Analysis of the Effect of Time Delay for Unmanned Aerial Vehicles with Applications to Vision Based Navigation

In this paper, we analyze the effect of time delay dynamics on controller design for Unmanned Aerial Vehicles (UAVs) with vision based navigation. Time delay is an inevitable phenomenon in cyber-physical systems, and has important implications on controller design and trajectory generation for UAVs. The impact of time delay on UAV dynamics increases with the use of the slower vision based navigation stack. We show that the existing models in the literature, which exclude time delay, are unsuitable for controller tuning since a trivial solution for minimizing an error cost functional always exists. The trivial solution that we identify suggests use of infinite controller gains to achieve optimal performance, which contradicts practical findings. We avoid such shortcomings by introducing a novel nonlinear time delay model for UAVs, and then obtain a set of linear decoupled models corresponding to each of the UAV control loops. The cost functional of the linearized time delay model of angular and altitude dynamics is analyzed, and in contrast to the delay-free models, we show the existence of finite optimal controller parameters. Due to the use of time delay models, we experimentally show that the proposed model accurately represents system stability limits. Due to time delay consideration, we achieved a tracking results of RMSE 5.01 cm when tracking a lemniscate trajectory with a peak velocity of 2.09 m/s using visual odometry (VO) based UAV navigation, which is on par with the state-of-the-art.