Nonlinear H ∞ Optimal Control for a Free-Floating Space Manipulator with Reaction Wheels under Modeling Uncertainties

This paper presents a case study on a nonlinear ${\mathcal{H}}_{\infty}$ optimal control strategy for a free-floating space manipulator system equipped with reaction wheels. To this end, the system dynamics are reformulated in a reduced form with respect to the active joints, while preserving the structural properties of Euler-Lagrange systems. This structural consistency allows for the direct application of the nonlinear ${\mathcal{H}}_{\infty}$ controller. Furthermore, modeling uncertainties in the inertia matrix are incorporated into the kinematic formulation to ensure accurate mapping between the task-space velocity and the active joint velocity. Simulation studies under load uncertainties at the endeffector and in the presence of active joint frictions confirm the effectiveness of the proposed controller, demonstrating superior performance over a conventional inverse dynamicsbased controller in both base satellite attitude regulation and 6-degrees-of-freedom trajectory tracking tasks.