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Abstract

Environmental sensors are important for collecting data to understand environmental changes and analyze environmental issues. In order to effectively monitor environmental changes, high-density sensor deployment and evenly distributed spatial distance between sensors become the requirements and desired properties for such applications. In many applications, sensors are deployed in locations that are difficult and dangerous to reach (e.g. mountaintop or skyscraper roof). To collect data from those sensors, unmanned aerial vehicles are used to act as data mules to overcome the problem of collecting data in challenging environments. In this article, we extend the adaptive return-to-home sensing algorithm with a parameter-tuning algorithm that combines naive Bayes classification and binary search to adapt adaptive return-to-home sensing parameters effectively on the fly. The proposed approach is able to (1) optimize number of sensing attempts, (2) reduce oscillation of the distance for consecutive attempts, and (3) reserve enough power for drone to return-to-home. Our results show that the naive Bayes classification–enhanced adaptive return-to-home sensing scheme is able to avoid oscillation in sensing and guarantees return-to-home feature while behaving more cost-effective in parameter tuning than the other machine learning–based approaches.

Keywords

Adaptive sensing naive Bayes classification environment monitoring drone coordination sensor network

Introduction

Environmental information provided us important messages to understand environmental changes. It should be collected as much as possible to oversee and analyze any environmental issues. In conventional methods, wireless sensor networks (WSNs) with stationary sensors are deployed to monitor and collect environmental data. Unfortunately, there are some challenging issues when using stationary sensor nodes to collect data. First, the cost is high in terms of deployment, maintenance, and extension. In order to gather useful amount of environmental information, large number of sensor nodes should be deployed to collect valuable environmental data. However, the operation cost to deploy and maintain huge number of sensor nodes is high. Second, sensing areas might be dangerous or inaccessible. For example, it is quite dangerous to set up sensors for sensing a cave filled with deadly gas for its environmental information. Third, a network infrastructure is required for sensor nodes to transmit environmental data. Therefore, mobile nodes (e.g. unmanned aerial vehicles (UAVs)) can be leveraged to solve the problems mentioned above.

To overcome the problem of collecting data in challenging environments, UAVs can act as data mules to collect data from sensors. Another type of sensing platform, called remote sensing, uses aircraft-based sensor technology to detect environmental changes and collect data without physically setting up fix sensors as the on-site observation approaches. In this type of sensing, a UAV usually carries a sensing module (i.e. a computation device with different sensors and a data storage) to different remote sites for sensing environment and then comes back with collected data, periodically.

The major issues of remote sensing approach are battery capacity and power consumption using mobile nodes like UAVs. First, the battery capacity of UAV is limited and small; the larger the battery, the heavier the weight. Also, UAV will consume more power by carrying a heavy and huge battery. Second, the UAV needs to reduce power consumption and reserve energy for flying back to a specified home location in order to transmit data and recharge battery. In addition, sensor nodes consume lots of energy when sensors have been turned always on. Therefore, scheduling a duty cycle for sensors to monitoring environment is an effective way to reduce power consumption. Nodes would follow the schedule to turn on and off the sensors for monitoring and collecting environmental information.

In the environment monitoring and collecting environmental information, the spatial distance between each sensing sampling attempts is highly desirable to be evenly distributed (i.e. un-oscillated) around the sensing area. A number of works have been proposed to address power conservation and return home guarantee in adaptive sensing area. However, to the best of our knowledge, oscillation issue in remote environmental sensing is not previously addressed.

In this article, we extend the adaptive return-to-home sensing (ARS) algorithm¹ with a parameter-tuning algorithm that combines naive Bayes classification (NBC) and binary search (BS) to adapt ARS parameters effectively on the fly. In addition to guaranteeing drone always return-to-home (RTH), the proposed ARS extension reduces the oscillation of spatial distance between each sampling while lowering computational complexity compared with other machine learning–based schemes.

The contributions of this article are as follows: (1) the extension of ARS scheme that combines NBC and BS for ARS parameters tuning is presented, (2) the proposed scheme is able to guarantee RTH by reserve enough of power while reducing oscillation between each sampling, and (3) our extensive simulation results show the ability of the extended ARS+NBC scheme in terms of reducing oscillation in sampling and dynamically adjusting energy reservation for RTH to address any changes (e.g. crosswind) in the environment which can cost addition power consumption.

