Navigation with foraging

We propose and study the navigation with foraging problem, where an agent with a limited sensor range must simultaneously: (1) navigate to a global goal and (2) forage en route as opportunities to forage are detected. Each foraging act causes a deviation from the shortest path to the long-term goal, with consequences for path length, mission duration, and fuel usage. We analytically calculate and/or bound the expected distance the robot actually travels, given the initial distance to the the global goal. In particular, for either of two non-trivial greedy strategies: (A) forage the point that minimizes goal-heading deviation. (B) forage the closest point ahead of the robot. Our results generalize to problems in higher dimensions.