ADJUSTABLE-RATE SEMIGLOBALLY EXPONENTIAL OBSERVER/ CONTROLLER FOR TRACKING IN ROBOTS WITH ACTUATOR DYNAMICS AND ONLY LINK POSITION MEASUREMENT

S. Malagari and B.J. Driessen

Keywords

Velocity observer, actuator dynamics, semi-globally exponentialtracking, robot, non-linear controls, brush motor, RLED, SGES,semi-global exponential

Abstract

In this work, we present an observer and controller for a multiple degree of freedom robotic plant with actuator dynamics and without velocity measurement, without link torque measurement/knowledge, and without measurement of the states of the actuator dynamics. The only measurement is that of link position. For this considered plant, we propose and present an observer/controller that estimates or observes the velocity and the actuator’s states and drives the position tracking error to zero. We prove that the combined tracking error and observer error converges to zero semi-globally exponentially, and we prove that the closed-loop exponential rate is adjustable by the user. Brush motor dynamics are a special case (sub-set) of the actuator dynamics covered in the present paper. Previous work ([Lim et al., an output feedback controller for trajectory tracking of RLED robots using an observed backstepping approach, Proceedings of the Third IEEE Conference on Control Applications, Glasgow, UK, 1994, 71–76 and Lim et al., Output feedback controller for trajectory tracking of RLED robots using an observed backstepping approach, International of Journal of Robotics and Automation 11 (4), 1996, 149–160]) for this plant sub-set (also with only link position measurement) presented a semi-globally exponential observer/controller whose (closed-loop) exponential rate was artificially limited by the speed of the (open- loop) actuator dynamics. To the contrary, the observer/controller of the present paper has an exponential rate that we herein prove explicitly, by construction, to be adjustable by the user, for the entire class of actuator dynamics considered (which includes the brush motor as a special case). In the present paper, a nominal observer for the actuator states is driven by a (fictitious) momentum error estimate. ∗ Mechanical Engineering Department, Wichita State Univer- sity, 1845 N. Fairmount, Wichita, KS 67260, USA; e-mail: sricnu@gmail.com ∗∗ Mechanical Engineering Department; Wichita State Univer- sity; 1845 N. Fairmount, Wichita, KS 67260, USA; e-mail: brian.driessen@wichita.edu Recommended by Dr. S. Alavandar

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