Prior to the mission, the communication maps for two base stations were obtained as shown in Fig 30. It can be seen that as the position becomes distant from the base station, the corre- sponding RSSI value decreases. In addition, the communication quality degrades further when there is no line-of-sight (LOS) obstructed by walls. In the experiments, the clients are planned
(a) base 1 (b) base 2
Figure 30: Communication maps of base station 1 and 2.
to visit three sets of client mission positions. When the clients reach the corresponding target position, the proposed algorithm provides the optimal relay positions, and the relays are dis- patched to those positions. In order to validate the performance of the algorithm, RSSI values are collected at each of the relay positions for 15 seconds and the average of the collected RSSIs is compared with the predicted channel qualities. The WCC is used for the performance metric in this experiments.
Figure 31a shows the experiment result for the rst client positions. For Relay1, the communi- cation qualities on Relay1-Client1 and Relay1-Base2 are almost the same. This is because Relay1
belongs to only two connections in the network. If Relay1 approaches to Client1, the communi- cation quality between Relay1 and Client1 would increase but the quality between Relay1 and Base2 would decrease; it results in the decrease of the WCC cost. Thus, the proposed algorithm tries to place the relays at points where the communication qualities for the relay are balanced.
On the other hand, Relay2 is not placed where the communication qualities on Relay2-Base1, Relay2-Client2, and Relay2-Client1 are close to each other. This is because of the obstructions and the geometrical constraints of the indoor environment. Overall, the communication quality levels between nodes in the network are made similar across the all ve connections. Besides, the
original WCC of the MST without using relays (i.e. the communication performance of the orig- inal network) was -69.2 dBm whereas the WCC with the two relays in the optimized positions is -50.5 dBm, which is signicantly improved.
(a) Network congurations
(b) WCC cost change with respect to SL-PSO iterations
Figure 31: Experiment results at the rst mission position of the clients.
Figure 31b shows the SL-PSO cost with respect to the iterations. Note that the sign of the WCC cost is ipped. The cost was gradually improved as the number of iterations increases. The terminal condition was reached by the maximum iteration number 89 times. Figure 32 shows the changes of relay positions and the network topology as the iteration number increases, and the four yellow dots in Fig. 31b denote the four cases with the corresponding iteration numbers. The topology kept varying until about 30th iteration as shown in Figs. 32a and 32b. The optimization process took 74.1 seconds. Note that the optimization duration could be dramatically improved by using a faster programming language such as C/C++ and Java instead of MATLAB if necessary.
It is worthwhile mentioning that the aforementioned optimized communication qualities are obtained from the proposed channel prediction algorithm. However, actual signal qualities could be dierent from the predicted ones due to the stochastic nature of wireless communication and signal behavior in indoor environments such as reection, refraction, and diraction. In Table 6, the predicted channel quality is compared with the average of the actual RSSI measurements collected in 3Hz for 15 seconds. It should be noted that we assume that communication quality in both directions on one connection is equivalent since identical XBee modules are used for all nodes. The bold values represent the worst connectivity (i.e. WCC value). Besides, the error and the normalized error (error per standard deviation) represent how good the predicted RSSI is.
In the rst client mission position, the predicted RSSI values were reasonably close to the actual signal measurements. In the case of the connection Base1-Relay2, the error was larger than that of the other connections as the measurements are more noisy (i.e. high standard deviation) than that of other four connections.
Table 6: Signal strength (RSSI) on the connections in the rst client mission.
connection Prediction, dBm Measurement, dBm Error, dBm
value mean standard
deviation |error| |error|per standard deviation
Base1-Relay2 -47.4 -44.3 3.49 3.09 0.884
Client2-Relay2 -50.5 -50.1 0.804 0.399 0.496
C1ient-Relay2 -50.5 -51.3 3.25 0.747 0.230
C1ient-Relay1 -50.5 -50.7 1.09 0.207 0.190
Base2-Relay1 -50.4 -51.3 1.91 0.857 0.448
For the second client mission position, only Client1 has moved from the rst case. It caused the change of the network topology as shown in Fig. 33a. The optimization of the SL-PSO stack took 76.2 seconds for 89 iterations as shown in Fig. 33b. The prediction performance of channel quality of the algorithm is consistent to the rst mission case as shown in Table 7. The normalized error on the connection Client -Relay is relatively larger than that of the other
(a) iteration number = 1 (b) iteration number = 20
(c) iteration number = 35 (d) iteration number = 60
Figure 32: Relay positions and the network topology at each of the iteration numbers.
connections. Due to the huge distance between the Base2 and the others, the original WCC without relays was -76.0 dBm while the WCC with the two relays in the optimized positions is -55.0 dBm.
(a) Network congurations
(b) WCC cost change with respect to SL-PSO iterations
Figure 33: Experiment results at the second mission position of the clients.
