Robotic automation and unsupervised cluster assisted modeling for solving the forward and reverse design problem of paper airplanes

Although often regarded a childhood toy, the design of paper airplanes is subtly complex. The design space and mapping from geometry to distance flown is highly nonlinear and probabilistic where a single airplane design exhibits a multitude of trajectory forms and flight distances. This makes optimization and understanding of their behavior challenging for humans. By understanding the behavior of paper airplanes and predicting flight behavior, there is a potential to improve the design of aerial vehicles that operate at low Reynolds numbers. By developing a robotic system that can fabricate, test, analyze, and model the flight behavior in an unsupervised fashion, a wide design space can be reliably characterized. We find there are discrete behavioral groups that result in different trajectories: nose dive, glide, and recovery glide. Informed by this characterization we propose a method of using Gaussian mixture models to extract the clusters of the design space that map to these different behaviors. This allows us to solve both the forward and reverse design problem for paper airplanes, and also to perform efficient optimization of the geometry for a given target flight distance.