# On Sharing Spatial Data with Uncertainty Integration Amongst Multiple Robots Having Different Maps
## 6 Experimental Results
\begin{bmatrix} \sigma_{x}^{2}&\sigma_{xy}&\sigma_{x\theta}\\ \sigma_{xy}&\sigma_{y\theta}^{2}&\sigma_{x\theta}\\ \sigma_{x\theta}&\sigma_{y\theta}&\sigma_{\theta}^{2}\end{bmatrix} \right)\)
14\(\#\)\(n\): degree of decay curve, \(t_{th}\): threshold time, \(c_{th}\): threshold confidence, \(t_{z}\): time to decay to zero. \(n=\dfrac{\log(1-c_{th})}{\log\left(\frac{t_



### Experiments with Heterogeneous Maps

In this section, we describe the results of the proposed method with heterogeneous maps. The environment for experiments is shown in Figure 9b,c. The dimensions of the environment are shown in Figure 9d. The environment had two static obstacles 'Obstacle1' and 'Obstacle2' marked in Figure 9d. The start and goal positions are marked as 'S' and 'G', respectively, in Figure 9d. The T-node map is shown in Figure 9e. The two robots used in the experiment were both equipped with 2D Lidar and RGBD sensors. As shown in Figure 9a, the Pioneer P3 DX robot was equipped with a Sick-Lidar of 10 m range and ASUS Xtion-Pro RGBD camera. Turtlebot was equipped with a Hokuyo Lidar of 20 m range and a Kinect RGBD camera. Figure 9: Experiment setup. (**a**) Differential drive robots Kobuki-Turtlebot2 and Pioneer-P3 Dx. (**b**) Environment with initial position of robots. (**c**) Another view of the environment. (**d**) Environment dimensions. (**e**) Node-map of the environment where S and G are the start and goal points. To test the proposed method with heterogeneous maps, Pioneer P3 DX robot was programmed to use only the RGBD sensor to build a 3D map, and navigate in the environment. Pioneer P3 DX first started navigation from location 'S' to the goal location 'G' as shown in Figure 10a. A* algorithm [47] and SHP algorithm [48; 49] were used for path planning and path smoothing, respectively. As soon as the P3 DX robot started moving, a long new obstacle was placed in the environment as shown in Figure 10b, well outside the range of the sensor. As shown in Figure 10c, the person moves in front of the robot and blocks its way purposefully. The details of dynamic obstacle are discussed in the next Section 6.2. P3 DX perceives the new obstacle and alters its path towards the goal as shown in Figure 10d-f, while also updating the map with the newly added obstacle. P3 DX was programmed to come back to its initial position 'S' and the navigation in shown in Figure 10g,h. The updated 3D map build by P3 DX robot is shown in Figure 11a. In this experiment, Turtlebot used only the 2D Lidar sensor with 2D gridmap. Hence, P3 DX could not directly share the 3D point-cloud information due to the heterogeneous maps used by the two robots. By using the T-node map, P3 DX blocked the path between nodes \(n_{6}\) and \(n_{7}\) and shared this information with the Turtlebot to plan appropriate path. More information regarding the dimensions of the new obstacle could also be shared for better path planning. Hence, the 3D information was converted to a 2D information to be shared with Turtlebot. Grid maps are the most commonly used 2D maps in which each grid-value represents whether the grid is occupied, free or unknown. The 3D point-cloud were projected to the ground which was detected using a RANSAC based plane detection [50]. This 2D information was shared by P3 DX robot with Turtlebot and the updated T-node map is shown in Figure 11b. In the updated T-node map of Figure 11b, the obstacle is placed between the nodes \(n_{6}\) and \(n_{7}\) blocking it. Turtlebot was programmed to navigate from the same start location 'S' to the goal location 'G'. In the absence of the proposed information sharing mechanism, the path planned by Turtlebot would be (Figure 11b),

\[S\to n_{2}\to n_{5}\to n_{6}\to n_{7}\]

The Turtlebot would encounter a new obstacle between the nodes \(n_{6}\) and \(n_{7}\) and would have to re-plan a new path towards the goal.