Swing-Up of Underactuated Compliant Arms via Iterative Learning Control

The swing-up is a classical problem of control theory that has already been widely studied in the literature. Despite that, swinging up an underactuated compliant arm considerably increases the problem complexity. Indeed, in addition to the problem of underactuation, compliant systems usually present also hard-to-model dynamics. Moreover, the control authority of feedback components should be limited to avoid radical alteration of the robot natural elasticity. In this letter, we tackle the swing-up problem of underactuated compliant arms via an Iterative Learning Control approach, proving its convergence. The proposed control law combines feedforward and feedback terms. Tracking the desired trajectory, i.e., bringing the robot up to its vertical equilibrium, is achieved thanks to the feedforward components. Conversely, the feedback of the output signal is used to stabilize the system at the equilibrium point. Additionally, we study the stiffness variation caused by the employed feedback, deriving a condition to preserve the elasticity of the compliant arm. Finally, we validate the proposed method via simulations and experiments underactuated compliant arms with unstable vertical equilibrium varying number of unactuated joints, payload, stiffness, model uncertainties, and noise.