The remainder of the article is organized as follows. The related works are discussed in section “Related works.” To make this article self-contented, the original ARS scheme and the extension of ARS with a parameter-tuning algorithm that combines NBC are introduced in section “ARS scheme.” Our experimental results are presented in section “Evaluation.” Finally, conclusions are drawn in section “Concluding remarks.”

Related works

The adaptive sensing means dynamically adjusting the schedule for the sleep-wake duration of sensors. It can be classified into three categories: event trigger scheme, model-based scheme, and energy harvesting scheme. In the event trigger scheme, sensors turn on and off according to specific events. Usually, lower cost sensors are used as the first tier to detect an event. When the first-tier sensors detected an event, second-tier sensors are triggered to collect fine-grained information. Y Chon et al.² designed a three-level structure to trace a user and minimize the energy usage. The first level uses cell connection and battery state to infer the place change and to trigger the next level sensors. The second level uses Wi-Fi fingerprints to confirm place change and do place learning. The third level will turn on the GPS to get the location when the mobility pattern is new. SensLoc³ is an energy-efficient framework for tracking. It uses the accelerometer to detect movements. If the entrance is determined and movement is detected, the movement detector wakes Wi-Fi up to detect departure. Then, path tracking is starting to record the path using GPS.

FJ Wu et al.⁴ proposed a user-centric mobility sensing system. They use an accelerometer to detect movement and use Wi-Fi to detect the place. GPS would be triggered when the user is moving in an unknown place. T Kijewski-Correa et al.⁵ presented a structural health monitor scheme for a bridge. They use accelerometers to detect structural movement and use strain gauges to measure stress on materials. Initially, only accelerometers activate to collect data. If the possible damage is detected, strain gauges are activated to get more accurate information. Cyclops⁶ is an interface between the camera and the mote. It configures the camera to provide low-resolution images for reducing energy consumption. If the target has been detected, it configures the camera to provide high-resolution images for analyzing. A Singh et al.⁷ introduced a two-tier system for sampling. The first tier provides low-fidelity global information about the environment. If any interest has been found, the second tier would provide high-fidelity information by mobile robots. Unlike the event trigger schemes that emphasize power conservation of sensors, the main difference of our approach is the energy consumption for the data mule (e.g. UAV or drone) that collects data from sensors by dynamically adjusting its environmental sensing frequency to reserve energy for flying back home.

In the model-based scheme, the sensor waking scheduling depends on mathematical models. R Jurdak et al.^8,9 proposed the uncertainty estimation model. Once uncertainty is greater than the absolute acceptable uncertainty (AAU), the system will enable GPS to obtain new location. Entracked¹⁰ formalized the tracking problem and minimized the power consumption to schedule the GPS on and off. RAPS¹¹ uses space-time history to estimate uncertainty and uses Bluetooth to reduce the position uncertainty. It increases the lifetime of smartphones by reducing GPS energy usage. S Sundaresan et al.¹² presented an event-driven scheme based on Markov decision process (MDP) theory to adjust the wake–sleep pattern of sensors. Z Zhuang¹³ proposed four principles to make energy efficient. They are Substitution, Suppression, Piggybacking, and Adaptation. In Adaptation, the framework would dynamically adjust the location sensing frequency when the battery level is low.

In the energy harvesting scheme, the sensor waking scheduling is based on remaining energy and the forecasted harvesting energy. There are many kinds of resources that could be transformed into energy and extend the system lifetime, for example, solar,^14–17 wind,^18–21 thermal,^22–25 and hybrid resources.^26,27 A Kansal et al.²⁸ proposed an energy model by considering the solar energy harvesting and energy consumption simultaneously. CM Vigorito et al.²⁹ introduced a model-free scheme without the need for a priori information about the harvesting source. J Kho et al.³⁰ designed decentralized control of the adaptive sampling algorithm. They formulated the adaptive sensing in a linear programming problem and solved using binary integer programming. Similar to the event trigger scheme, the model-based scheme and the energy harvesting scheme are also focused on the power consumption of sensors by adjusting the wake–sleep pattern based on different models. The main difference of proposed ARS algorithm is that our algorithm emphasizes the power consumption and energy reservation on UAV to guarantee RTH feature.

