Continuous UAV Trajectory Design with Uncertain User Location in ISAC Networks

Unmanned aerial vehicles (UAVs), also known as drones, have already been widely used in wireless networks. UAV-assisted integrated communication and sensing (ISAC) networks are feasible solutions to many challenging scenarios in which ground users (GUs) are inaccessible by terrestrial networks. However, the uncertainty of GU's locations undermines the performance of UAV-assisted networks, especially for UAV trajectory designs. To tackle this issue, we formulate this optimal UAV trajectory design problem to a catenary shape determination problem, which transforms the objective of maximizing the overall performance to that of minimizing the potential of the catenary. In the proposed scheme, an arbitrary partial distribution of GU's locations is represented by a matter with areal mass density in an artificial potential field (APF). To obtain an optimal solution, we derive a second-order mechanical equation representing the shape of this catenary, by analyzing its static equilibrium state when achieving minimal potential. Different from conventional path discretization methods, the obtained trajectory solution in this paper is a continuous-form second-order equation with remarkable path compression. The numerical results show that, when compared to conventional UAV trajectory optimization methods, the proposed approach can achieve an optimal solution of UAV trajectory with low computational complexity. It further demonstrates that the proposed approach can flexibly and continuously adjust the UAV trajectory under the scenario of uncertain GU's locations.