Hybrid Path-Lifting Algorithm and Equivalence of Stability Results for MRP-Based Control Strategies

This article proposes an innovative hybrid dynamic mechanism to uniquely and robustly lift a path from the 3-D special orthogonal group to the modified Rodrigues parameters (MRP) space. The path-lifting mechanism leverages the unique properties of the MRP representation and is crucial for developing a novel framework for the equivalence of stability results between these topological spaces. The new hybrid methodology allows the design and analysis of an attitude feedback controller in the topologically less complex MRP space with the guarantee that its asymptotic and exponential stability properties directly translate to the attitude dynamics in the base space. Furthermore, the resulting interconnection is impervious to the unwinding phenomenon. The design and evaluation of an MRP-based controller demonstrate the application, practical relevance, and advantages of the proposed algorithm alongside the novel results for equivalence of stability between spaces. The solution renders the attitude space dynamics robustly globally asymptotically stable and robustly semi-globally exponentially stable, illustrating the potential of this novel approach.