RTH guaranteed is an important scheme for doing drone sensing continuously by autonomy recharging automatically. RC Luo et al.³¹ proposed a power prediction algorithm and virtual spring model to determine the energy level of the robot and to the dock. YC Wu et al.³² introduced an automatic battery exchanging and charging scheme in the docking station. The battery-monitor-module sent a low-battery message to the robot if the voltage of the battery is lower than the threshold. The robot will move to the docking station to exchange battery automatically. A Ravankar et al.³³ designed a docking station manager to schedule multiple mobile robots according to their priority and location. The robots could access the docking station when their battery is below a certain threshold. A robot will get the highest priority if its battery power is just about to go off. MC Silverman et al.³⁴ presented the docking station, robot docking mechanism, and docking algorithm. When the battery voltage level is lower than the user-defined minimum level, the robot will do the docking procedure. Therefore, the robots could stay alive. We combine the idea of adaptive sensing and RTH guaranteed to form a new automatic and sustainable sensing. Instead of determining the level of the reserved energy for RTH based on user-defined or predefined power prediction model in the existing approaches, our proposed ARS algorithm dynamically tuned the reserved energy needed using NBC based on the route (e.g. a straight line or a turn) and different factors (e.g. a headwind or a tailwind).

ARS scheme

First, in section “Problem formulation,” the problem is formulated with a guarantee that a sensing drone will be able to return home. To make the article self-contained, we introduce our previously proposed ARS algorithm in section “ARS algorithm.” Next, we present a search algorithm for ARS to adapt its parameter settings in the optimal operating range in section “Parameter-tuning algorithm for ARS with NBC.”

Problem formulation

To conduct environmental sensing, a drone needs to fly with a constant speed V along a route $R$ which begins and ends in the same location. The length of $R$ is equal to $| R |$ . Power is consumed at $P_{F}$ per distance unit at $V$ . For a mission, there is $N$ number of sensing attempts. Each sensing attempt consumes $P_{S}$ power. For sensing, a drone needs to reserve $E$ amount of energy to guarantee RTH. The objective is to achieve the maximum number of sensing attempts $(N)$ with initial energy $(E)$ reserved the drone to RTH location while minimizing the oscillation in the spatial distance $(D)$ between sensing attempts. Thus, a sufficient condition must be obtained for the drone and is as follows

$E \geq P_{F} \times | R | + P_{S} \times N$ (1)

Next, equation (2) obtains the maximum $N$ allowed in a mission

$N = ⌊ \frac{E - P_{F} \times | R |}{P_{S}} ⌋$ (2)

In most of the environmental sensing applications, the minimum spatial distance, $δ$ , between two consecutive sensing attempts is given. In addition, the spatial distance, $D$ , for two consecutive sensing attempts needs to adapt based on the route length $(| R |)$ and the maximum number of sensing attempts $(N)$ . Therefore, $| R | / N$ gives the largest $D$ value based on $| R |$ and $N$ . However, $D$ cannot be less than the minimum spatial distance $(δ)$ which is required by the sensing application. Thus, the spatial distance, $D$ , for two consecutive sensing attempts is obtained in equation (3)

$D = \max (\frac{| R |}{N}, δ)$ (3)

In a real environment, different aspects and settings are needed to take into account. Although a drone may move at a constant speed $V$ , power consumption $P_{F}$ is different according to its route (e.g. a straight line or a turn) and under different factors (e.g. a headwind or a tailwind). From our previous experiments,³⁵ turns has a minimum effect on the power consumption which is negligible. However, wind direction can affect the power consumption of a drone which is noticeable. In addition, a drone often required to land (and then take-off) for an accurate environmental sensing reading results in additional power consumption.

Thus, the calculations of $P_{F}$ and $P_{S}$ must take into account the additional power consumed from the environmental factors (i.e. different wind directions) and the sensing procedures (i.e. landings and take-offs), respectively. In this study, we assume that the route $R$ and drone speed $V$ are assigned by a mission with the requirement for the drone to always RTH. Our objectives are maximizing the number of sensing attempts $N$ with as spatial uniformly distributed attempts as possible on the route.

ARS algorithm

We briefly describe the ARS¹ in order to make the article self-contained. The flowchart of the ARS scheme is shown in Figure 1. In equation (4), each considered factor is a function of distance (i.e. route length traveled). ARS scheme calculates the optimal number $(N (d))$ of sensing attempts in the remaining mission with a fixed traveled distance $d$ as follows

$N (d) = ⌊ \frac{(E (d) - P_{F} (d) \times (| R | - d)) \times β (d)}{P_{S} (d)} ⌋$ (4)

where $E (d)$ is the remaining energy after drone traveled $d$ distance; $P_{F} (d)$ is the average energy consumed by drone after $d$ distance at speed of $V$ ; $(| R | - d)$ is remaining distance of the route; $β (d)$ is a budget function (see equation (4)) that determines the ratio of the leftover energy allowed to be spent on sensing in the remaining mission (i.e. $0 \leq β (d) \leq 1$ ); and $P_{S} (d)$ is the average energy consumed for environmental sensing after $d$ distance.

