Optimal control of differentially flat underactuated planar robots in the perspective of oscillation mitigation

TL;DR

This paper explores using optimal control combined with differential flatness to enhance trajectory tracking and reduce oscillations in underactuated planar robots, especially considering passive joint dynamics and robustness to parameter variations.

Contribution

It demonstrates that optimal control of flat variables can minimize control effort and potential energy, improving robustness and oscillation mitigation in underactuated robots.

Findings

Optimal control improves trajectory tracking accuracy.

Minimizing potential energy enhances robustness against stiffness and damping variations.

Numerical simulations validate the effectiveness of the proposed approach.

Abstract

Underactuated robots are characterized by a larger number of degrees of freedom than actuators and if they are designed with a specific mass distribution, they can be controlled by means of differential flatness theory. This structural property enables the development of lightweight and cost-effective robotic systems with enhanced dexterity. However, a key challenge lies in managing the passive joints, whose control demands precise and comprehensive dynamic modeling of the system. To simplify dynamic models, particularly for low-speed trajectories, friction is often neglected. While this assumption simplifies analysis and control design, it introduces residual oscillations of the end-effector about the target position. In this paper, the possibility of using optimal control along with differential flatness control is investigated to improve the tracking of the planned trajectories. First, the study was carried out through formal analysis, and then, it was validated by means of numerical simulations. Results highlight that optimal control can be used to plan the flat variables considering different (quadratic) performance indices: control effort, i.e. motor torque, and potential energy of the considered underactuated joint. Moreover, the minimization of potential energy can be used to design motion laws that are robust against variation of the stiffness and damping of the underactuated joint, thus reducing oscillations in the case of stiffness/damping mismatch.