Extremum Seeking Control for Beacon Detection in Avalanche Disasters using Multiple UAV

Extremum Seeking Control for Beacon Detection in Avalanche Disasters using Multiple UAV Joel Enrique Esparza Ramirez Falculty of Engineering Free University of Bolzano Bolzano, Italy JoelEnrique.EsparzaRamirez@st udent.unibz.it Santos Miguel Orozco Soto Faculty of Engineering Free University of Bolzano Bolzano, Italy SantosMiguel.OrozcoSoto@unib z.it Karl von Ellenrieder Faculty of Engineering Free University of Bolzano Bolzano, Italy [email protected] Abraham Mejia-Aguilar terraXcube terraXcube Bolzano, Italy [email protected] Abstract— This paper presents simulations of Search and Rescue (SaR) using multiple Unmanned Aerial Vehicles (UAVs) equipped with ARVA (Appareil de Recherche de Victimes d'Avalanche) beacons that use Extremum Seeking Control (ESC) to reduce the time operation of rescue avalanche victims. ESC, a real-time optimization technique, enables UAVs to autonomously navigate toward the signal source without requiring a detailed system model. The simulations compare rescue times using single and multiple UAVs configurations in a 100m x 200m area. Results show that using four UAVs reduces the victim detection time from 230 seconds (single UAV) to 160 seconds, demonstrating improved efficiency. This work includes mathematical modeling of the magnetic field generated by ARVA transmitters and validates the ESC strategy through simulations. Keywords—UAV, Search and Rescue, Avalanche I. INTRODUCTION Search and Rescue (SaR) has been an integral part of human society for centuries. When humans face difficulties and require assistance due to a natural disaster, rescue people use equipment and techniques to provide assistance. In the wilderness environment, there are avalanches, to be more specific, snow avalanches that refer to snow masses that rapidly descend mountainside [1]. Over the years, people have died due to these disasters; between 1967 and 2009, 827 people died in avalanche accidents in Italy, with an average of 19 victims per year [2]. Data show that for completely buried victims in open areas, the survival probability drops from 91% at 18 minutes to 34% at 35 minutes, remaining constant until a second drop after 90 minutes (Figure 1) [3]. Fig. 1 Survival chances. Source: [3] The ARVA consists of two elements: the transceiver, which is worn by the person in need of help to send the signal, and the receiver, which is used by the rescuer to detect the victim through the signal. The search process begins with the reception of the first signal and continues until the buried individual is located. Initially, the search for the signal starts with the device in the 'search' mode and, depending on the number of people assisting in the search, different strategies can be used. When the signal is detected, the process starts with an approximate search guided by the distance and direction indicators displayed on the screen. Once the signal is detected, the device orients towards it. II. STATE OF THE ART A. Extremum Seeking Control Unmanned aerial vehicles (UAV) represent a significant advance in the field of SaR because they can perform tasks that take humans longer and with the advantage of being able to do so without endangering people's lives. In recent years, the use of UAVs and ARVA has been proposed as a solution to find people buried under snow, with the drone carrying the ARVA device to detect the signal more quickly. One solution to accelerate search time is the use of Extremum Seeking Control (ESC). Extreme-seeking control is a real-time optimization technique that allows a system to autonomously adjust its inputs to find and maintain operation at an optimal point, typically a maximum or minimum of a performance function, without the need for a detailed model of the system. ESC is especially useful in situations where the system dynamics is complex, nonlinear, or unknown, making it ideal for applications in wild environments. Azzollini et al. proposed a solution that uses the