Figure 1.

The flowchart of the ARS scheme.

Thus, $E (d) - P_{F} (d) \times (| R | - d)$ calculates the energy leftover after finish flying the entire route. The part of the leftover energy will be used for environmental sensing, that is, times the $β (d)$ budget function. Therefore, the part of the leftover energy for environmental sensing divided by the average energy cost per sensing $(P_{S} (d))$ is the optimal number of sensing attempt $(N (d))$ .

Notice that the greater the value of $β (d)$ , the more aggressive strategy resulted in sensing attempts. However, a greater $β (d)$ also tends to result in a bigger oscillation of the path distance between sensing attempts because there is not much energy reserved to accommodate unexpected power assumption encountered in the mission (e.g. flying against the wind).

To minimize the path distance oscillation between sensing attempts, as well as utilizing available energy in drone sensing, we define $β (d)$ as a linearly increasing function in the range of $β_{\min}$ and $β_{\max}$ , as shown in equation (5)

$β (d) = \frac{β_{\min} \times (| R | - d) + β_{\max} \times d}{| R |}$ (5)

where $β_{\min}$ and $β_{\max}$ are adjustable factors. The $β_{\min}$ is a conservativeness factor that limits the number of sensing attempts in order to save energy for potentially unexpected power consumption in the remaining mission. In contrast, $β_{\max}$ is an aggressiveness factor that promotes sensing attempts to utilize the available energy. The behavior of the ARS scheme is thus determined by the combination of the two factors, which we will investigate further in the next section.

Once the optimal number of sensing attempt is calculated, we can obtain the distance $(D (d))$ from the current sensing location to the next attempt after traveling $d$ distance by

$D (d) = \max (\frac{| R | - d}{N (d)}, δ)$ (6)

where the remaining distance of the route is given by $(| R | - d)$ , $N (d)$ is the optimal number of sensing attempt, and $δ$ is the minimum distance between two consecutive sensing attempts required by sensing application.

Parameter-tuning algorithm for ARS with NBC

In this subsection, we propose a search algorithm that combines NBC and BS for ARS parameter tuning. In the previous proposed ARS scheme, sufficient energy is reserved to guarantee for the drone to RTH. However, the scheme is not adaptive to any environmental changes (e.g. wind condition). Thus, there are a number of drawbacks in the previous scheme. First, the number of sensing attempts is not maximized when the energy is over reserved for RTH. Second, the spatial distance for two consecutive sensing attempts oscillated drastically when the remaining energy level fluctuated between the reserved energy level for RTH. The enhanced ARS parameters tuning algorithm dynamically adjusts energy reservation to optimize the number of sensing attempts and reduce oscillation of the spatial distance in those attempts. To address those issues, the proposed algorithm contains three phases:

Synthetic data collection (SDC). In the SDC phase, we conduct simulations using an exhaustive set of parameter settings, including $| R |$ , $β_{\min}$ , $β_{\max}$ , and the headwind rate $W$ . $| R |$ is set between 2000 and 4000 M. Both $β_{\min}$ and $β_{\max}$ are set between 0.05 and 1.0. The headwind rate $W$ is set between 0 and 100. We assume that the headwind is uniformly randomly distributed on the route, and we collect the synthetic data from the results of 100 simulation runs for each parameter configuration with a 95% confidence interval. Then, for each configuration, the ARS performance is deemed to be Success if the two conditions are met:

The mission completion (i.e. RTH) rate is greater than 99%;

The coefficient of variation (CV) of spatial distance between every two consecutive sensing attempts is lower than 0.1;

and the ARS performance is considered to be Fail otherwise.

