In recent years, physical health monitoring has received extensive attention. Respiratory rate (RR) monitoring is one of the crucial indicators for evaluating the physiological status [1] , especially in scenes of doctors diagnosing respiratory diseases [2] , such as chronic obstructive pulmonary disease (COPD), asthma, interstitial lung disease, pulmonary sarcoidosis, pneumoconiosis [3] , and sleep apnea [4] . The recent advances in artificial intelligence and big data technology led to the development of robot-based health monitoring systems [5] [6] . Health monitoring robots could help us understand physical and mental health [7] [8] [9] [10] , which are widely applied to medical human-robot interaction scenarios, intervention for children with autism spectrum disorder (ASD) [11] , efficient human activity recognition [12] , and other fields of healthcare. extremely difficult situations such as the high risk of crossinfection, shortage of protective clothing, and high work pressure. Traditional physiological monitoring equipment is difficult to meet the needs of this unusual scenario. There is an urgent need for a robot system with non-contact physiological parameter detection and remote interaction functions to be deployed into the epidemic area to help epidemic prevention and control. The outbreak of COVID-19 has accelerated the development of healthcare-related robots [13] , which have been widely used in non-contact ultraviolet (UV) surface disinfection, remote interaction [14] , and mental health improvement [15] .
In the medical field, mobile robots usually have severely limited power supplies and low computing power. It is challenging to complete tasks that require intensive computing by themselves [16] [17] . It poses a huge challenge to the requirements of computing power and low latency. The increasing interaction between users and clouds may cause delays in data transmission and service requests [18] . Delayed diagnostic response directly affects medical safety and even patients' life or health, especially for patients diagnosed with acute diseases. Edge computing is applied to the healthcare field [19] , which effectively solves data transmission and computing resource allocation. In recent years, deep learningbased solutions have been widely used in many edges [20] .
In traditional medical scenarios, mobile robots could generally support ward inspections and remote interactions, but they could not monitor physiological indicators in real-time. In the medical scene of non-contact monitoring of physiological indicators, the mobile robot needs to track the target by the video frames captured by the camera mounted on the mobile robot at a near real-time speed. Moreover, mobile robots use video frames to obtain physiological signals and assess physical health. These mobile robots have limited resources and could not meet the needs of unique medical scenarios. In such a situation, task decomposition of the lightweight target tracking network with physiological monitoring is an effective way to handle the issues.
To overcome the above problems, we design a Deep Learning-based Respiratory Rate Monitoring System (DLRRMS) to decompose the task of a lightweight target tracking network with physiological monitoring. The network consists of three parts: robot layers, edge layers, and cloud layers. Robot layers are applied to complete the calculation task of the convolutional layer. Edge layers are used to calculate the similarity between the candidate area and the target, and extract Spatio-temporal features. Cloud layers are adopted to process breathing signals. We summarize our main contributions as follows.
i) We have achieved a safer RR monitoring system using a three-tier architecture: robot layers, edge layers, and cloud layers. We decompose the task into a three-tier architecture of a lightweight network according to the computing resources of different devices. Heavy computing tasks are put on edge layers. Light computing tasks are placed on robot layers and cloud layers.
ii) We have adopted a lightweight deep learning network to extract respiratory signals and provide sufficient information for doctors to achieve rapid diagnoses.
iii) We have collected thermal imaging face video data of 15 subjects, such as medical staff, researchers, and patients in the hospital, and verified that the method proposed in this paper still works when the face is blocked or the head moves unconsciously.
The paper is organized as follows. Section II presents the related works of respiratory rate monitoring methods (including contact monitoring methods and no-contact methods), robotbased health monitoring, and deep learning on edge. Section III describes our RR monitoring system using a three-tier architecture, including thermal infrared facial features extraction based on robot layers, Spatio-temporal features tracking at edge layers, respiration signals extraction and preprocessing at cloud layers. Section IV discusses the evaluation results and our conclusions in Section V.
