Global Adaptive Partial State Feedback Tracking Control of Rigid-Link Flexible-Joint Robots
Introduction
Due to the elastic nature in which some gearing mechanisms (i.e., harmonic drives, belts, long shafts, etc.) transmit torque to the robot links, it is a widely accepted fact that the inclusion of joint flexibility in the dynamics for robot manipulators yields a more accurate model. In addition, the model for a rigid-link flexible-joint (RLFJ) robot includes uncertain parameters (i.e. stiffness effects); hence, controllers that can account for the parametric uncertainty seem highly desirable.. Furthermore, from an implementation point of view, it is desirable that controllers be designed to require fewer measurements (i.e., due to the increased cost, complexity, and/or noise that additional sensors add to the system).For some background on the design of controllers for rigid-link (RL) robot manipulators without link velocity measurements, the reader is referred to [5] and the references therein. With regard to the control of RLFJ robot manipulators, much of the previous research targeted setpoint control (i.e., see [30],[1], [11], and the references therein); although, current research efforts have targeted the tracking control problem (i.e., see [22], [20], [16], [17], [5], and the references therein). Specifically, in [23], Qu proposed an input-output robust partial state feedback RLFJ tracking controller; however,link velocity measurements are required. Motivated by the desire to eliminate the dependance on velocity measurements, Nicosia and Tomei [20] proposed a semi-global exact model knowledge (EMK) RLFJ tracking controller which only requires link position measurements. In [16], Lim et al. was able to employ a model-based observer approach to eliminate link and actuator velocity measurements to obtain semi-global exponential link position tracking for RLFJ robot manipulators. Moreover, Lim et al. [17], also proposed an adaptive controller for the same problem given in [16]. Recently, solutions to the global output feedback\ tracking control problem were presented by Loria [18] and Zhang et al. [31]. Specifically, the one-degree-of-freedom (DOF) robot manipulator control strategy, proposed in \[18], provided motivation for the global adaptive and robust output feedback tracking controller designs for the n-DOF RL robot manipulator, proposed in [31] and [6]. Based on the nonlinear link velocity filter structure of [31], and a model based observer for actuator position and velocity measurements, a global EMK link position tracking controller for RLFJ robot manipulators was proposed by Dixon et al.[5].
In this paper, we build on the previous work of [16] and [31] to design a global asymptotic link position tracking controller for RLFJ robot manipulators that only requires link and actuator position measurements and adapts parametric uncertainty throughout the entire mechanical system. Specifically, the proposed global adaptive partial state feedback tracking controller utilizes: i) a nonlinear link velocity filter, which is instrumental in eliminating link velocity measurements and maintaining the global stability result, ii) the output feedback control paradigm presented in [13] to eliminate actuator velocity measurements, and iii) the integrator backstepping technique to fuse the two aforementioned, dissimilar techniques together. The paper is organized in a progression from the problem statement to the conclusion. Specifically, section II provides a mathematical model for a n-RLFJ, revolute, direct-drive robot and its associated properties. Section III presents the control objective and control design based on the RLFJ dynamics. Section IV gives the main result of the paper. Section V provides experimental verification of the proposed controller. Finally, some concluding remarks are presented in section VI.
Experimental Configuration
The controller was implemented on a 2-link, direct-drive robot manipulator manufactured by Integrated Motion Inc. The links of the manipulator are directly actuated by switched-reluctance motors which are controlled through NSK torquecontrolled amplifiers. A Pentium 166 MHz PC operating under QNX (a real-time micro-kernel based operating system) hosts the control algorithm. The control algorithm was written in the 'C' programming language and implemented via an in-house graphical user-interface which allows the user to view real-time graphing, log control variables for future comparison, and vary control gains without recompiling the program. Data acquisition and control implementation were performed at a frequency of 2.5kHz using the MultiQ I/O board.
Experimental Results
Also see a movie of the experiment in [1.67 MB .rm format] .
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