2. Naive Bayes classifier (NBC). In the NBC phase, we first compute $P (Fail)$ by taking the number of Fail results over the number of parameter configurations used in the SDC phase, and we also obtain $P (Success) = 1 - P (Fail)$ . Next, the parameters are set according to a normal distribution for $| R |$ , $β_{\min}$ , $β_{\max}$ , and $W$ as follows. The mean and the variance of $β_{\min}$ are computed when the ARS performance is Fail in the synthetic dataset for each particular $β'_{\min}$ . With the obtained mean and variance values, the conditional probability of $P (β_{\min} | Fail)$ is approximated by fitting a Gaussian distribution. With each particular $β'_{\max}$ , $W'$ , and $| R |'$ , the same procedure is applied to the other affecting factors of $β_{\max}$ , $W$ , and $| R |$ . Similarly, when the ARS performance is Success, $β_{\min}$ , $β_{\max}$ , $W$ , and $| R |$ are computed for each particular $β'_{\min}$ , $β'_{\max}$ , $W'$ , and $| R |'$ , respectively. Finally, we obtain a set of Gaussian distributed approximation for $P (β_{\max} | Fail)$ , $P (W | Fail)$ , $P (| R | | Fail)$ , $P (β_{\min} | Success)$ , $P (β_{\max} | Success)$ , $P (W | Success)$ , and $P (| R | | Success)$ .

Therefore, for each particular parameter configuration $Θ = (β'_{\min}, β'_{\max}, W', | R' |)$ , the posterior for the classification as Fail is obtained by

$\begin{matrix} P_{Bayes}^{Fail} (Θ) = \\ \frac{P (Fail) P (β'_{\min} | Fail) P (β'_{\max} | Fail) P (W' | Fail) P (| R' | | Fail)}{P_{evidence} (Θ)} \end{matrix}$ (7)

and the posterior for the classification as Success is derived by

${}_{Bayes}^{Success}{(Θ)} = \frac{P (Success) P (β'_{\min} | Success) P (β'_{\max} | Success) P (W' | Success) P (| R' | | Success)}{P_{evidence} (Θ)}$ (8)

where $P_{evidence} (Θ)$ is a normalizing factor that can be obtained by

$\begin{matrix} P_{evidence} (Θ) = P (Fail) P (β'_{\min} | Fail) P (β'_{\max} | Fail) (W' | Fail (| R' | | Fail) \\ + P (Success) P (β'_{\min} | Success) P (β'_{\max} | Success) P (W' | Success) P (| R' | | Success) \end{matrix} (9)$ (9)

Finally, the NBC phase yields a prediction that the ARS performance under the configuration $Θ$ to be Success when $P_{Bayes}^{Success} (Θ) > P_{Bayes}^{Fail} (Θ)$ , and it predicts Fail otherwise.

3. BS. In this phase, we search for the optimal settings of $β_{\min}$ and $β_{\max}$ , given the headwind rate $W'$ and the route length $| R' |$ , using the classifier obtained in the NBC phase. We present the detailed algorithm in Algorithm 1.

Algorithm 1

The search algorithm in the BS phase

Require:

N

: the number of distinct

β_{\min}

and

β_{\max}

values in the synthetic dataset

β_{value} [N]

: all possible

β_{\min}

and

β_{\max}

values in increasing orderEnsure: The return values

(δ, γ)

are the optimal settings for

(β_{\min}, β_{\max})

in the ARS scheme given the headwind rate

W'

and the route length

| R' |

i = 0

;

j = N - 1

;

d = - 1

; 2: while true do 3:

k = ⌊ (i + j) / 2 ⌋

; 4: if

i \geq j

then 5: if

NBC (β_{value} [k], β_{value} [k], W', | R' |) = = Success

then 6:

d = k

; 7: end if 8: break; 9: else if

NBC (β_{value} [k], β_{value} [k], W', | R' |) = = Success

then10:

i = k + 1

;

d = k

;11: else12:

j = k - 1

;13: end if14: end while15: if

d < 0

then16: return

(β_{value} [0], β_{value} [0])

;17: end if18:

i = d + 1

;

j = N - 1

;

g = - 1

;19: While True do20:

k = ⌊ (i + j) / 2 ⌋

;21: if

i \geq j

then22: if

NBC (β_{value} [d], β_{value} [k], W', | R' |) = = Success

then23:

g = k

;24: end if25: break;26: else if

NBC (β_{value} [d], β_{value} [k], W', | R' |) = = Success

then27:

i = k + 1

;

g = k

;28: else29:

j = k - 1

;30: end if31: end while32: if

g < 0

then33: if

d = = 0

then34: return

(β_{value} [0], β_{value} [0])

;35: else36:

d = d - 1

; Goto Line 18;37: end if38: end if39: return

(β_{value} [d], β_{value} [g])

;

Specifically, we first conduct a BS to obtain the maximum value $δ$ among all possible $β_{\min}$ and $β_{\max}$ values, such that the parameter configuration $Θ = (δ, δ, W', | R' |)$ can result in a prediction of Success based on the classifier obtained in the NBC phase (Lines 1–14). There are two cases:

(a) If the search cannot find a solution, both $β_{\min}$ and $β_{\max}$ are set to the smallest $β_{\min}$ and $β_{\max}$ values in the synthetic dataset (Lines 15–17). In this case, the sensing strategy is kept as conservative as possible to guarantee the sensing drone always RTH.

