# UAV Formation Trajectory Planning Algorithms: A Review
## 5 Local Trajectory Planning Algorithm
### Mathematical Optimization Algorithm  
The mathematical optimization algorithm (MOA) is based on the established UAV trajectory planning model, using nonlinear optimization, mixed integer linear programming (MILP), mixed integer nonlinear programming (MINLP) and dynamic programming (DP) to solve the optimal control problem into an easily solvable model to generate feasible trajectories for formation UAVs. Figure 27 is a mathematical optimization algorithm (MOA) model. [PERSON] et al. [144] proposed CPLEX, which is a collaborative trajectory planning method for UAV formation. This method combines the failure probability of each UAV  
Figure 26: DWA velocity vector space diagram. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Reference** & **Challenge** & **Optimization Criteria** & **Method** & **Dimension** \\ \hline C. [PERSON] et al. [131] & UAV clustering & Distributed, UAV communication & AFF & 3D \\ [PERSON] et al. [132] & UAV & Constrain virtual leads & AFF + Dubins & 2D \\ [PERSON] et al. [133] & UAV clustering, Trajectory & Climb strategy, Dynamic step size & AFF & 3D \\ [PERSON] et al. [134] & Trajectory & Judging mechanism, 90\% jump mechanism & IAPF & 3D \\ [PERSON] et al. [135] & Trajectory & Improve the model, Target exchange, Add constraints & AFF & 3D \\ [PERSON]. [PERSON] and [PERSON] [136] & Trajectory, UAV clustering & Improved function, Dynamic step size & IAPF & 3D \\ [PERSON] et al. [137] & Environment, UAV clustering & Communication topology, Coordination gain, & IAPF & 3D \\ [PERSON] et al. [138] & Trajectory, UAV clustering & \
\begin{tabular}{c} Impact factor \\ \end{tabular} & IAPF & 3D \\ [PERSON] et al. [139] & Trajectory, UAV clustering & Second-order model, Consistency theory & IAPF & 3D \\ [PERSON] et al. [140] & Environment &
\begin{tabular}{c} Improved time variation \\ \end{tabular} & IAPF + MPC & 2D \\ [PERSON] et al. [142] & Trajectory & Impact factor, Auxiliary force & IAPF & 3D \\ [PERSON]. [PERSON] et al. [141] & Trajectory & Rotational potential field, Leader–Follow & IAPF & 3D \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Summary of the methods of artificial potential field in the survey. with the selected task and puts forward a new formula to solve the problem of mission failure caused by UAV loss in UAV formation trajectory planning. [PERSON] and [PERSON] [145] proposed a method based on polygonal area decomposition and efficient coverage (PADEC). This method introduces the concepts of regional division and computational scanning into the UAV formation coverage trajectory planning and solves the problem of multi-UAV cooperative search. [PERSON] et al. [146] proposed a trajectory planning method based on multi-UAV for RF source localization. The method combines the differential received signal strength indicator (DRSSI) method, the extended Kalman filter (EKF) and the Cramer-Rao lower bound (CRLB) objective function; finally, using the local value of the CRLB in the current waypoint and the next possible waypoint to determine the optimal trajectory, it solves the problem of slow convergence of the heuristic algorithm. [PERSON] et al. [147] proposed a decoupled sequence convex programming (SCP) collaborative trajectory planning method for UAV formations. This method represents the UAV formation trajectory planning problem as a non-convex optimal control problem; then, it uses the decoupled sequence convex programming (SCP) method to parameterize the problem into a non-convex programming sub-problem and solves it in parallel to obtain the UAV best trajectory for formation coordination tasks. The problem of insufficient efficiency of the sequence quadratic programming algorithm (SQP) in UAV formation cooperative trajectory planning is solved. [PERSON] et al. [148] proposed an algorithm for multi-UAV trajectory planning under heterogeneous Global Navigation Satellite System (GNSS) coverage.