The contact monitoring method collects breathing signals through contact sensors. Contact monitoring devices, such as conventional electrocardiograms (ECG) [21] , pulse oximetry [22] , and innovative wearable devices [23] , are currently available in the fields of medicine [24] . They require physical contact between skin and electrodes, infrared sensors, or pressure sensors [25] . As for RR monitoring, they need patients to go to the hospital or wear special equipment, for example, a thermistor [26] , a spirometer [27] , and a breathing belt sensor [28] . They are usually based on measuring one of the following parameters: breathing sound [29] , breathing airflow, breathingrelated chest or abdominal movement, and breathing carbon dioxide emissions. Although traditional methods could effectively monitor the physiological parameters of the human body, most methods are cumbersome.
The non-contact monitoring methods include visible light technology, Doppler effect technology, infrared thermography technology. Visible light technologies mainly include remote PPG (rPPG). The technology of rPPG mainly collects face videos remotely through a visible light camera to obtain PPG signals [30] [31] . However, the contaminated motion artifact (MA) in remote PPG (rPPG) signals seriously interferes with physiological indicators' estimation. Changes in blood flow caused by exercises are the leading cause of MA. So far, many noise reduction techniques have been proposed, such as independent component analysis [32] , wavelet denoising, and empirical mode decomposition.
Radar technology, electromagnetic induction technology, and wifi technology [33] monitor RR through the Doppler effect principle. Radar technology uses bio-radar to transmit to the human thoracic cavity at a wavelength λ, which generates an echo signal due to the chest cavity's undulating motion. There is a phase difference between the echo signal and the transmitted signal, and the phase difference will change with the displacement of the thoracic cavity. Respiration signals could be extracted from echo signals for respiration rate estimations. In normal physiological activities of the human body, breathing motion may cause changes in the lungs' conductivity. Electromagnetic induction technology could be applied to detect tissue conductivity changes to monitor the RR [34] .
With the emergence of a new generation of detectors, nearinfrared and mid-infrared regions have also been used for medical thermal imaging [35] . Thermal imaging, also known as infrared thermal imaging (IRT), a remote non-contact monitoring method, has become a promising monitoring and diagnostic technology in the medical field [36] . RR monitoring technology based on thermal imaging mainly collects thermal imaging face in successive frames and tracks the ROI (such as nose and carotid artery) to obtain the breath signals. G. Scebba et al. proposed a novel method based on multispectral data fusion that aims at estimating RR and addressing apnea detection tasks [37] .
Contact monitoring equipment needs to be in direct contact with the human body. Prolonged contact would cause much discomfort to the tested body. Non-contact physiological health monitoring has the characteristics of non-interference, noninvasiveness, and remote control. In non-contact monitoring methods, methods other than thermal infrared are susceptible to environmental factors, such as light, noise, and magnetic fields. IRT has the characteristics of high blur and unclear contours, so it is difficult to track the ROI to extract physiological signals. In previous research, infrared face ROI could not be tracked accurately when the subject spoke, head moves or face is partially obscured. Also, it is rarely considered to use deep learning methods to track infrared face ROI to extract physiological signals.
Due to the rapid development of artificial intelligence technology and the convenience of remote interaction with robots, health monitoring robots are widely used in the fields of medicine [8] body sensor networks (BSNs) in medical human-computer interaction scenarios to improve the performance of fusion decision-making [39] . Al-Taee et al. designed a new eHealth platform that incorporates humanoid robots to support emerging multidimensional care methods to treat diabetes [10] . Social robots are applied to intervention research on children with ASD [11] . The purpose of that research is to improve the social skills of children with ASD. The children interact with caregivers and robots in a three-way interaction 30 minutes per day to complete activities related to emotional storytelling, opinion acquisition, and sorting.
At present, most of the robot research in the field of public health is aimed at non-contact ultraviolet (UV) surface disinfection, remote interaction, improvement of mental health [13] [14] [15] . There are few reports of real-time health monitoring robots for special public health scenarios of COVID-19. They are deployed in different wards to reduce the dare of frontline medical staff.
