Parameterizing robust manipulator controllers under approximate inverse dynamics: A double-Youla approach

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.