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The modified Rodrigues parameters (MRP) consist of two numerically differenttriplets that, by switching between them, yield a minimal globally non-singularattitude description with advantageous properties. The MRP space results fromthe Alexandroff compactification of the three-dimensional Euclidean space andis a double cover of $\mathrm{SO(3)}$. By capitalizing on instrumentalproperties of the covering map, this paper proposes a novel hybrid dynamicpath-lifting mechanism to unambiguously and robustly extract the MRP from theattitude space. This hybrid solution allows applying an MRP-based feedbackcontroller to the attitude dynamics in the base space while preserving itsasymptotic and exponential stability properties. Furthermore, by profiting fromthe distinct characteristics of the MRP, the resulting interconnection isimpervious to the unwinding phenomenon. The design and validation of anMRP-based controller exemplify the application of the proposed algorithmalongside the novel results for equivalence of stability between spaces. Thesolution renders the attitude space tracking dynamics robustly globallyexponentially stable, demonstrating the potential of this novel methodology.

Hybrid path-lifting algorithm and Equivalence of Stability results for MRP-based control strategies