(b) If there exists a $δ$ that is the maximal one yielding a Success prediction, we conduct BS again among all possible $β_{\max}$ values (i.e. $δ < β_{\max} < 1$ ) in the synthetic dataset, and we obtain the maximal value $γ$ that can yield a prediction of Success for the configuration $Θ = (δ, γ, W', | R' |)$ based on the classifier obtained in the NBC phase (Lines 18–31).

In contrast, if there are no $γ$ values that can yield a classification result of Success for the parameter configuration $Θ = (δ, δ, W', | R' |)$ , we replace $δ$ with a new value $δ'$ , which is the greatest value among all possible $β_{\min}$ and $β_{\max}$ values in the synthetic dataset such that (1) $δ'$ is smaller than $δ$ and (2) the parameter configuration $Θ = (δ', δ', W', | R' |)$ yields a Success classification result. Then, the search algorithm repeats the same process to find the $γ$ value (Lines 32–38).

Evaluation

The performance of the enhanced ARS algorithm with NBC and BS is evaluated in this section. The results show the effects under different environmental scenarios (i.e. wind directions) and mission requirements (i.e. the number of sensing attempts and route length). Two performance metrics are compared as follows: (1) RTH rate ratio of a mission is completed and drone returns to home and (2) CV of distance for two consecutive sensing attempts.

Simulation is implemented in Ruby under macOS 10.11 on an iMac (27-inch, Late 2012) with 3.4 GHz Intel Core i7 and 32 GB 1600 MHz DDR3 RAM. For the evaluation, our simulation settings follow Parrot AR Drone 2.0 (AR.Drone 2.0. Parrot new wi-fi quadcopter; http://ardrone2.parrot.com) technical specifications as follows: (1) the battery capacity is 2000 mAh with voltage of 11.1 V, (2) the maximum speed is 5 m/s, and (3) the power consumption for traveling at the maximum speed is 55.5 W. When the drone travels in a headwind direction, the power consumption is assumed to be doubled. The position of headwind is randomly placed on the route. The spatial granularity of moving distance is set to 1 s $(δ = 5 m)$ .

In addition, multiple sensors are fitted on the drone. Power consumption for each sensor is 3 mW for a temperature and humidity sensor (Sensirion SHT15; http://www.sensirion.com/en/products/humidity-temperature/humidity-temperature-sensor-sht1x/), 300 mW for a $C O_{2}$ sensor (Alphasense NDIR IRC-A1; http://www.alphasense.com/index.php/products/ndir/), 80 mW for an $O_{3}$ sensor (SGX Sensortech MICS-2610; http://www.cdiweb.com/ProductDetail/MICS2610/333414), and 450 mW for a PM2.5 sensor (Shinyei PPD42NS; https://www.dropbox.com/s/zluzrn4ikumusjd/PPD42NS.pdf). Thus, the total power consumption for all sensors is about 49.98 W for each sensing attempt.

Therefore, the simulation parameters are set according to the specifications of drone and sensors as follows: the drone fly at a constant speed (V = 5 m/s), the minimum spatial distance $(δ = 5 m)$ , the power consumption for the drone per distance unit at $V$ (P_F = 55.5 W), and the power consumption per sensing attempt (P_S = 49.98 W). We varied the length of route $(| R |)$ , the number of sensing attempts $(β_{\min} and β_{\max})$ , and headwind rate in different experiments to show the effectiveness of the proposed algorithm. Multiple simulation runs (100 runs per setup) with different seed numbers were conducted for each scenario and collected data were average over those runs with 95% confidence intervals. The evaluation results are discussed in the following sections.

