3D Smooth Trajectory Planning for UAVs under Navigation Relayed by Multiple Stations Using Bézier Curves

Navigation relayed by multiple stations (NRMS) is a promising technique that can significantly extend the operational range of unmanned aerial vehicles (UAVs) and hence facilitate the execution of long-range tasks. However, NRMS employs multiple external stations in sequence to guide a UAV to its destination, introducing additional variables and constraints for UAV trajectory planning. This paper investigates the trajectory planning problem for a UAV under NRMS from its initial location to a pre-determined destination while maintaining a connection with one of the stations for safety reasons. Instead of line segments used in prior studies, a piecewise Bézier curve is applied to represent a smooth trajectory in three-dimensional (3D) continuous space, which brings both benefits and complexity. This problem is a bi-level optimisation problem consisting of upper-level station routing and lower-level UAV trajectory planning. A station sequence must be obtained first to construct a flight corridor for UAV trajectory planning while the planned trajectory evaluates it. To tackle this challenging bi-level optimisation problem, a novel efficient decoupling framework is proposed. First, the upper-level sub-problem is solved by leveraging techniques from graph theory to obtain an approximate station sequence. Then, an alternative minimisation-based algorithm is presented to address the non-linear and non-convex UAV trajectory planning sub-problem by optimising the spatial and temporal parameters of the piecewise Bézier curve iteratively. Computational experiments demonstrate the efficiency of the proposed decoupling framework and the quality of the obtained approximate station sequence. Additionally, the alternative minimisation-based algorithm is shown to outperform other non-linear optimisation methods in finding a better trajectory for the UAV within the given computational time.