# On Sharing Spatial Data with Uncertainty Integration Amongst Multiple Robots Having Different Maps
## 6 Experimental Results
However, with the proposed information sharing mechanism, Turtlebot could directly plan a path considering the newly added obstacle and the planned path was (Figure 11b),

\[S\to n_{2}\to n_{5}\to n_{6}\to n_{9}\to n_{8}\to n_{7}.\]

Figure 10: Timely snapshots of the experiment. (**a**) P3 DX starts moving with old map. (**b**) Person adds a new obstacle. (**c**) Person moves in front of P3 DX. (**d**,**e**) P3 DX observes the new obstacle, changes trajectory and updates map. (**f**-**h**) P3 DX return to the starting position. (_Supplementary Materials_)

Notice that, this appropriate path was generated by Turtlebot'remotely' before actually encountering the new obstacle. Figure 12 shows the navigation of Turtlebot after considering the new obstacle. The entire navigation is illustrated between Figure 12a-h. In particular, it can be seen from Figure 12e-g, that Turtlebot maintains a safe threshold from the start itself. Turtlebot itself updated its map using the attached Lidar and the updated grid-map is shown in Figure 13.

The dimensions of the obstacles in the experiment are given in Table 3.

The decay curve is shown in Figure 14. In the experiment, \(C_{th}\) was set to 0.45 and \(t_{z}\) to 20 min. Based on the uncertainty of the obstacle, the Ufactor was calculated as approximately 15% of \(t_{z}\). Figure 14 shows the decay of confidence considering the uncertainty of the obstacles. Figure 15 shows different decay curves for different amounts of estimated positional uncertainties of the new obstacle. Although Figure 14 shows the actual decay curve of the experiment, Figure 15 shows theoretical values for different values of uncertainty. Figure 15a-d shows the confidence decay with increasing uncertainty of 35%, 45%, 55% and 65%, respectively. It can be seen that, for increasing uncertainty, the curve decays much faster, as desired. Thus, the T-node enables robots to share information across heterogeneous maps. Indeed, there is a need to transform the newly added obstacle's information to spatial coordinates but it can easily be achieved in real-time. Moreover, to avoid the overheads of such computation for time-critical

Figure 11: (a) RGBD map updated by P3 DX. (b) Node-map. S and G are the start and goal points. The new obstacle is shown on nodes \(n_{6}n_{7}\). Ellipse represents positional uncertainty. Figure 12: Timely snapshots of the experiment. (a–h) Turtlebot starts navigation with the updated information and plans a trajectory considering the new obstacle. (_Supplementary Materials_)



### Results with Dynamic Entities (Moving Obstacle)

The proposed method was tested under complex scenarios by purposefully moving a person in front of the robot and blocking its way. This is shown in Figure 16. As P3 DX robot started navigation from start location 'S' to goal location 'G', a person blocked its way by randomly moving in front of the robot. This is shown in Figure 16a-j. Similarly, the path of P3 DX robot was blocked again while it was navigating back from the goal location 'G' to its start location 'S'. This is shown in \[S\to n_{2}\to n_{5}\to n_{6}\to n_{7}\]0 The person randomly moved in front of the robot blocking its path as shown in Figure 17a-j. In both the cases of Figures 16 and 17, the robot attempted to avoid collision and planned alternate trajectories or stopped if the person stands dangerously close to the robot. Moreover, in both the cases, the robot did not update the map corresponding to the person as a new obstacle in the map. This is because the positional uncertainty corresponding to the moving obstacle was large as calculated by Algorithm 2. Even if the person is falsely identified as a new obstacle and the map is updated, it has no adverse effects in the proposed method, as uncertainty is integrated in the confidence decay mechanism. Any wrong map update corresponding to dynamic obstacles has high probability of larger positional uncertainty corresponding to the dynamic obstacle and therefore a quicker decay given by Equation (6), (7) and (9).