Iterative feedback tuning for optimal repetitive constraint-following control of uncertain mechanical systems using Udwadia-Kalaba theory

This article presents a novel optimal constraint-following controller for uncertain mechanical systems (MSs). The MS's uncertainty is unknown (possibly time-varying) and bounded, but the bound is unspecified. Employing the frame of Udwadia-Kalaba theory, we design a robust controller with two tunable control gains for MSs, which guarantees some deterministic performances. Assuming the constraints to be holonomic and periodic, we transform the controlled MSs and introduce an iterative feedback tuning method for optimizing the proposed controller. After optimization, the final control scheme can achieve the equilibrium between the system performance and control cost for an arbitrary single constraint period. Simulations on a two-link rotational manipulator are provided at last to demonstrate the proposed approach.