Energy Shaping Control in Underactuated Robot Systems With Underactuation Degree Two

Stabilizing a 6DOF underactuated mechanical system (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbb {R}^{3} \times SO(3)$</tex-math></inline-formula>) 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.