An algebraic solution for tracking Bernoulli’s lemniscate flight trajectory in airborne wind energy systems

In this paper we present a method to greatly enhance the computing performance of kinematic controllers responsible of defining the direction a power kite of an airborne wind energy system should fly to in order to track a Bernoulli's lemniscate trajectory. The method employs the orthogonal trajectories of the Cassini ovals, allowing for the algebraic computation of the kite velocity reference. The advantage of the proposed approach when compared to numerical methods found in the literature is the reduction in the computational load by two orders of magnitude. Also, the proposed solution could be promptly used in virtually any other application where Bernoulli's lemniscate should be tracked by a moving object. The effectiveness of the proposed method is demonstrated by computer simulation results.