To be able to play soccer, a robot needs a good estimate of its current position on the field. Ideally, multiple features are visible that have known locations. By applying trigonometry we can estimate the viewpoint from where this observation was actually made. Given that the Nao robots of the Standard Platform League have quite a limited field of view, a given camera frame typically only allows for one or two points to be recognized. In this paper we propose a method for determining the (x, y) coordinates on the field and the height h of the camera from the geometry of a simplified tetrahedron. This configuration is formed by two observed points on the ground plane plus the gravitational direction. When the distance between the two points is known, and the directions to the points plus the gravitational direction are measured, all dimensions of the tetrahedron can be determined. By performing these calculations with rational trigonometry instead of classical trigonometry, the computations turn out to be 28.7% faster, with equal numerical accuracy. The position of the head of the Nao can also be externally measured with the OptiTrack system. The difference between externally measured and internally predicted position from sensor data gives us mean absolute errors in the 3-6 centimeters range, when we estimated the gravitational direction from the vanishing point of the outer edges of the goal posts.

Sitting in New York City, looking up at the clear June skies, I wonder if I am staring at an endangered phenomena. According to many in the Unmanned Aircraft Systems (UAS) industry, skylines across the country soon will be filled with flying cars, quadcopter deliveries, emergency drones, and other robo-flyers. Moving one step closer to this mechanically-induced hazy future, General Electric (GE) announced last week the launch of AiRXOS, a "next generation unmanned traffic" management system. Managing the National Airspace is already a political football with the Trump Administration proposing privatizing the air-control division of the Federal Aviation Administration (FAA), taking its controller workforce of 15,000 off the government's books. The White House argues that this would enable the FAA to modernize and adopt "NextGen" technologies to speed commercial air travel.