Integrated control‐structure co‐design for flexible manipulators

Abstract

This work aims to develop a methodology for the integrated control‐structure design of flexible multibody systems. Such an issue is linked to a generalization of the inverse dynamics problem, where both the feedforward control and mechanical parameters are designed to perform a desired trajectory optimally. The resulting constrained motion is aimed at improving the dynamic performance of the system, which is underactuated, with less power demand but possible elastic deformation. Stable inversion methods are required to deal with the internal dynamics related to underactuation. The proposed methodology is based on the optimal control theory. For illustrative purposes, we considered a fully actuated linear time‐invariant (LTI) system, establishing the integrated design results in a least‐squares homogeneous system and in an optimization problem. An additional formulation is proposed for the integrated design of the flexible multibody systems, where both a multi‐criterion optimization and a scalarized problem of a corresponding nonlinear programming problem are formulated to deal with the unstable zero‐dynamics related to non‐minimum phase systems and nonlinearity. The numerical simulation of an underactuated two‐masses‐spring‐damper system and a flexible robotic manipulator in planar motions are used for validation. Finally, the beneficial aspects of the integrated design are analyzed.