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About

Apurva Mudgal’s research lies at the intersection of robotics, algorithm design, and computational geometry, with a primary focus on robot navigation and localization under uncertainty. His most influential work addresses the fundamental challenge of how a robot can efficiently determine its location—the “kidnapped robot problem”—where a robot with a compass and map must identify its position while minimizing travel cost. Mudgal proved that this problem is NP-hard to approximate within a factor of \(c \log n\), and he developed near-tight approximation algorithms that provide both lower bounds and practical solutions. His contributions extend to analyzing greedy navigation heuristics, including D*, a widely used planning method in Mars rover prototypes and Nomad-class robots. Notably, he derived nearly sharp bounds of \(\Omega(n \log n / \log \log n)\) and \(O(n \log n)\) on travel cost for these heuristics, offering theoretical grounding for real-world robotic systems. With over 35 citations across his most-cited papers, Mudgal’s work provides essential theoretical frameworks that inform both algorithm design and autonomous navigation in unknown environments.