Fully decoupled reduced dynamics and globally exponentially stable tracking control of floating-base robots

The dynamic coupling in floating-base robots leads to nonlinear, high-dimensional models that significantly complicate dynamic analysis and tracking controller design. This paper develops a geometric mechanics framework that yields a fully decoupled, reduced dynamic model and a globally exponentially stable joint tracking controller. By formulating the system on a principal bundle, we propose a shaping map and exploit a zero-momentum constraint to derive a fully decoupled, minimal-order model on the reduced phase space preserving the intrinsic geometric structures and momentum constraint. The model analytically eliminates the residual base vehicle velocity-dependent Coriolis and Centrifugal (CC) terms in prior inertially decoupled formulations, yielding reduced nonlinearity and complete independence from the base vehicle states. Based on this model, a tracking controller is synthesized with the Controlled Lagrangian (CL) method. This controller guarantees globally exponentially stable joint tracking control and physically interpretable tuning, while requiring no real-time feedback of base vehicle states. Numerical simulations on a free-floating space robot validate the proposed dynamic modeling and control framework. The results demonstrate high-performance tracking control and rigorous preservation of physical constraints and intrinsic geometric structures.