Lie-Algebraic Approach to Geometric Nonlinear H∞ Inverse Optimal Attitude Tracking on SO(3)

초록

This letter presents a geometric nonlinear H-infinity inverse optimal attitude tracking framework formulated on SO(3) using its Lie algebra so(3). By adopting exponential coordinates xi is an element of so(3), attitude errors are mapped directly onto the Lie algebra. This preserves a bijective, distortion-free relationship with the geodesic distance within the injectivity radius (parallel to xi parallel to < pi), while eliminating singularities and unwinding issues inherent in Euler angles and quaternions. A sliding-mode-inspired nonlinear H-infinity controller is developed, with robust stability established using the exponential coordinates and a systematic tuning methodology provided to facilitate practical implementation. Quadrotor simulations demonstrate faster convergence in large-angle maneuvers by mitigating the vanishing error and sluggish response of conventional methods. Experiments on a robotic manipulator validate the tuning rule for the prescribed disturbance attenuation level gamma, showing that the peak tracking error scales as O(gamma(2)) for small gains and O(gamma) for large gains. These results demonstrate the robustness and predictability of the proposed framework and the effectiveness of Lie algebra-based attitude control on SO(3).

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