Nonlinear Industrial Robot Stabilization Based on Differential Topology

This study presents a nonlinear stabilization framework for industrial robotic systems based on differential topology and geometric control theory. System dynamics are modeled on smooth manifolds, where stabilization is achieved through topological invariants and non-smooth feedback control laws. The approach extends classical nonlinear control by incorporating global geometric structures, enabling stabilization of non-triangular and highly coupled systems. Stability analysis is conducted using global asymptotic and finite-time convergence criteria, supported by Lyapunov-topological equivalence principles. Results demonstrate enhanced robustness, rapid convergence, and strong disturbance rejection capabilities in complex nonlinear robotic systems.