Global Output Feedback Tracking Control for Rigid-Link Flexible-Joint Robots
Background :
Over the past several years, many researchers have proposed solutions for the output link position tracking control problem for rigid-link (RL) robot manipulators. As indicated by a review of the previously proposed RL OFB tracking controllers (i.e., see [3], [4],[5], [9], [15], [19], [21], [28], and the references therein), it seems that the previous work for this problem was limited in that only semi-global stability results were obtained. In contrast, researchers have been able to obtain global stability results ([2], [6], [10], [18], and [7]) for the RL setpoint control problem. Recently, Loria [17] designed a global output feedback tracking controller for a one degree-of-freedom (DOF) nonlinear system while in [29], Zhang et al. designed an adaptive global OFB tracking controller for n-DOF RL robot manipulators. With regard to partial state feedback control of rigid-link flexible- joint (RLFJ) robot manipulators, several setpoint and tracking controllers have been proposed (see [27], [1], [11], and the references therein for early setpoint control work). In [22], Qu proposed a robust partial state feedback RLFJ tracking controller which only requires measurement of link position and link velocity. In [20], Nicosia and Tomei proposed an exact model knowledge RLFJ controller which only requires link position measurements and delivers semi-global asymptotic link position tracking. Using a model-based observer approach, Lim et al. in [15] eliminated link velocity and actuator velocity measurements in the design of a RLFJ partial state feedback controller which guaranteed semi-global exponential link position tracking. In [16], Lim et al. eliminated link velocity and actuator velocity measurements in the design of an adaptive RLFJ partial state feedback controller which guaranteed semi-global asymptotic link position tracking.
Research Objective:
In this paper, we present a global OFB link position tracking controller for RLFJ robot manipulators which improves upon the previous result presented in [20]. That is, the stability result presented in [20] was semi-global asymptotic link position tracking; however, in contrast, the proposed controller provides global asymptotic link position tracking. The proposed controller achieves the improved stability result through the injection of a nonlinear feedback term, which is coupled to a nonlinear filter, into the link dynamics. This nonlinear feedback/filter action compensates for the lack of velocity measurements and the difference between the actual link dynamics and the injected, desired trajectory-based feedforward term. An observed backstepping procedure is applied to the injected link dynamic control term to design the actuator torque control input.
Simulation Results
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