## 9 Conclusions

Table 3: The basic building blocks that are encountered in trajectory planning problems as described in the paper. \begin{table}
\begin{tabular}{c c c c} \hline
**Approach** & **Specific Features** & **Performance Indices** \\ \hline Aspiformer [211] & A path-guided optimization (PCO) approach to address infeasible local minima problems, red limited to a specific one & Computation time (t=15 ms), perform aggressive maneuvers \\ Aspiformer [23] & A dynamically feasible time parameterized trajectory generation to overcome the limitations of the greedy search, not limited to a specific & Computation time (t=30 ms), limited maneuvering capabilities \\ \hline Aspiformer [101] & Samples for smooth, minimum-time trajectories using a set of short-duration motion primitives, and limited to a specific one & Computation time (t=15 ms), limited maneuvering capabilities \\ Touch-dependent-weight [14] & Generate safe local trajectories (smooth, safe, and low-complexity) feasible loop routing strategies, infrastructure inspection, aerial & Computation time (t=15 ms), perform aggressive maneuvers \\  & transportation, and search-and-inference & \\ \hline Fast Planet [119] & Know-dynamic feasible and sometimes more trajectory generation in the shortest-cost space, and limited to a specific one & Computation time (t=30 ms), perform aggressive maneuvers \\ ECO-Planner [134] & A Euclidean signed algorithm defined (SSPC) _for implementation_, we limited to a specific one & Computation time (t=20 ms), perform conservative capabilities \\ \hline ILQR [19] & LQR smoothing to compute a locally optimal feedback control policy, can avoid with nonlinear dynamics and nonquadratic cost, limited & Computation time (t=30 ms), limited maneuvering capabilities \\ \hline Monocular visual-inertial fusion [28] & A monocular visual-inertial navigation system (VINS), consisting only an inertial measurement unit (MM) and a camera, VINS supports an inertial-vehicle collision & Computation time (t=30 ms), limited maneuvering capabilities \\ \hline Safe flight corrid  
Our hypothesis was to investigate trajectory planning for multirotor aerial vehicles (MAVs) in the plan-based control paradigm, focusing on analytical approaches rather than fully learnable approaches, such as machine learning and deep learning. In future work, we plan to investigate other types of trajectory planning approaches, such as those based on imitation learning and inverse reinforcement learning. We also plan to conduct simulated and real-world experiments to compare the performance of the considered approaches in various conditions, such as high-dense and less-dense environments, and with static and dynamic obstacles. These considerations were not included in this work, as we focused on the theoretical aspects of trajectory planning. G.K. proposed the structure of the paper and carried out a comprehensive review in the field of motion planning targeting multirotor aerial vehicles. G.K. wrote the manuscript in consultation with A.K. A.K. made a critical reviewing the manuscript and final approval for publication. All authors have read and agreed to the published version of the manuscript. This research received no external funding. The authors declare no conflict of interest. The following abbreviations are used in this manuscript: