fix typos

chapters/whatSlam.tex

@@ -127,7 +127,7 @@ \section{Classical Visual SLAM Framework}
 
 The classic visual SLAM framework is the result of more than a decade's research endeavor. The framework itself and the algorithms have been basically finalized and provided as essential functions in several public vision and robotics libraries. Relying on these algorithms, we can build visual SLAM systems performing real-time localization and mapping in static environments. Therefore, we can reach a rough conclusion that if the working environment is limited to fixed and rigid with stable lighting conditions and no human interference, the visual SLAM problem is basically solved~\cite{Cadena2016}.
 
-The readers may not have fully understood the concepts of the modules mentioned above yet, so we will detail each module's functionality in the following sections. However, a deeper understanding of their working principles requires certain mathematical knowledge, which will be expanded in this book's second part. For now, an intuitive and qualitative understanding of each module is good enough.
+The readers may not have fully understood the concepts of the modules mentioned above yet, so we will detail each module's functionality in the following sections. However, a deeper understanding of their working principles requires certain mathematical knowledge, which will be explained in this book's second part. For now, an intuitive and qualitative understanding of each module is good enough.
 
 \subsubsection{Visual Odometry}
 
@@ -185,7 +185,7 @@ \subsubsection{Mapping}
 
 Let's take the domestic cleaning robots as an example. Since they basically move on the ground, a two-dimensional map with marks for open areas and obstacles, built by a single-line laser scanner, would be sufficient for navigation for them. And for a camera, we need at least a three-dimensional map for its 6 degrees-of-freedom movement. Sometimes, we want a smooth and beautiful reconstruction result, not just a set of points but also a texture of triangular faces. And at other times, we do not care about the map, just need to know things like ``point A and point B are connected, while point B and point C are not'', which is a topological way to understand the environment. Sometimes maps may not even be needed. For instance, a level-2 autonomous driving car can make a lane-following driving only knowing its relative motion with the lanes.
 
-For maps, we have various ideas and demands. Compared to the previously mentioned VO, loop closure detection, and backend optimization, map building does not have a particular algorithm. A collection of spatial points can be called a map. A beautiful 3D model is also a map, so is a picture of a city, a village, railways, and rivers. The form of the map depends on the application of SLAM. In general, they can be divided into to categories: \emph{metrical maps} and \emph{topological maps}.
+For maps, we have various ideas and demands. Compared to the previously mentioned VO, loop closure detection, and backend optimization, map building does not have a particular algorithm. A collection of spatial points can be called a map. A beautiful 3D model is also a map, so is a picture of a city, a village, railways, and rivers. The form of the map depends on the application of SLAM. In general, they can be divided into two categories: \emph{metrical maps} and \emph{topological maps}.
 
 \paragraph{Metric Maps}
 Metrical maps emphasize the exact metrical locations of the objects in maps. They are usually classified as either sparse or dense. Sparse metric maps store the scene into a compact form and do not express all the objects. For example, we can construct a sparse map by selecting representative landmarks such as the lanes and traffic signs and ignore other parts. In contrast, dense metrical maps focus on modeling all the things that are seen. A sparse map would be enough for localization, while for navigation, a dense map is usually needed (otherwise, we may hit a wall between two landmarks). A dense map usually consists of a number of small grids at a certain resolution. It can be small occupancy grids for 2D metric maps or small voxel grids for 3D maps. For example, in a 2D occupancy grid map, a grid may have three states: occupied, not occupied, and unknown, to express whether there is an object. When a spatial location is queried, the map can provide information about whether the location is passable. This type of maps can be used for various navigation algorithms, such as A$^*$, D$^*$\footnote{ See \url{https://en.wikipedia.org/wiki/A*_search_algorithm}.}, etc., and thus attract the attention of robotics researchers. But we can also see that all the grid status are store in the map, thus being storage expensive. There are also some open issues in building a metric map. For example, in large-scale metrical maps, a small steering error may cause the walls of two rooms to overlap, making the map ineffective.