Robust Global Position and Heading Tracking on SE(3) via Saturated Hybrid Feedback

Abstract

This letter presents a novel control solution to the robust global position and heading tracking problem for underactuated vehicles, equipped with single-axis thrust and full torque actuation, operating under strict, user-defined actuation limits. The architecture features a saturated position tracking controller augmented with two first-order filters. This formulation ensures the boundedness of the first and second derivatives, yielding less conservative bounds and systematically generating bounded attitude references whose limits are easily tuned via design parameters. To track these dynamic references, the inner loop comprises a saturated, modified Rodrigues parameter (MRP)-based controller paired with a hybrid dynamic path-lifting mechanism. This approach allows the attitude tracking law to be designed on a covering space of the configuration manifold. By leveraging a stability equivalence framework, the methodology establishes that the resulting interconnected system achieves robust global asymptotic and semi-global exponential tracking on SE(3), while complying with user-defined input saturation bounds. Numerical simulations validate the proposed solution.