Moreover, understanding close-in obstacles' positions relative to the multirotor aerial vehicle (MAV) is crucial for making decisions in real time; this raises a new challenge: the one of the rapidity and accuracy of relative environment reconstruction, which essentially is how obstacle constraints are added to the problem formulation. Yet another challenge is of the impact of the obstacles and constraints on the smoothness and dynamic feasibility of the generated trajectory. After conducting an extensive literature review on the topic of trajectory planning for multirotor aerial vehicles (MAVs), we were able to isolate basic building blocks that are essential for optimal motion planning, as shown in Figure 2. Each of the primary components plays a key role in the process of trajectory generation. Figure 2: The basic building blocks are encountered in trajectory planning problems. In general, a considered trajectory planning problem can be composed of one or more blocks sequentially or in parallel to fulfil the desired needs. Details explanation of each of the blocks are explained in the following sections: motion model selection (Section 2), intermediate waypoint identification (Section 3), initial trajectory generation (Section 4), free space segmentation (Section 5), continuous trajectory refinement (Section 6), and receding horizon trajectory planning (Section 7). We survey the existing literature and identify the main building blocks of trajectory planning for MAVs: free-space segmentation, motion model selection, initial waypoint identification, initial trajectory generation, continuous trajectory refinement, and receding horizon trajectory planning. For each building block, we discuss and examine how previous research has addressed it. Furthermore, we used the same benchmark example to fairly compare different strategies. Also, we aim to provide a comprehensive overview of the recent advances and the most prominent results in trajectory planning for multirotor aerial vehicles (MAVs) from 2010 to 2022, with a focus on real-time generation of optimal trajectories as follows [3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32;  
approaches based on imitation learning, inverse reinforcement learning, and evolutionary computing. Further investigations also include a comparison of different paradigms in a simulated environment and through real-world experiments for different operating scenarios: trajectory planning for high-dense and less-dense environments, static and dynamic obstacle avoidance, and high-speed and low-speed maneuvers. These considerations were outside of the scope of this work since we focused on the theoretical aspects of the plan-based trajectory planning paradigm. The rest of the paper is organized as follows:  
* Section 2--Motion Modeling--discusses the type of motion model suitable for defining the dynamics of the robot based on the chosen trajectory generation technique. Exact, empirical, and differential flatness models are presented. * Section 3--Initial Waypoint Generation--surveys state-of-the-art techniques for finding initial tentative waypoints for trajectory generation, focusing on graph search-based algorithms, motion-primitive-based approaches, and fast marching methods. * Section 4--Initial Trajectory Generation--comprehensively reviews initial trajectory generation techniques. It begins by defining how to formulate a trajectory, followed by a detailed explanation of several interesting techniques, including minimum-snap, polynomial trajectory generation as quadratic programming (QP), unconstrained polynomial trajectory generation, covariant gradients, B-spline, and Bernstein. Finally, it compares several trajectory techniques to highlight their respective strengths and weaknesses. * Section 5--Free Space Extraction--explains how to extract and incorporate free space into trajectory planning. OctoMap, IRIS, and SFC are the main methods discussed in this section.