| Summary: | The constant technological developments recently observed on unmanned aerial vehicles allow its use on diverse activities. With the arrival of new opportunities new challenges arrive as well. Nowadays the navigation methods used is limited to following pre-defined points in space, waypoints, by using the flight parameters values in its control. This work proposes an alternative method, consisting in creating trajectories from 4D waypoints, i.e. three spatial coordinates plus a temporal one. So, it is possible to foresee the path e guarantee that it will be on the desired place at the right time. Because passing through the exact position of a waypoint is rather difficult and not always required, a tolerance is used around it, allowing the passage on the vicinity defined by a sphere whose radius is equal to that tolerance. In this work an algorithm is proposed to find the tridimensional point in the interior of that said sphere which minimizes the path length between the previous and next waypoint. The trajectory is defined interpolating the waypoint coordinates, using a fifth order polynomial function. This way, it is possible to constrain said function in order to create a trajectory whose flight parameters comply with navigation limits associated with the vehicle. By using the limits associated with a small unmanned aerial vehicle, it was possible to create a trajectory defined by 4D waypoints with a consistent behavior and quite smooth. The path chosen is a Racetrack Pattern loiter defined by six waypoints whose time was defined in order to attempt to maintain a constant velocity through the path. The simulation was a successfully performed, being the limits imposed respected through the entire domain of time. Therefore, the possibility of creating 4D waypoint based trajectories is proven, generating a new area of opportunities for time based missions where time plays a critical role, or the shape of the path is crucial.
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