Fair-Energy Trajectory Planning for Multi-Target Positioning Based on Cooperative Unmanned Aerial Vehicles

Owing to the flexibility and low cost, cooperative Unmanned Aerial Vehicles(UAVs) have been attractive in multi-target positioning recently. Although it is popular and easy to accomplish, positioning based on trilateration method still faces challenges under scenarios with multiple UAVs. First, large accumulated errors will be brought if a single UAV is used to perform trilateration on same targets. Second, due to the mobility of targets, the time interval between UAVs performing twice successive distance measurement on one target cannot be long for positioning precision. Finally, the limited energy provided by onboard battery limits the time for UAVs to perform tasks. Once the energy used by some of the UAVs reaches limitation, the whole positioning mission will fail. Thus, to complete the mission of locating multiple targets, this paper is intended to minimize the maximum energy consumption among all UAVs. We formulate the problem, and decompose it into two subproblems, one of which plans the routes for UAV groups and the other plans the routes for UAVs in a group. To solve the first subproblem, a heuristic algorithm called adjusted genetic algorithm (AGA) is proposed to plan trajectories for all UAV groups under constraints on maximum energy consumption. To guarantee stable performance and reduce computation complexity, we propose an approximation algorithm, Tree Decomposition united with Christofides Algorithm (TDCA), and the approximation ratio is proved to be $(3*N'/(2*(N'-1)))$ , where $N'$ denotes the number of UAV groups. For the second subproblem, a two-step greedy heuristic algorithm is proposed to plan trajectories for UAVs in same groups. Extensive simulations show that compared to existing algorithms, the proposed algorithms can reduce up to 26.6% maximum and 26.3% average energy consumption.