Parameterizing robust manipulator controllers under approximate inverse dynamics: A double‐Youla approach. (28th July 2019)

• Record Type: Journal Article
• Authors: Friedrich, Stefan R.; Buss, Martin
• Other Names: Quevedo Daniel E. guestEditor.; Chatterjee Debasish guestEditor.
• Is Part Of: International journal of robust and nonlinear control. Volume 29:Number 15(2019)
• Page Start: 5137
• Page End: 5163
• Publication Date: 2019-07-28
• Subjects: approximate inverse dynamics -- dual‐Youla parameterization -- robust robot manipulator control -- robust/adaptive control -- uncertainty quantification; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.4671
• Languages: English
• ISSNs: 1049-8923

Abstract

Summary: We consider the goal of ensuring robust stability when a given manipulator feedback control law is modified online, for example, to safely improve the performance by a learning module. To this end, the factorization approach is applied to both the plant and controller models to characterize robustly stabilizing controllers for rigid‐body manipulators under approximate inverse dynamics control. Outer‐loop controllers to stabilize the nonlinear uncertain loop that results from approximate inverse dynamics are often derived by lumping uncertainty in a single term and subsequent analysis of the error system. Here, by contrast, the well‐known norm bounds of these uncertain dynamics are first recast into a generalized plant configuration that preserves the characteristic uncertainty structure. Then, the overall loop uncertainty is expressed with respect to the nominal outer‐loop feedback controller by means of an uncertain dual‐Youla operator. Therefore, using the dual‐Youla parameterization, we provide a novel way to rigorously quantify permissible perturbations of robot manipulator feedforward/feedback controllers. The method proposed in this paper does not constitute another robust control law for rigid‐body manipulators, but rather a characterization of a set of robustly stabilizing controllers. The resulting double‐Youla parameterization for the control of robot manipulators is amenable to numerous advanced design methods. The result is thoroughly discussed by a planar elbow manipulator and exemplified with a six‐degree‐of‐freedom robot scenario with varying payload.