bring the robot into any arbitrarily small neighborhood of the upright equilibrium point with all links in the upright position. First we introduce some of our theoretical and experiment works on the swing-up control for a 2-link robot with passive second joint known as the Acrobot via the energy based control approach. Second, we address how to study a swing-up control problem of an n-link (n >=3) robot with its first joint being passive, the rest of joints being active. We show that different from the 2-DOF case, it is difficult to analyze the motion of the n-link robot under the swing-up controller designed by using the conventional energy based control approach. We address the problem of how to iteratively devise a series of virtual composite links to be used for designing a coordinate transformation on the angles of all the active joints. We devise an energy-based swing-up controller that uses a new Lyapunov function based on that transformation. Third, we analyze the global motion of the robot under the controller and establish conditions on the control parameters that ensure attainment of the swing-up control objective. This study not only unifies some previous results for acrobots and three-link robots with a passive first joint,
but also provides insight into the energy- and passivity-based control of underactuated multiple-degree-of-freedom systems.


About the Speaker

Xin Xin received the BS degree in 1987 from the University of Science and Technology of China, China, and PhD in 1993 from the Southeast University, China. From 1991 to 1993, he did his PhD studies in Osaka University as a co-advised student of China and Japan with the Japanese Government Scholarship. He also received the Doctor degree in engineering in 2000 from Tokyo Institute of Technology.

From 1993 to 1995, he was a postdoctoral researcher and then became an associate professor in Southeast University. From 1996 to 1997, he was with the New Energy and Industrial Technology Development, Japan as an advanced industrial technology researcher. From 1997 to 2000, he was an assistant professor of Tokyo Institute of Technology. From 2000, he has been with Okayama Prefectural University as an associate professor, where he is now a professor since 2008. He has over 130 publications in journals, international conferences, and book chapters. He received the division paper award of SICE 3rd Annual Conference on Control Systems in 2004. His current research interests include robotics, dynamics and control of nonlinear and complex systems. He is senior member of IEEE.