## 1 Introduction  
The technological variety of unmanned vehicles has grown with the development of ground and robotic aerial systems. On the one hand, robotic aerial systems tend to be faster, although they require more effort to control. On the other hand, terrestrial vehicles can move better in confined spaces, with the disadvantage of limited movements on elevated surfaces, as described by [PERSON] et al. [1].  
Studying this type of robot leads to the development of algorithms to make such movements autonomous by following an optimal trajectory. For example, in [1], [PERSON] et al. use a fast exploration random tree method called RRT, a heuristic search algorithm based on sampling. [PERSON] et al. [2] use a combinatorial multi-objective evolutionary algorithm, allowing all combinations of subtasks to be explored simultaneously. Such combinations are a series of steps to be followed for robot locomotion.  
Using a three-layer neural network, [PERSON] et al. [3] have one of the three inputs connected to a sensor, an output connected to the actuators, and a hidden layer connecting the previous two layers. A simple evolutionary algorithm is also used to synthesize the control of the robot. [PERSON] et al. [4] proposed a multi-objective trajectory planning method for collaborative robots; the higher-order-B-spline interpolation method is utilized to construct a continuous trajectory. Then, a trajectory competitive multi-objective particle swarm optimization is used to optimize the joint trajectory.  
The algorithms and others whose purpose is the autonomous motion of mobile robots generally explore a wide range of possible solutions simultaneously. Such exploration involves significant wear and tear on the physical robot, which is why a simulator is commonly used; with a simulator, an algorithm can be run and optimized as many times as necessary. This strategy was developed by [PERSON] et al. [5] for a wheeled robot employing an improved dolphin swarm algorithm on a real platform with the help of a simulation.  
Another example is JBotEnvolver, a Java-based software with an open-source multi-robot simulation platform used by [PERSON] et al. [3]. Alternately, [PERSON] et al. [2] and [PERSON] et al. [6] use PyBullet, a python module, to simulate robots utilizing a physics engine and machine learning.  
[PERSON] et al. in [7] used a simulation environment in a mixed reality implementing a modified vector field histogram (VFH) based routing algorithm as a path planning algorithm. The simulated environment and the modified VFH algorithm showed that this method proposed valid motion paths for the four-wheeled mobile robot concerning the operator's requirements for obtaining good obstacle avoidance performance.  
[PERSON] et al. [8] presented a long short-term memory (LSTM) neural network that allows a mobile robot to find the trajectory between two points and navigate while avoiding a dynamic obstacle. The authors used a LIDAR sensor to measure the distance between the robot and obstacles. The linear and angular velocity of the robot is obtained using a model to learn the mapping between input and output data. The mobile robot and its dynamic environment are simulated in Gazebo. The computer simulation showed that the network model could plan a safe navigation route in a dynamic environment.  
In [1], [PERSON] et al. use MATLAB to simulate the scenario and the proposed algorithm, solving the traveling salesman problem. Finally, in [9], [PERSON] et al. use Gazebo, an open-source 3D robotics simulator, to create a high-performance physics engine.  
Other techniques are found in [10] and [11], where [PERSON] et al. describe a path planning of mobile robots based on a multi-population migration in the genetic algorithm (see Figure 1).  
Figure 1: Flowchart for trajectory planning of mobile robots.  
The heterogeneous contributions in the literature are classified into relevant metrics and compared, as shown in Table 1.