As miniaturization continues and computing power increases, the edge becomes more powerful. It paves the way for autonomous decision-making in the periphery. Ning et al. [40] proposed a transmission strategy based on deep learning in edges to reduce waiting time and improve the throughput of data transmission between vehicles. C. Zhang et al. proposed a novel cyber-physical systems (CPS) edge computing platform based on joint learning [41] . They trained machine learning models in a trusted joint learning framework to realize smart services and ensured the trustworthiness of smart services that used joint learning frameworks to test and monitor CPS behavior. W. Yang et al. designed a finger vein recognition system with template protection based on deep learning to improve its security [42] . Due to the limited processing power of existing edge nodes, H. Li et al. [20] designed a novel offloading strategy to optimize the performance of the internet of things (IoT) deep learning applications through edge computing. T. Zhang et al. designed a voting strategy so that fog nodes can be selected as coordinators based on distance and computing power indicators to help speed up the training process [43] . Based on distributed deep learning, Z. Tian et al. [44] designed a distributed deep learning system for web attack detection on edges. J. Chen et al. [45] adopted a distributed intelligent video surveillance (DIVS) system using deep learning (DL) algorithms and deployed it in an edge computing environment to reduce the huge network communication overhead. T. Zhang et al. proposed a fog-based democratic, collaborative learning program [46] , which used fog to obtain a deep learning model with good performance in a cloud-free IoT environment and reduced the data locality problem of each fog node.
In medical scenarios, higher real-time performance is required. A large number of interactions between users and the cloud may cause communication delays. It would lead to medical safety accidents and even affect the patient's health diagnosis or life safety, especially for patients diagnosed with acute disease. In this case, we not only need to consider realtime performance but also the accuracy of physiological indicators. Only after both of them meet the requirements simultaneously, it becomes possible to provide doctors with decision-making assistance in real-time scenarios.
A. Overall framework The system architecture for RR monitoring is shown in Fig.1 . We employ a lightweight computing architecture to divide the different computing tasks into three-tier architecture: robot layers, edge layers, and cloud layers, which realize real-time calculation of RR. Respiration rate calculation tasks include facial feature extraction, Spatio-temporal features tracking, respiratory signal extraction and preprocessing. We decompose respiratory rate calculation tasks into robot layers, edge layers, and cloud layers, respectively.
We deploy robot layers to mobile robots. Suppose there are N mobile robots. Each mobile robot is responsible for collecting infrared face videos. Each video lasts for one minute. Moreover, each video contains m picture frames. We regard the feature extraction task of m picture frames as a task. We stipulate that a robot can only handle one subtask. One minute picture frames are divided into K subtasks for feature extraction by CNN. Each subtask is calculated on the corresponding robot. The process of decomposing the i-th task of robot layers into several subtasks is described as
Where K subtaskR is the k-th subtask of robot layers, and KN  .
means that the i-th robot is not idle. Feature extraction is regarded as mapping the original image features to another feature space. This process could be described as
Where () Ft and '( ) Ftare the original feature and feature after mapping at time t, respectively. () x  is a mapping function, including an activation function of ReLU, and dimensionality reduction and compression by a max pool.
We deploy the task of facial feature extraction to robot layers. Robot layers adopt a siamese network to extract facial features. The siamese network consists of two lightweight convolutional neural networks (CNN) with five convolutional layers, ReLU layers, and Pooling layers. One CNN is used to extract features of searched image Z, and the other CNN is used to extract features of sample image X. They are prepared for the next layers to measure the similarity and track Spatio-temporal features.
In this case, Z is a picture containing an infrared face. Moreover, X is the target area of interest in image Z, such as the nose. One input of the siamese network is a sample image X pre-selected by the user, and the other input is a larger search image Z.
We deploy the task of Spatio-temporal features tracking to edge layers. Suppose there are M edges. We use these idle edges to decompose similarity calculation tasks. The process of decomposing the similarity calculation task is described as
Where j taskE is the j-th similarity calculation task of edge layers. We deploy edge layers to edges. We adopt edge layers to calculate the similarity between searched image Z and sample image X to track face ROIs when robot layers complete a feature extraction of Z and X. By measuring the similarity between the sample image X and each part of the search image Z, edge layers could give a similarity score map. The target is located and tracked according to the similarity score map. According to the maximum value of similarity, we could locate and track the nose ROI. Besides, in order to reduce the computational cost, the process of calculating the similarity score of each sector could be replaced with only one crosscorrelation layer by a fully convolutional network (FCN) [48] , which could accept any size image as input.
The fully-convolutional siamese (SiameseFC) network [49] based on a siamese network achieves the similarity evaluation of the current target and historical candidate target [50] . Accurately tracking face ROI is one of the key factors in obtaining respiratory signals. We use the SiameseFC network to track thermal imaging face ROI to ensure the accurate extraction of the temporal-spatial features and get high-quality breathing signals. SiameseFC network is used to evaluate the similarity between the current frame X and the search image Z. 
