Reachability Analysis of Rigid-Body Rotational Dynamics Under Parametric Uncertainty Using Sensitivity-Based Lipschitz Bounds

Kurzfassung

The rise of orbital debris demands autonomous proximity operations with uncooperative targets with uncertain orientation and inertia. This work proposes a reachability analysis framework for orientation dynamics on the Lie group SO(3) under parametric uncertainty. The method integrates sensitivity equations to compute exact flow Jacobians, enabling numerical estimates of the Lipschitz constant to characterize local trajectory expansion. The resulting reachable-sets over-approximations are provably correct up to the estimation error on the Lipschitz constant, avoiding the rapid bound inflation typical of classical conservative methods -- particularly challenging on compact spaces like SO(3) where they can cover the entire domain over short time horizons. Tightness increases as the inter-sample distance decreases, a refinement achievable with minimal runtime impact through GPU-based parallelization. Validation on two ENVISAT case studies with uncertain inertia matrices shows stable Lipschitz estimates, accurate reachable-set characterization, and robustness over long horizons, demonstrating suitability for real-time analysis of tumbling rigid bodies in orbit.