Robust Global Exponential Attitude Tracking on SO(3) via Optimal MRP-Based Hybrid Feedback

This letter presents an innovative robust attitude tracking controller for fully actuated rigid bodies. The approach relies on the modified Rodrigues parameters (MRP) description, which is a double covering of the three-dimensional rotation group SO(3), and the feedback linearization technique to formulate a Lyapunov-based quadratic programming problem. The resulting optimal controller ensures the exponential decay of the attitude tracking errors with minimum control effort and operates within a hybrid system structure to overcome the topological obstructions of the rotation group, rendering the attitude tracking dynamics globally exponentially stable on the MRP space. By combining this MRP-based optimal controller with a hybrid dynamic path-lifting mechanism, this novel approach yields an equivalent tracking result on SO(3). Furthermore, the resulting closed-loop system is nominally robust to perturbations, including external disturbances, parameter variations, or measurement noise. Numerical simulations demonstrate the performance and efficiency of the optimal hybrid strategy.