Building structures can allow a robot to surmount large obstacles, expanding the set of areas it can reach. This paper presents a planning algorithm to automatically determine what structures a construction-capable robot must build in order to traverse its entire environment. Given an environment, a set of building blocks, and a robot capable of building structures, we seek a optimal set of structures (using a minimum number of building blocks) that could be built to make the entire environment traversable with respect to the robots movement capabilities. We show that this problem is NP-Hard, and present a complete, optimal algorithm that solves it using a branch-and-bound strategy. The algorithm runs in exponential time in the worst case, but solves typical problems with practical speed. In hardware experiments, we show that the algorithm solves 3D maps of real indoor environments in about one minute, and that the structures selected by the algorithm allow a robot to traverse the entire environment. An accompanying video is available online at https://youtu.be/B9WM557NP44.
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