We present methods for efficiently maintaining human head orientation using low-cost MEMS sensors. We particularly address gyroscope integration and compensation of dead reckoning errors using gravity and magnetic fields. Although these problems have been well-studied, our performance criteria are particularly tuned to optimize user experience while tracking head movement in the Oculus Rift Development Kit, which is the most widely used virtual reality headset to date. We also present novel predictive tracking methods that dramatically reduce effective latency (time lag), which further improves the user experience. Experimental results are shown, along with ongoing research on positional tracking.

For the task of transferring a group of robots from one formation to another on a connected graph with unit edge lengths, we provide an efficient hierarchical algorithm that can complete goal assignment and path planning for 10,000 robots on a 250,000 vertex grid in under one second. In the extreme, our algorithm can handle up to one million robots on a grid with one billion vertices in approximately 30 minutes. Perhaps more importantly, we prove that with high probability, the algorithm supplies paths with total distance within a constant multiple of the optimal total distance. Furthermore, our hierarchical method also allows these paths to be scheduled with a tight completion time guarantee. In practice, our implementation yields a total path distance less than two times of the true optimum and a much shorter completion time.

This paper considers a robot that moves in a plane and is only able to sense the distance order of landmarks with respect to its current position. The robot has no access to either metric information about the location of landmarks and its own position, or to odometry or speed controls. We propose several algorithms for the robot that allow it to navigate to certain points in the plane and to learn global information about the landmark locations. We, furthermore, demonstrate example tasks, such as convex hull computation, that can be performed using this information.

This paper defines and analyzes a simple robot with local sensors that moves in an unknown polygonal environment. The robot can execute wall-following motions and can traverse the interior of the environment only when following parallel to an edge. The robot has no global sensors that would allow precise mapping or localization. Special information spaces are introduced for this particular model. Using these, strategies are presented to solve several tasks: 1) counting vertices, 2) computing the path winding number, 3) learning a combinatorial map, which is called the cut ordering, that encodes partial geometric information, and 4) solving pursuit-evasion problems.