We deploy the task of respiration signal extraction and preprocessing to cloud layers. Once the face ROI information in a frame is obtained from edge layers, respiratory signal feature extraction tasks are decomposed at robot layers. After the respiratory signal feature extraction of one minute is completed, initial respiration signals are obtained. We get the respiration rate by preprocessing the initial respiration signal. Respiratory signal preprocessing includes detrending, normalization, and Butterworth filtering. 
Respiratory signal extraction is mainly to convert the face ROI into a gray image and then calculate the gray image's average pixel. The tasks of calculating the average pixel are implemented at cloud layers. Suppose there are L clouds at cloud layers. Tasks of calculating the pixel average are divided into L subtasks, which are calculated in different clouds.
During human breathing, due to thermal fluctuations in nostrils ROI, or airflow under the nostrils [26] [51] , the pixel intensity of the infrared video frames changes. Assuming that at time t, infrared face ROI of the t-th frame is converted into a grayscale image. The average pixel value of the grayscale image ROI is Since respiratory signal processing requires minimal computing resources, we process the signals through clouds. 
Where m is the total number of frames of a thermal infrared video.
The initial respiratory signal itself has a certain degree of oscillation, and low-frequency components may also affect the respiratory signal. In addition, due to the instability of the signal acquisition device and the sensitivity to interference from the surrounding environment, this often causes the signal to deviate from the baseline over time. The entire process of deviating from the baseline over time is called the "trend-term" of the signal. It would affect the quality and accuracy. The initial respiratory signals are detrended using a technique based on a smoothness priors approach [52] .
Secondly, the respiratory signal needs to be normalized. At present, there are many methods of data normalization, which could be divided into linear methods (such as extreme value method and standard deviation method), polyline methods (such as trifold method), and curvilinear methods (such as seminormal distribution). We adopt the following approach to normalize the respiration rate signal [52] .
Where  is a standard deviation,  is the mean of the original signal, SN is the signal before normalization, and ' SN is the signal after normalization.
In the RR monitoring method based on PPG, frequency domain features are also widely used to obtain heart rate information. This method usually uses a bandpass filter to obtain signals in the frequency range related to heart rate. The normal RR is 9-42 bpm, and the corresponding frequency band is 0.15-0.7 Hz. We use a fast Fourier transform (FFT) to convert the time-domain signal into the frequency domain. We retain data from 0.15 to 0.7 Hz through bandpass filtering and set the data in other frequency ranges to zero. The noise frequency could be eliminated in this way.
Moreover, frequency domain information useful for respiration rate analysis should be extracted. The waveform of breathing is relatively stable, and it corresponds to a lowfrequency signal. We decompose the original signal to achieve the purpose of denoising. The low-frequency part is retained, and the high-frequency part is filtered out. Butterworth filters have the maximum flat amplitude characteristic in the passband, and the amplitude in the positive frequency decreases monotonically with increasing frequency [53] . It is usually used for low-pass filtering, which could filter out the noise of respiratory signals. Butterworth filter is defined as
Where p  and  are the upper and lower cut-off frequencies of the passband, and N is the Butterworth filter's order.
After signal preprocessing, initial breathing signals are obtained. We need to detect peaks in the initial breathing signal and eliminate false peaks. The signal of RR peaks always fluctuates within a specific range. Moreover, the peak point should satisfy two properties: i) its position is near the maximum amplitude point in the current cycle; ii) its amplitude is greater than other points in its neighborhood. We only need to find such a point.
