Hybrid Feedback Control for Global Navigation with Locally Optimal Obstacle Avoidance in n-Dimensional Spaces

We present a hybrid feedback control framework for autonomous robot navigation in n-dimensional Euclidean spaces cluttered with spherical obstacles. The proposed approach ensures safe navigation and global asymptotic stability (GAS) of the target location by dynamically switching between two operational modes: motion-to-destination and locally optimal obstacle-avoidance. It produces continuous velocity inputs, ensures collision-free trajectories and generates locally optimal obstacle avoidance maneuvers. Unlike existing methods, the proposed framework is compatible with range sensors, enabling navigation in both a priori known and unknown environments. Extensive simulations in 2D and 3D settings, complemented by experimental validation on a TurtleBot 4 platform, confirm the efficacy and robustness of the approach. Our results demonstrate shorter paths and smoother trajectories compared to state-of-the-art methods, while maintaining computational efficiency and real-world feasibility.