Effect on number of sensing attempts ( $β_{\min}$ and $β_{\max}$ )

In this study, the length of route $(| R |)$ is equal to 3000 m. The rate of headwind on the route is set to 50%. We varied the minimum number of sensing attempts $(β_{\min})$ and the maximum number of sensing attempts $(β_{\max})$ from 0% to 100%. The results are presented in Figures 2 and 3. When $β_{\min}$ is less than or equal to 60%, a 100% RTH rate is achieved by the proposed scheme. As $β_{\min}$ increases, the performance of RTH rate decreases. Since it is hard to predict the additional power consumption in a mission due to environmental conditions, smaller the $β (d)$ results in better RTH rate to guarantee the drone always RTH.

Figure 2.

Effect of $β_{\min}$ and $β_{\max}$ on RTH rate.

Figure 3.

Effect of $β_{\min}$ and $β_{\max}$ on CV of distance for two consecutive sensing attempts.

The CV of distance for two consecutive sensing attempts are presented in Figure 3. This shows consistent results of CV with an increase in $β_{\max}$ . However, as $β_{\min}$ increases, the performance of CV decreases because a low CV value represents that the distance of two consecutive sensing attempts is more uniformly distributed. In addition, the results show a performance trade-off between RTH and CV with $β_{\max}$ and $β_{\min}$ . In most applications, drones are expected to RTH. Thus, it is required that RTH rate be 100% with highest $β_{\min}$ and $β_{\max}$ as possible. For our simulation settings (i.e. route length is 3000 m with headwind rate is 50%), the ideal $β_{\min}$ and $β_{\max}$ values are 50% and 70%, respectively.

Effect of headwind rate

In this study, we set the mission route length $(| R |)$ equal to 3000 m with different headwind rates. To show the improvement of the proposed technique, a baseline scheme with consistent power consumption and fixed spatial distance derived from equation (3) is compared. Furthermore, $β_{\min}$ and $β_{\max}$ values are varied (0.3, 0.7), (0.5, 0.7), and (0.5, 0.9) for the proposed ARS scheme. The results of RTH and CV are presented in Figures 4 and 5, respectively.

Figure 4.

Effect of headwind rate on RTH ratio.

Figure 5.

Effect of headwind rate on CV of distance for two consecutive sensing attempts.

In Figure 4, the results of the ARS scheme with three different $β_{\min}$ and $β_{\max}$ settings outperform the baseline scheme in terms of RTH rate. The reason is that the headwinds produce unforeseen power consumption for the baseline scheme. The ARS scheme is able to adapt the additional power consumption to improve the RTH rate. However, as we continue to increase the headwind ratio, the ARS scheme is also unable to guarantee drone always RTH. Compare the three different settings of the ARS scheme, $β_{\min}$ , and $β_{\max}$ values set equal to (0.3, 0.7) yield best RTH ratio. However, between the settings (0.5, 0.7), and (0.5, 0.9), RTH ratio only improves marginally as $β_{\max}$ decrease. The observation confirms our previous results which RTH rate decreases as the $β_{\min}$ increases.

In Figure 5, the results of the CV performance show that the baseline scheme is able to achieve better results when the upwind is less than 50%. As the upwind increases to greater than 50%, the ARS scheme outperforms the baseline scheme. In addition, the ARS scheme produces more sensing attempts with larger $β_{\min}$ and $β_{\max}$ values (i.e. 0.5, 0.9 setting). However, as the headwind rate increases, the number of sensing attempts for all three settings decrease to recover the additional power cost due to fly headwind direction. Nevertheless, the ARS scheme is able to adapt the headwind ratio without drastically reducing the performance of the CV and the number of sensing attempts.

Effect of route length $(| R |)$

In this study, we vary the route length $(| R |)$ to show the effect on RTH rate and CV performance. The results are presented in Figures 6 and 7. First, the ARS scheme is able to adapt as $| R |$ increases to more than 3000 m. The baseline scheme is unable to guarantee the RTH feature when $| R |$ is longer than 3000 m due to fixed spatial distance of sensing attempts and power consumption. The ARS scheme with smaller $β_{\min}$ and $β_{\max}$ values has less power consumption in a number of sensing attempts. As a result, a higher RTH rate compares to the other two settings for ARS scheme.

Figure 6.

Effect of route length $(| R |)$ on RTH ratio.

Figure 7.

Effect of route length $(| R |)$ on CV of distance for two consecutive sensing attempts.

In Figure 7, the baseline scheme shows a higher number of sensing attempts and the worst CV performance as $| R |$ increases. Again, the ARS scheme produces more sensing attempts with larger $β_{\min}$ and $β_{\max}$ values. However, the number of sensing attempts for the ARS scheme with all three settings decrease after $| R |$ longer than 3000 m. In fact, most of the mission cannot be complete when $| R |$ reaches the maximum travel distance of a drone. Nevertheless, the ARS scheme results in better CV performance with a smaller $β_{\min}$ setting.

