The research question that this investigation seeks to answer is whether its possible to localize a drone in two dimensional space using a one dimensional LIDAR or range finder. The investigation has two main aspects; hardware development and integration, and software and simulation. The progress in the software domain will be decribed here.
Firstly we assumed ideal characteristics of the system and developed the infrastructure upon which more advanced techniques can be investigated. This included developing a LIDAR sweep simulation:
A room is defined by \(n\) walls which are linear interpolations between two points. The drone position is defined as a point in the room and the LIDAR rays are computed from this position. A LIDAR sweep is then simulated by rotating the LIDAR by 360 degrees and computing the length of the LIDAR ray from the drone to the wall.
The number of LIDAR hits per revolution will be a characteristic of the system and can be variable ranging from only several points, two hundreds of points. The more points that are gernerated per sweep the more accurate the localization will be. The image above shows the family of curves that are generated as the number of points is swept from 2 to 100. It can be seen that the curves converge to the true value as the number of points increases.