A Geometric Mechanics Method for Totally Decoupled Dynamics and Tracking Control of Floating-Base Robots
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Dynamic analysis and control of floating-base robots remain a significant challenge due to the strong, nonlinear dynamic coupling between the manipulator and the base vehicle. This coupling leads to coupled, high-dimensional models and complicates control design, thereby limiting practical applicability. A novel geometric mechanics framework formulated on a principal bundle is proposed to fundamentally addresses this issue. Our core contribution is a complete dynamic decoupling method. First, by constructing a shaping map and under a zero-momentum constraint, a minimal, totally decoupled reduced-order model is derived on the reduced phase space with symmetry reduction. This model analytically decouples the shaping dynamics from all vehicle’s base states. Subsequently, based on this intrinsically decoupled model, a globally exponentially stable tracking controller is designed using the Controlled Lagrangian method. It requires no real-time base-state feedback and admits intuitive performance tuning. Finally, numerical validations on a free-floating space robot demonstrate the effectiveness of the framework and show high-performance tracking control alongside the precise preservation of momentum and geometric structure.