Effect on parameter-tuning algorithm

In this study, the NBC and BS select an appropriate parameter pair ( $β_{\min}$ , $β_{\max}$ ) for ARS after each sensing attempt. ARS(0.5, 0,7) is one of the optimal parameter pairs when the route length $| R |$ is 3000 m and 50% of the route is against the wind from observation in Figures 2 and 3. Based on the previous evaluation settings, we also evaluate ARS(0.5, 0.9) and ARS(0.3, 0.7) to illustrate the comparison. Support vector machine (SVM) is a common and famous technique in the machine learning field. Therefore, we not only compare the performance between the ARS and ARS+NBC but also compare them with ARS+SVM. The BS has been applied to both ARS+NBC and ARS+SVM. Then, we implement NBC by ourselves and use LIBSVM (LIBSVM; https://www.csie.ntu.edu.tw/∼cjlin/libsvm/) with RBF kernel in SVM scheme.

From the results shown in Figure 8, we observe that none of ARS schemes could return to home when the route length $| R |$ is greater than 3300 m. The lower conservativeness and aggressiveness factor could increase RTH rate. The ARS+NBC and ARS+SVM could return to home in all cases due to dynamically adjust parameters. The performance of ARS+SVM is better than ARS+NBC when $| R |$ is less than 2400 m from Figure 9. Although the performance of ARS+SVM is better than ARS+NBC, ARS+SVM is more complex than ARS+NBC. From the results shown in Figure 10, it shows the time spent by schemes per round. The cost of ARS+SVM is greater than ARS+NBC 50 times on average. The drone will spend more energy when using ARS+SVM.

Figure 8.

The RTH rate of the ARS, NBC, and SVM scheme under different route lengths $| R |$ when the headwind rate is 50%.

Figure 9.

The coefficient of variation of spatial distance between two consecutive sensing attempts achieved by the NBC and SVM scheme under different route lengths $| R |$ when the headwind rate is 50%.

Figure 10.

The time cost of NBC and SVM scheme under different route lengths $| R |$ when the headwind rate is 50%.

Another environmental factor is headwind rate. Figure 11 shows that all ARS schemes still fail to return to home when headwind rate is greater than 60%. Either ARS+NBC or ARS+SVM can survive till the end. From the results shown in Figure 12, both of them have the similar CV performance. The cost of ARS+SVM is greater than ARS+NBC 29 times on average shown in Figure 13. Compared with ARS, ARS+NBC and ARS+SVM could provide great performance in most cases. ARS+NBC not only provides good performance but also costs lower energy. Therefore, ARS+NBC is more suitable for drone sensing due to the energy issue.

Figure 11.

The RTH rate of ARS, NBC, and SVM scheme under different headwind rates when the route length $| R |$ is 3000 m.

Figure 12.

The coefficient of variation of spatial distance between two consecutive sensing attempts achieved by the NBC and SVM scheme under different headwind rates when the route length $| R |$ is 3000 m.

Figure 13.

The time cost of NBC and SVM scheme under different headwind rates when the route length $| R |$ is 3000 m.

Concluding remarks

UAVs have been used as data mule for environmental sensing applications. In this article, an extension of ARS algorithm with a parameter-tuning algorithm that combines NBC is proposed. The proposed scheme is able to effectively identify appropriate parameters for ARS. By combining the NBC algorithm, the enhanced ARS scheme not only survives till the end of the mission in all test cases but also yields more cost-effective in terms of computational complexity than the other machine learning–based schemes. The comprehensive evaluation results showed the enhanced ARS scheme is able to adapt environmental factors (i.e. follow/against wind and headwind rate) and improve the number of sensing attempts by dynamically adjusting parameter settings in a mission while conserving enough energy for the drone to RTH. The proposed scheme is simple, reliable, and effective in mitigating the oscillation of spatial distance between consecutive sensing attempts; it can go a long way in facilitating drone sensing for environment monitoring in the future.

Footnotes

Handling Editor: Pietro Manzoni

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research,authorship,and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research,authorship,and/or publication of this article: This research was supported in part by the Ministry of Science and Technology of Taiwan and Academia Sinica under grants MOST 105-2221-E-001-016-MY3,AS-105-TP-A07,and AS-104-SS-A02.

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