My PhD research addresses three interconnected challenges in mobile robot navigation: (a) navigating nontrivially shaped narrow passages, (b) ensuring robust collision avoidance under uncertainty, and (c) achieving computational efficiency for practical MPC deployment. The proposed solution comprises three complementary components: (a) dense point-cloud representations with critical point selection for complex environments, (b) ellipsoidal uncertainty bounding combined with state-feedback policies for robustness, and (c) zero-order optimization of uncertainty sets and heuristic optimization of feedback policies for real-time feasibility. Comprehensive numerical studies demonstrate the computational efficiency of the proposed solution. Extensive real-world experiments highlight its effectiveness for robust collision-free navigation of industrial mobile robots in confined spaces.