Global adaptive partial state feedback tracking control of rigid-link flexible-joint robots

Abstract

This paper presents a solution to the global adaptive partial state feedback control problem for rigid-link, flexible-joint (RLFJ) robots. The proposed tracking controller adapts for parametric uncertainty throughout the entire mechanical system while only requiring link and actuator position measurements. A nonlinear filter is employed to eliminate the need for link velocity measurements while a set of linear filters is utilized to eliminate the need for actuator velocity measurements. A backstepping control strategy is utilized to illustrate global asymptotic link position tracking. An output feedback controller that adapts for parametric uncertainty in the link dynamics of the robot manipulator is presented as an extension. Experimental results are provided as verification of the proposed controller.

A Survey on the Control of Flexible Joint Robots

“…It was proven in [91] that using this filter would preserve the global asymptotic stability which is one of the required specifications. The same idea (using a filter instead of rate measurement) was employed in an adaptive controller in [90,92]. In [90], to estimate link velocity from link position, a filter was used and, in order to estimate motor velocity from other states (which are motor position, link position and applied torque), an adaptive estimator was employed.…”

Dynamic surface controller for flexible joint robots without velocity measurements

“…Assumption 1: The system states q and q m are only available for feedback, that is, the outputs of the FJ robot system are q and q m . [2,4,6]. In Assumption 3, ω 1 does not mean a tight upper bound for q , that is, any upper bound does.…”

“…In [5], an adaptive partial state feedback controller for FJ robots without velocity measurements was designed via an integrator backstepping procedure. Dixon et al [6] suggested the global adaptive partial state feedback tracking controller for FJ robots using the backstepping technique. However, the backstepping algorithm has the "explosion of complexity" problem which is caused by the repeated differentiations of virtual controllers [7,8].…”

Bounded backstepping control and robustness analysis for time-varying systems under converging-input-converging-state conditions

“…This paper continues our group's quest (begun in [12], [13], [14], [15], [18], and [19]) for novel backstepping results that help overcome the obstacles to using classical backstepping; see [8] and [10] for traditional backstepping. Classical backstepping entails synthesizing globally asymptotically stabilizing feedback controls, by recursively building globally asymptotically stabilizing controls and corresponding Lyapunov functions for subsystems; see [5], [7], [8], and [11] for improved backstepping theory that can include nonlinearities and uncertainties, and see [2], [3], and [4] for backstepping applied to adaptive, aerospace, and robotic systems. However, there are significant instances that call for backstepping but where the existing backstepping literature does not apply, e.g., systems with general nonlinear subsystems where there are bounds on the allowable sup norms of the controls, which produce challenges that we overcome in this work.…”