Nonlinear H Control for Uncertain Flexible Joint Robots with Unscented Kalman Filter

Abstract

Todays, use of combination of two or more methods was considered to control of systems. In this paper is
presented how to design of a nonlinear H∞ (NL-H∞) controller for flexible joint robot (FJR) based on bounded
UKF state estimator. The UKF has more advantages to standard EKF such as low bios and no need to
derivations. In this research, based on spong primary model for FJRs, same as rigid robots links position are
selected as differential equations variables. Then this model was reformed to NL H differential equations.
The results of simulations demonstrate that mixed of NL H controller and UKF estimator lead to
conventional properties such as stability and good tracking. Also, Simulation results show the efficiency and
superiority of the proposed method in compare with EKF.

[1] L.M. Sweet and M.C. Good, "Re-definition of the
robot motion control problems: Effects of plant
dynamics, drive system constraints, and user
requirements," IEEE Int. Conf. on Decision and
Control, 1984.
[2] G. Cesareo and R. Marino, "On the controllability
properties of elastic robots," Int. Conf. Analysis
and Optimization of Systems, 1984.
[3] M.W. Spong, "The control of FJRs: A survey," in
New Trends and Applications of Distributed
Parameter control systems, G.Chen, E.B.Lee,
W.Littman, L.Markus , 1990.
[4] S. Ozgoli, “Design and implementation of a
position controller for a flexible joint robot in
presence of actuator saturation,” PhD thesis
proposal, Electrical Eng. Dept., K.N.Toosi
University of Technology, 2003.
[5] A.Isidori and W.kang, "H∞ Control via
measurement feedback for general nonlinear
systems," IEEE Transaction on Automatic control,
Vol. 40, PP.466-472, 1995.
[6] Yusun Fu, Zuohua Tian, Songjiao Shi, "Robust H∞
control of uncertain nonlinear systems," Elsevier,
Automatica 42 (2006) 1547 – 1552
[7] Huang, J., & Lin, C. F. "Numerical approach to
computing nonlinear H∞ control laws," Journal of
Guidance, Control and Dynamics, 1995, 18(5),
989–993.
[8] Matthew Rhudy1,*, Yu Gu1 and Marcello R.
Napolitano1 "An Analytical Approach for
comparing Linearization Methods in EKF and
UKF" Int J Adv Robotic Sy, 2013, Vol. 10,
208:2013
[9] Mark W. Spong, Seth Hutchinson, M. Vidyasagar,
(2006) "Robot Modeling and Control", Industrial
Robot: An International Journal, Vol. 33 Iss: 5,