Autonomous $\$20$ Drone via Pose Estimation Core-sets

In the pose-estimation problem we need to align a set of n markers (points in 3D space) and choose one of their n! permutations, so that the sum of squared corresponding distances to another ordered set of n markers is minimized. We prove that every set has a weighted subset (core-set) of constant size (independent of n), such that computing the optimal orientation of the small core-set would yield exactly the same result as using the full set of n markers. A deterministic algorithm for computing this core-set in O(n) time is provided, using the Caratheodory Theorem from computational geometry. We can then boost the performance of inefficient algorithms or popular heuristics (such as ICP) by running them (maybe many times) on our small coreset. Based on this coreset, we developed a low-cost (< $100) real-time tracking system. As an example application, we turn a toy quadcopter (< $20) with no sensors into an “autonomous drone” that is controlled by a mini-computer (< $30). Experimental results show that, unlike uniform sampling of features, our suggested coreset yields error that is comparable to commercial (> $10, 000) tracking systems for such simple but common applications. Open source code is provided [1].