ESC strategy to autonomously steer the drone to the victim's location [4] . B. ARVA system Since the first minutes of the search are very important in terms of survival probabilities, the use of multiple UAVs carrying the beacon for searching victim reduces the time and therefore the probabilities of survival. The generated magnetic dipole, represented by the vector m, aligns with the xt axis of Ft and maintains an approximately constant amplitude [4]. The electromagnetic vector field generated by the dipole is indicated by h. Its strength is significantly affected by the under-snow depth of the transmitter and the type of snow. Denoting by 𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛(𝑥,𝑦,𝑧) () Where the components of the vector tpr expressed in Ft, then the mathematical model of the magnetic vector field is given by ℎ(𝑡𝑝𝑟) = ||𝑚|| 4 𝜋 ||𝑡𝑝𝑟||5𝐴(𝑡𝑝𝑟) () where 𝐴(𝑡𝑝𝑟)∶=[2𝑥2−𝑦2−𝑧2 3𝑥𝑦 3𝑥𝑧 ] () 2025 I-RIM Conference October 17-19, Rome, Italy ISBN: 9788894580570 10.5281/zenodo.17629844 209 and m ϵ ℝ3 is the magnetic moment, so the norm of the magnetic field ht given by ||ℎ𝑡||= ||𝑚|| 4 𝜋 ||𝑡𝑝𝑟||5 √1+ 3 𝑥2 ||𝑡𝑝𝑟||2 () and finally the output nonlinear function is [4] 𝑦𝑡(𝑖𝑝,𝑖𝑅𝑡,𝑡)∶=||𝑖ℎ𝑚||−1/3 () III. ALTERNATIVE METHOD To demonstrate the reduction in the time needed to find a victim, a simulation was performed using (5) in MatLab, obtaining the time difference between a single drone and multiple UAVs in a 100 m x 200 m area 1 all of them with a velocity of 5 m/s. In the first simulation, a UAV is used to cover the entire area, from (1) the initial position is singleUAV = [0, 0, 40]T and the position of the victim is victim = [42, 70 , -0.5]T. We selected 40 m as the range limit of the ARVA device and -0.5 m as the average depth of the victim. The UAV started with a pre-defined flight pattern until it found the first signal from the ARVA and then started to use the ESC to reach the position of the victim shown in Figure 3. The time to find the victim is 230 seconds, as shown in Figure 4. Fig. 3 Single UAV trajectory position Fig. 4 Single UAV time In the second simulation, four UAVs were placed (1) at: UAV1 = [0, 0, 40]T, UAV2 = [50, 0, 40]T, UAV3 = [50, 200, 40]T and UAV4 = [0, 200, 40]T. All UAVs started flying in a pre-defined pattern until they found the first signal from the ARVA and then started to use the ESC to reach the position of the victim shown in Figure 5. The time to find the victim is 160 seconds as shown in Figure 6, which is less than using a single UAV. Fig. 5 Multiple UAVs trajectory Fig. 6 Multiple UAVs time IV. CONCLUSIONS Our simulations indicate that extremum-seeking– controlled, ARVA-equipped UAVs can autonomously home to buried-victim signals without an explicit system model, and that scaling from one to four vehicles in a 100 m × 200 m sector cuts first-detection time from 230 s to 160 s (~30% faster). This quantifies the swarming advantage for timecritical avalanche SaR. The next steps in this research are HIL/field trials to handle EMI, wind, and latency, plus multiagent deconfliction and fusion for non-transceiver cases as well as a more robust simulations and baseline comparisons. ACKNOWLEDGMENT This project has received funding from the European Union's Horizon Europe research and innovation programme under grant agreement No 101168017 (HURRICANE). REFERENCES [1] M. Boensch, F. Rudolf-Miklau, S. Sauermoser, and A. Mears, The technical avalanche protection handbook. John Wiley & Sons, 2015. [2] M. Valt, I. Chiambretti, and R. Zasso, “1985–2009 twenty-five years of avalanche accidents in italy,” in Proceedings of the International Snow Science Workshop, 2009. [3] H. Brugger, B. Durrer, L. Adler-Kastner, M. Falk, and F. Tschirky, “Field management of avalanche victims,” Resuscitation, vol. 51, no. 1, pp. 7–15, 2001. [4] I. A. Azzollini, N. Mimmo, and L. Marconi, “An extremum seeking approach to search and rescue operations in avalanches using arva,” IFAC-PapersOnLine, vol. 53, no. 2, pp. 1627–1632, 2020. 1 An average extensions of an Avalanche 210