**2. Localization problem**

Mobile robots aiming to perform tasks without human interference, i.e., autonomously, must know their pose within the environment. The same necessity applies for MAVs that have only GPS sensor as position estimation. Estimating the robot's pose would be a simple task, but only if all the sensors of the robot were perfect and the environment fully static. Given that this scenario is not realistic, in which the sensor readings are not precise and many agents are moving through the environment, the difficulty level of the localization problem increases, and hence, it is necessary to estimate the robot's pose.

Despite its difficulty level, localization is a fundamental problem in the mobile robotics field [13]. It is defined as the robot's pose estimation relative to a previously known environmental map [12]. Even though its definition is simple, this problem has two main variations: local and global estimations. In the former, the initial robot pose in the map is known, and the local localization approach only tracks the robot as it moves through the environment. The error of the first pose estimation is low, and the goal is to keep it low using the sensor readings and the motion information from the robot. In contrast to the former variation, the second one is significantly harder. In this case, the initial robot pose is unknown, and hence, the error of the pose estimation is originally high. Instead of considering just a small part of the map at the beginning, in the global localization, the whole map must be considered for the estimation since the initial pose is unknown [14]. **Figure 1** illustrates the differences between local and global localization. The global localization is illustrated in **Figure 1(a)**, in which the error estimation is high at the begging, and the goal is to reduce it as the robot moves through the environment. The opposite happens in **Figure 1(b)**, which depicts the local localization. The error estimation begins considerably low, and even though it increases through time, as well as the global localization, the goal is to reduce it.

The most popular approaches that deal with localization in the mobile robotics field are grouped either as probabilistic or as deterministic. In the first group, there are two main approaches that are worth it to be mentioned, Kalman filter [15] and particle filter (Monte Carlo) [16]. Even though both implement the Bayes filter, each one has its specific advantages, and therefore, they are suitable for different situations and constraints. On the other hand, the most popular approach for the second group is based on interval analysis, and the estimation is defined through boxes that must be minimized [17]. As the goal of this chapter is not to go deep into these approaches, the reader is invited to look at the references for more details about them.

Independent of the approach used to deal with the localization problem, all of them have the same characteristics: as input, they require an environment representation, a sensor to read the environment, and odometry data; and as output, the robot's position in the environment representation that was estimated, as shown by **Figure 2**. Hence, localization systems try to find the best pose in the map that fits both the sensor reading and the odometry information. The best the system is, the more accurate is the pose estimation. **Figure 2** presents an example of using Lidar and 2D map, but it is important to highlight that the same idea also applies to other sensors or types of maps.

Even though the setup of the mobile robot localization problem seems quite simple, with input and output well defined, the difficulty level is considerably high. The robot's pose is not sensed directly, it must be estimated, and that is where the problem lies. Usually, the robot's sensors, both to read the environment and to measure the odometry, are noisy, and hence, the data that they provide does not correctly represent the real world. In addition to that, some types of robots have restrictions about which kind of sensor they support, and they can not have the

**Figure 1.** Comparison between the error estimation of (a) global and (b) local localization methods. Both localizations were made considering the robot movement in a (c) 2D map.

**Figure 2.** The concepts of a localization system, in which a 2D map, sensor reading, and odometry information are used as input in (a), processed by the system in (b), and the estimated robot's pose is the output in (c).

best sensor for their tasks. In MAVs, for example, a camera is the most popular sensor used for this purpose, since they are smaller, lighter, and cheaper than most range-finder lasers, for instance. However, using images to estimate the odometry information is not ideal, although there are algorithms that compute this estimation.

The localization approaches overcome the noise data problem modeling the error of the sensors. Besides, since just one reading is insufficient to the pose estimation, these approaches also have to integrate the data over time to reduce the error estimation. In environments that have different regions that look alike, such as a building with many corridors and doors, it is quite impossible to estimate the robot's pose considering just one reading. For example, imagine that at some point, the robot is observing a door after having observed a wall and a frame. Then, instead of searches for all the spots in the map that contain a door, the localization system searches for spots that also matches with the wall and the frame. In this way, the past observations are also considered when estimating the robot's pose.

Despite the generic localization problem explanation presented so far, the research community has explored the UAV localization problem throughout the years, and many different approaches have been proposed. The most significant difference between them relies on the map representation and also on the method that they use to compare the sensor readings and the small parts of the map. The next section covers the most popular proposed approaches aiming to deal with this problem and how they differ from each other.
