Periodic Motion Optimization for an Underactuated Mechanical System through Synergistic Structure-Control Design

In this work, we present the integrated structure-control design of a 2-DOF underactuated mechanical system, aiming to achieve a periodic motion of the end-effector. The desired behavior is generated via input-output linearization, followed by structural optimization of the zero dynamics. Inspired by recent works on the control-oriented design of multibody systems, we define an optimization problem based on the simulation of the system's response. In particular, relevant model parameters are used to match the reference with a specific orbit of the zero dynamics, while also penalizing the input energy. For the considered application, the selected parameters are related to the mechanism's elasticities and mass distribution. Notably, we show that it is possible to reach a desirable trade-off between mass reduction and periodic motion accuracy. With an optimal zero dynamics response available, the control scheme can be completed with established orbital stabilization techniques, ensuring a robust oscillating behavior.