If the peaks at points A and B are equal, and they both satisfy two conditions above, but only one of them could be used as a peak. We mark the first occurrence as the default peak. The peak detection algorithm detects the peaks of the preprocessing signal and marks the peak information according to the above principle. An example of RR calculation is shown in Fig.3 . Due to various factors, some erroneously detected peaks may still be retained after preprocessing respiratory signals. These erroneous peaks need to be eliminated. We set an amplitude threshold to eliminate false peaks. The main steps for removing false peaks are the following.
i) After eliminating the peaks in 1 2, , ,
that are less than zero, the candidate peak position information
M is the total number of peaks after the filtered signal is less than zero. N is the total number of peaks of the filtered signal. Due to the influence of low-frequency signals, error peaks different from the breathing signal would be generated. The value of these peaks is less than zero.
ii) Calculate average peak amplitude avg_value_peaks in the candidate peaks by formula 9. iii) Calculate peak threshold low_value_peak according to formulas 9 to 10. If the amplitude value of candidate peaks is greater than or equal to low_value_peak, one breath is accumulated. _ _ _ _ _ _ * low value peak avg value peaks avg value peaks  = − (10) ε is an amplitude parameter (adjust the ε through experimentation) during the process of error peak detection.
Suppose peak_num is the number of peaks obtained after removing the wrong peaks. Then we mark the index of the first peak and the last peak as peak_start and peak_end, respectively. The average distance between two adjacent peaks is __ avg dis peak . Suppose the total number of frames of thermal infrared video acquired in one minute is total_frame. The final respiration rate is calculated as follows [54] . _ ( _ _ ) _ _ _ peak start total frame peak end RR peak num avg dis peak
Since the breathing information [0, _ ] peak start and [ _ , _ ] peak end total frame is not considered, the number of breaths in this part needs to be considered.
In the Second Affiliated Hospital of Anhui Medical University, medical staff participated in collecting clinical data. Fifteen healthy subjects were recruited. They are between 20 and 31 years old, and their weight between 46 and 105 kg. Participation in the study was voluntary, and all participants provided informed consent. The local ethics committee approved this study. 
The robot layers consist of many mobile robots. There are three cameras and a display on a mobile robot. Two visible light cameras are on the bottom (Logitech HD Webcam C310) and top of the robot (c922 Pro Stream Webcam). The visible light camera on the top enables interaction with subjects, which is designed to provide a view for robot navigation. Another thermal infrared camera (Guide Sensmart IPT640) on the top is used to collect thermal infrared videos. The wavelength range of this camera is 8~14 μm, the temperature measurement range is -20 to 150 degrees Celsius, and the working environment temperature is -10 to 50 degrees Celsius. The resolution of the three cameras is 640*480 pixels.
The computing tasks of edge layers are undertaken by a workstation, which simulates the computing power of the cloud. Its configuration is Intel (R) Core (TM) i7-8565 with main frequency 1.8 GHz and highest turbo frequency 4.6 GHz, NVIDIA Geforce MX150, and RAM 8GB.
The computing tasks of cloud layers are implemented by a workstation with Intel (R) Core (TM) i7-10510, main frequency 1.8 GHz and highest turbo frequency 2.30 GHz, and RAM 16.0 GB.
The architecture is implemented by python language. We have performed different subtasks in cloud layers and edge layers on the workstation's multi-core to achieve the effect of decomposing computing tasks. Subtasks and each layer communicate through interfaces to exchange data and compete for shared resources.
We collected data in an environment with a temperature of 23-26°C. We started collecting data on March 14th. The amount of data collected per day was 5 to 30 minutes. Subjects were allowed to perform unconscious head movements in the process of data collection. As of April 14th, we collected a total of 305 minutes of data. Due to equipment and subjects, a portion of the data collected was invalid. After removing invalid data, 274 minutes of useful video was used for our experiment.
We have designed three experiments to evaluate architecture performance, consistency, and accuracy of DLRRMS, respectively. Firstly, the purpose of our first comparative experiment is to analyze the differences between the "Robot+Edge+Cloud" architecture of ours, the "Edge+Cloud" architecture, and cloud architecture. Moreover, we use time costs and system utility to evaluate the performance of each architecture. Time costs are composed of two parts: communication time costs and computation time costs. The former refers to network delay and time costs of data exchange between subtasks. The latter refers to the computational cost of performing calculation tasks related to RR calculation at robot layers, edge layers, and cloud layers. In the process of computing task decomposition, we use the amount of decomposed tasks to evaluate system utility. Our goal is to maximize the tasks decomposed per unit time. It is described as
is an average utility of t-th edge at time t, () i Et refers to whether the i-th edge is idle at time t.
On this basis, we have explored the impact of task arrival factors (TAF) on system utility. TAF is a ratio between the number of frames arrived and 1500 frames. We regard a queue of 1500 frames as a task. We adopt TAF to explore the impact of different subtask sizes on system utility.
