UAV geometry and control

For the general public, a drone is often seen as a self-stabilizing, remote-controlled flying object equipped with a camera. It is also often referred to as an unmanned warplane with a degree of autonomy capable of carrying out military missions. However, a drone is not necessarily flying. It's a mobile robot that can be airborne, terrestrial or underwater, navigating or rolling. A drone can therefore be considered at first glance as a vehicle without a person on board, of any size, with a high degree of autonomy. It is capable of navigating from one point to another, avoiding obstacles and often with a mission to carry out.

Different types of mission can be assigned to a drone, such as mapping an area, transporting a parcel or searching for an underwater wreck. Drones are increasingly used for long, arduous missions, such as agricultural work, cleaning (like vacuuming) or missions that are dangerous to humans (intervention in irradiated areas, searching for people following an avalanche or earthquake). They are indispensable in areas that are inaccessible to humans (deep sea, distant planets, volcanoes, etc.).

One of the challenges facing drones is autonomy. For repetitive tasks requiring precise localization and compliance with specifications, drones will be able to carry out a logical procedure without risk of error, scrupulously obeying the computer program controlling it. What's more, in certain environments, such as the ocean floor or distant planets, teleoperation is almost impossible. These robots must therefore be given the highest possible degree of autonomy. Another challenge is safety. The drone must not be allowed to make any mistakes. We need to be certain that it won't cause a collision, that the robot won't take any risks, and that it won't fail in its mission.

To develop this autonomy, we need a good understanding of the robot's dynamics, so that we can simulate and control it. To achieve this, we need to understand precisely how the robot orients and moves. Non-Euclidean geometry plays a fundamental role in this representation. This article describes the geometric tools associated with UAV movement, and explains how to use these tools to model UAVs cleanly and gradually bring them to full autonomy.