Most aircraft are designed to be very good at going upwards, and also not bad at going forwards, with some relatively small amount of thought given to turning left and right. Thanks to gravity, downwards is usually taken care of. Even aircraft designed to hover, like helicopters and quadrotors, have preferential directions of orientation and travel where their particular arrangement of motors and control surfaces makes them most effective. ETH Zurich's Omnicopter goes about flying in a totally different way. With eight motors oriented in all directions, the Omnicopter doesn't have an up or down or front or back: It can translate and rotate in any direction, letting it play a very skilled game of fetch. We have developed a computationally efficient trajectory generator for six degrees-of-freedom multirotor vehicles, i.e. vehicles that can independently control their position and attitude.