**3. Grid map merging**

The key algorithm to ensure the performance of multi-robot SLAM with LiDAR sensors is the grid map merging algorithm because even if the performance of the SLAM results of individual robots are good, the performance of multi-robot SLAM depends on the quality of the map transformation between robots. The concept of the grid map merging in multi-robot SLAM with LiDAR sensors is shown in **Figure 4**. Quantitatively, the grid map merging can be performed by acquiring a map transformation matrix *T* (MTM) which consists of translation amounts and a rotation angle between robots as follows:

$$T(\Delta\_{\mathbf{x}}, \Delta\_{\mathbf{y}}, \Delta\_{\theta}) = \begin{bmatrix} \cos \Delta\_{\theta} & -\sin \Delta\_{\theta} & \Delta\_{\mathbf{x}} \\ \sin \Delta\_{\theta} & \cos \Delta\_{\theta} & \Delta\_{\mathbf{y}} \\ \mathbf{0} & \mathbf{0} & \mathbf{1} \end{bmatrix} \tag{2}$$

*Grid Map Merging with Ant Colony Optimization for Multi-Robot Systems DOI: http://dx.doi.org/10.5772/intechopen.98223*

where *Δx*, *Δ<sup>y</sup>* and *Δθ* are the translation amounts and a rotation angle between robots, respectively.

The method to find the MTM can be categorized into direct map merging and indirect map merging according to the existence of the direct sensor measurements between robots or common objects. The direct map merging is to directly acquire the map transformation matrix by obtaining the inter-robot measurements which consist of relative distance and orientation between robots, which can be performed under a rendezvous. The indirect map merging acquires the map transformation matrix by finding and matching the overlapping areas of the individual maps of robots, which is called map matching. The detailed categorization of them and the brief descriptions of the previous works are summarized in [7, 8]. They have their own advantages, but they require commonly an optimization method to update the MTM more accurately regardless of the type of map merging.
