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 feedback linearization, followed by structural optimization of the zero dynamics. Inspired by recent works on the control-oriented design of multibody systems, we define a simulation-based optimization problem where the response of the mechanism is shaped through relevant structural parameters. In particular, adjusting the stiffness and the mass distribution of the system, we match the periodic reference with a specific orbit of the zero dynamics, while also penalizing the linearizing input. With the adoption of the proposed strategy, we show that it is possible to reach a desirable trade-off between input energy reduction and periodic motion accuracy. Once an optimal trajectory of the zero dynamics is found, the control design is completed with established orbital stabilization techniques, ensuring a robust oscillatory behavior.