## 9 Conclusions  
All in all, we have thoroughly reviewed the trajectory planning problem in the paradigm of plan-based control for multirotor aerial vehicles (MAVs). Such a trajectory planning problem was broken down into a set of subproblems: free-space segmentation, motion model selection, initial waypoints identification, initial trajectory generation, continuous trajectory refinement, and receding horizon trajectory planning. Afterwards, for each subproblem, we examined how previous research has addressed those by presenting and evaluating various approaches to the considered subproblem. Finally, several selected recent approaches were listed (Table 3) according to the listed subproblems we have identified. Furthermore, Table 4 summarizes the key findings of the study, including features and performance. With that, we concluded that the trajectory planning problem can be designed by addressing those subproblems carefully for MAVs. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Approach** & **Gust 1** & **Topological Differential** & **Intermediate Wavepoint** & **Initial Trajectory Generation** & **Continuation Trajectory** & **Free Space Extraction** & **Receding Horizon Planning on** \\  & **Headings Off** & **Selection** & & & **Refinement and Subver** & **Controlling** & **Controlling** \\ \hline A _nplanner_[12] & DF & Sampling-based biological search & FCO-based 8-planes & GTO & ESOF & - \\ \hline A _nplanner_[23] & DF & Knowdynamic-based search & B-splines & LO using QCQP & ESOF & - \\ \hline A _nplanner_[10] & DF & Knowdynamic-based search & Linear quadratic minimum & Unconstrained QP & [132] & BMC \\ \hline A _nplanner_[10] & DF & Knowdynamic-based search & Linear quadratic minimum & BMC & ESOF & - \\ \hline A local inference [7] & DF & Informed-based & -Continuous time polynomial & BMCs & ESOF & - \\ \hline \multicolumn{1}{c}{Technology-region update} [4] & DF & Maximum-path & Elastic band optimization & Convex Cluster & - \\ \hline Fast parameter [5] & DF & A’s/Innov dynamic search & B-splines & NLopt [133] & ESOF & CTC \\ \hline Arplanner [21] & DF & B-spline/Innov dynamic search & BO & \(-\)QCQP & TSOF & - \\ \hline ACO-Comp [134] & DF & - & CIRMP & Functional gradient [132] & ESOF & CIRMP \\ \hline ECO-Comp [134] & DF & A* & Uniform-Bspline & T-NNVV [135] & ESOF & - \\ \hline A _nplanner_[23] & DF & Fast matching-based search & Bernstein polynomial & Monst [134] & ISOF & - \\ \hline A _nstst_ trajectory geometry [23] & DF & RBC combined with A* & Free-step polynomials & QCQP & KD-wave & CTC \\ \hline \multicolumn{1}{c}{\(\{\)IDQ[9]\(\}\)} & Exact & line search & Inbound IQQ Smoothing & Branch [100 Smoothing & - & - \\ \hline Monocular visual-inertial & Exact & A* & VINS & Confinet-based & TSOF & CTC \\ \hline A _nplanner_[7] & DF & BRT* & Uniform-Bspline & MMA and BFCs & OcstMap & GTC \\ \hline Safe flight controls [102] & DF & JPS & Minimum-span & Constrained QP & SIC & BNC \\ \hline SSOMM [103] & Empirical & Power-wise linear path & SSOMM & SSOMM & Constrained QP & - \\ \hline Faster [104] & DF & JPS & Cube Roller convex & MDP using Control [131] & SIC & - \\ \hline GMCC [114] & Empirical & - & CMPC & OSOF [138] & SIC & BNC \\ \hline Relative trajectory tracking & Empirical & - & NLPC & ACADO [124] & - & MHE \\ \hline A _nplanner_[7] & Expected & - & NLPC & SQP & - & BNC \\ \hline A _nplanner_[7] & DF & A* & Multi-agent polynomial & OOQP [14] & OcstMap & CTC \\ \hline Arplanner [135] & Exact & BRT* & Minimum-span & Unconstrained QP & OcstMap & CTC \\ \hline MARE [141] & DF & MINVVbias [124] & Uniform Bspline & Augmented Lagrangian [14] & OcstMap polyhedral & - \\ \hline SOS programming [41] & DF & Power-wise linear path & Place-wise-polynomial & MQP using Monst & BIS & - \\ \hline A _nplanner_[144] & DF & Nonuniform knowledge & Unknown Bspline & Constrained QP & ESOF & BNC \\ \hline A _nplanner_[145] & Empirical & Uniform Bspline & NLPC & CanAD [146] with kept [14] & ISOF & PID \\ \hline \hline \end{tabular}
\end{table}