Table 7: Signal strength (RSSI) on the connections in the second client mission
connection Prediction, dBm Measurement, dBm Error, dBm
value mean standard
deviation |error| |error|per standard deviation
Base1-Relay2 -49.2 -49.0 0.45 0.182 0.403
Client2-Relay2 -54.9 -57.4 2.41 2.55 1.06
C1ient-Relay2 -44.8 -45.5 1.20 0.753 0.629
Relay1-Relay2 -55.0 -53.7 2.73 1.34 0.492
Base2-Relay1 -55.0 -55.4 1.59 0.390 0.246
In the third client mission position case, both the clients move as shown in Fig. 34a. The optimization was terminated 34.6 seconds after the initiation (total 60 iterations) since the particles were stagnated for over 35 iterations. It converged faster than the other cases as the topology of the network was a simple relay chain (i.e. end-to-end communication). This case also shows a consistent result of the signal quality prediction in comparison to the previous cases as shown in Table 8. The original WCC without relays was -69.2 dBm whereas the WCC with the two relays in the optimized positions is -51.5 dBm.
Table 8: Signal strength (RSSI) on the connections in the third client mission
connection Prediction, dBm Measurement, dBm Error, dBm
value mean standard
deviation |error| |error|per standard deviation
Base1-Client2 -51.5 -51.0 0.783 0.562 0.718
Client2-Relay2 -50.8 -50.7 0.963 0.0767 0.0796
C1ient-Relay2 -44.9 -47.8 6.34 2.88 0.455
Client1-Relay1 -51.2 -51.7 1.75 0.543 0.310
Base2-Relay1 -41.9 -42.0 2.69 0.100 0.0372
The channel quality prediction of the proposed algorithm was quite accurate overall. Al- though there seems not much dierence between the model-based and GP-based communication quality predictions, it might be worthwhile reiterating that GP-based prediction does not require the map of the environment, which is benecial to be applied to an unknown environment. A movie clip for the experiment can be found at: https://youtu.be/ZWu5ndgj-08.
(a) Network congurations
(b) WCC cost change with respect to SL-PSO iterations
Figure 34: Experiment results at the third mission position of the clients.
6 Conclusion and future work
This thesis has proposed the optimal relay positioning algorithm for multi-agent systems in com- plex environments. Exploring the area of interest prior to the mission, the agent build not only the geometrical map but also the communication map with GP-based link quality prediction.
The communication performance is evaluated with the WCC. The cost of the communication performance is maximized with respect to the relay positions by the heuristic optimizer. The proposed algorithm outperformed the RRT-based methods in the networks with single base and single client in the simulations. The real experiments have been carried out to validate the pro- posed algorithm. The use of relay nodes in the optimal position improved the communication performance signicantly. The predicted signal quality was also assessed. Therefore, the experi- ments showed that the proposed algorithm is suitable for the relay positioning problem and the predicted network performance is accurate.
The following tasks remain as the future work. First, real-time trajectory planning algorithm could be developed to optimally maintain communication quality during the relay dispatches. In other words, the relay can be used to maximize the communication performance on the way to the target position (i.e. transient period). This idea helps to build more advanced relay systems.
Second, the relay positioning can be implemented while creating the geometrical and communi- cation maps. This came from the idea that the entire maps do not need for channel prediction.
It may be useful when the environment of interest is absolutely unknown and minimum time is required to place the communication relays. Third, the optimization process could be made faster as the relays may be required to be placed rapidly. In the proposed algorithm, the num- ber of communication relay increases the time complexity exponentially increases. It might be mitigated by using grid approach with a discrete optimizer. Finally, the sucient number of relay nodes could be determined autonomously depending on the communication performance requirement. The robotic system with the sucient number of relay nodes could use less energy compared to the proposed relay positioning system since consuming minimum energy is one of the most important concerns in pragmatic applications.
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Acknowledgements
Foremost, I would rst like to thank my thesis advisor Dr. Hyondong Oh of the associate professor in School of Mechanical, Aerospace and Nuclear Engineering at UNIST. The door to Prof. Oh oce was always open whenever I had a question about my research or ran into a trouble spot.
He not only consistently allowed this thesis to be my own work, but also steered me in the right direction whenever he thought I needed it.
Besides, I would also like to say that it was all thanks to all of the members of the autonomous systems laboratory at UNIST: Gangik Cho, Minkyu Park, Yeong Ho Song, Phone Nguyen Ngo, Bumsu Park, Dongmin Shin, Seungho Back, Minwoo Kim, Seul-bi An, Jinwoo Oh, Minjae Jung, Joonwon Choi, Geunsik Bae, and Dr. Xuan-Toa Tran. I could stay motivated while getting along with them. This was because they constantly encouraged me to keep working on research and inspired me a lot whenever I got lazy. Were it not for their help, I could have accomplished none of the research I have been done during the Master's course.
Finally, I must express my profound gratitude to my parents and my sister for providing me with continuous encouragement and unfailing support throughout my years of study and through the process of researching and writing this thesis. This accomplishment would not have been possible without them. I am very appreciative and very grateful.