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In this paper, we analyze the effect of time delay dynamics on controllerdesign for Unmanned Aerial Vehicles (UAVs) with vision based navigation. Timedelay is an inevitable phenomenon in cyber-physical systems, and has importantimplications on controller design and trajectory generation for UAVs. Theimpact of time delay on UAV dynamics increases with the use of the slowervision based navigation stack. We show that the existing models in theliterature, which exclude time delay, are unsuitable for controller tuningsince a trivial solution for minimizing an error cost functional always exists.The trivial solution that we identify suggests use of infinite controller gainsto achieve optimal performance, which contradicts practical findings. We avoidsuch shortcomings by introducing a novel nonlinear time delay model for UAVs,and then obtain a set of linear decoupled models corresponding to each of theUAV control loops. The cost functional of the linearized time delay model ofangular and altitude dynamics is analyzed, and in contrast to the delay-freemodels, we show the existence of finite optimal controller parameters. Due tothe use of time delay models, we experimentally show that the proposed modelaccurately represents system stability limits. Due to time delay consideration,we achieved a tracking results of RMSE 5.01 cm when tracking a lemniscatetrajectory with a peak velocity of 2.09 m/s using visual odometry (VO) basedUAV navigation, which is on par with the state-of-the-art.

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