Energy Shaping Control in Underactuated Robot Systems With Underactuation Degree Two

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Babak Salamat, Gerhard Elsbacher, Andrea M. Tonello

Published: 2025, Last Modified: 02 Mar 2026IEEE Robotics Autom. Lett. 2025EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: Stabilizing a 6DOF underactuated mechanical system ($\mathbb {R}^{3} \times SO(3)$) without a cascade structure while utilizing a full-state feedback controller presents a significant challenge. Furthermore, due to the complexities of its dynamics and the degree of underactuation, designing an energy-shaping controller for such a system has not been done until now. This letter introduces a solution to the potential energy shaping problem for 6DOF underactuated mechanical systems by employing the Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) approach. We extend the solution of partial differential equations (PDEs) from a 2D framework to a comprehensive 3D scenario. Simulation results using a quadrotor as a benchmark example demonstrate its effectiveness.