Nonlinear flight physics of the Lie Bracket roll mechanism

In this paper, we review the concept of Lie brackets and how it can be exploited in generating motion in unactuated directions through nonlinear interactions between two or more control inputs. Applying this technique to the airplane flight dynamics near stall, a new rolling mechanism is discovered through nonlinear interactions between the elevator and the aileron control inputs. This mechanism, referred to as the Lie Bracket Roll Augmentation (LIBRA) mechanism, possesses a significantly higher roll control authority near stall compared to the conventional roll mechanism using ailerons only; it produces more than an order-of-magnitude stronger roll motion over the first second. The main contribution of this paper is to study the nonlinear flight physics that lead to this superior performance of the LIBRA mechanism. In fact, the LIBRA performance in free flight (six DOF) is double that in a confined environment of two-DOF roll-pitch dynamics. The natural feedback from the airplane motion (roll, yaw, and sideslip) into the LIBRA mechanism boosts its performance through interesting nonlinear interplay between roll and yaw, while exploiting some of the changes in the airplane characteristics near stall.