# On Sharing Spatial Data with Uncertainty Integration Amongst Multiple Robots Having Different Maps
## 2 Correspondence Problem in Different Maps  
In dynamic environments, the new objects in the environment could be the temporary or new permanent obstacles. Both needs to be estimated in the map for correct path planning. A robot estimates the absolute position \((x_{obs},y_{obs})\) of an obstacle in its map through its SLAM module. This estimation also has an uncertainty (\(\Sigma_{obs}\)) associated with it which arises mainly from sensor errors. This information about the new obstacle \((x_{obs},y_{obs},\Sigma_{obs})\) is difficult to be directly shared with other robots.  
A common problem occurring in multi-robot systems is information sharing in different types of maps (e.g., 2D grid-map, 3D semantic map, feature map etc.) made from different sensors used by the robots for mapping and localization. Even the maps generated using the same sensor (e.g., Lidar) can vary in scale or rotation and the sensors used might have different specifications like resolution or range. In such scenarios, the 'correspondence problem' in different maps is a critical bottleneck in information sharing. Moreover, the uncertainty of localization also adversely affects the information sharing. In other words, it is important to consider how to easily correspond local spatial information in one map to spatial information in a separate map of different type or scale while considering the uncertainty.  
This is graphically explained in Figure 2. There is a scale difference between Map1 and Map2. Whereas, Map2 and Map3 differ by a rotation factor. A spatial obstacle information, for example, position \((x^{1},y^{1})\) will correspond to different spatial coordinates in Map2 and Map3. In most real world scenarios, these scale and rotation differences are generally not known. Some previously proposed  
\begin{table}
\begin{tabular}{l c c} \hline
**Feature** & **Previous Work**[12] & **Extended Work** \\ \hline Sharing New Obstacle’s Position Information & Yes & Yes \\ Consideration of Positional Uncertainty of Obstacles & No & Yes \\ Confidence Decay Mechanism & Yes & Yes \\ Uncertainty Influence Over Confidence Decay & No & Yes \\ Experiments in Very Dynamic Environment (e.g., Moving People) & No & Yes \\ Robots have Different Types of Sensors & No & Yes \\ Tests with Heterogeneous Maps & No & Yes \\ \hline \end{tabular}
\end{table}
Table 1: Comparison of this extended work with the previous work [12].  
techniques [30] to find the necessary translation and rotation can be applied to transform the spatial information in one map to another. However, the computation costs are expensive and could introduce undesired delays.  
Although the example in Figure 2 is simplified for illustration, in actual scenarios different maps may have different levels of noise and even feature dimensions. Moreover, some robots may only have a partial map information. Similarly, Figure 3 discusses the problem of robots having different types of maps [31]. Figure 3a is a map in the form of a graph, Figure 3b is a dense 3D map, while Figure 3c is the gridmap of the same environment. It is difficult to for the robots to correlate spatial information in such different types of maps.  
In the proposed work, it is assumed that the robots work in the common service area whose map is available to the robots. This map itself could be heterogenous, for example, grid-map, RGBD map and so forth, which is built using different sensors mounted on different robots. Moreover, the maps could be build from different anchor points. Thus, different robots could have heterogeneous maps.