Where NFA is the number of frames arrived. Secondly, the purpose of our second comparative experiment is to evaluate the accuracy among advanced methods and DLRRMS of ours. Advanced methods include DLRRMS without eliminating erroneous peaks (DLRRMS-EEP), Gaussian window (GW) [30] , and frequency domain analysis method (FDAM) [55] . DLRRMS-EEP is a method of DLRRMS without steps to eliminate error peaks. The purpose is to evaluate the effectiveness of false peaks elimination. GW is a scheme with a fixed width of the Gaussian window to process the respiratory signal after Butterworth filtering. FDAM is a method of converting time-domain signals into frequency domains to calculate RR. We use mean absolute error (MAE), root means square error (RMSE), and mean square error (MSE) to evaluate the performance of DLRRMS. MAE represents the average value of the absolute error between the predicted value and the observed value. RMSE represents the sample standard deviation of the difference between the predicted value and the observed value, which illustrates the degree of dispersion of the sample. MSE is the square of RMSE.
the i-th respiratory rate calculated according to the method proposed in this paper, m is the total number of respiration data. Thirdly, the purpose of our third comparative experiment is to evaluate the consistency between the respiration rate monitoring by advanced methods and the real respiration rate.
The consistency evaluation usually uses Bland-Altman. The problem of comparing two detection methods is often faced in clinical research. For example, A is a classic method, and B is a new method. It is by the 95% consistency limit of the measurement results of the two methods. The average of ground truth and predictive value is the horizontal axis. We draw a scatterplot and mark the 95% consistency limit. Finally, combining with the maximum error allowed by clinical practice, it is concluded whether the two methods are consistent.
To make our experimental results reproducible, the codes for monitoring respiration rate are available at https://github.com/1286705494/Non-contact-RR-monitoring.
We have done simulation experiments to simulate different numbers of robots, edges, and clouds to decompose calculation tasks. It aims to explore the impact of different architectures on time costs and system utility.
The experimental results of time costs are shown in Table 1 . One breathing signal is obtained by calculating 1500 picture frames through our RR monitoring system. We regard this process as a task. When NR=1, NE=1, and NC=1, the cost of convolution operation, similarity calculation, signal process, communication time costs, and computation time costs are 2.255 ms per frame, 27.483 ms per frame, 0.78 seconds (for processing one-minute length respiratory signals), 12.86 seconds, 58.25 seconds, respectively. "Robot +Edge+ Cloud" (REC) architecture could ensure the real-time monitoring of respiratory rate. It is supported by that its computation time costs are 58.25 seconds.
We have done simulation experiments using different numbers of robots, edges, and clouds. The effect of different numbers of devices on the three architectures is shown in Fig.4 to Fig.6. Fig.4 shows the communication time costs of the three architectures. Their communication times costs increase linearly as the number of frames increases. The communication time costs of "Robot+Edge+Cloud" architecture are less than that of cloud architecture and "Edge+Cloud" (EC) architecture.
From Fig.5 , computation time costs of three architectures increase linearly as the number of frames increases. Edges have the best computing power. The computing power of clouds is relatively weak, and clouds need more time to process tasks. Overall, the computation time costs of ERC architectures and EC architecture are not much different.
The results of Fig.6 show that we could increase the number of devices to increase computing power and system utility, which reduces computation time costs of task decomposition. It is supported by the REC curve (Robot=5, Edge=20, Cloud=20), and the REC curve (Robot=5, Edge=10, Cloud=10). Communication time costs increase, and system utility reduces when subtasks compete for computing resources in the early stage. It is supported by the curve of REC (Robot=5, Edge=20, Cloud=20) and the curve of EC (Edge=20, Cloud=20). When Robot=5, Edge=20, and Cloud=20, the size of each task queue is 5000 frames, and each task queue is divided into ten equal subtasks. When Edge=20 and Cloud=20, the size of each task queue is 7500 frames, and each task queue is divided into ten equal subtasks.
When the proportion of edges and mobile robots increases, our respiratory monitoring system has good scalability, which is supported by the curve of REC (Robot=10, Edge=20, Cloud=40; the size of each task queue is 7500 frames, and each task queue is divided into ten equal subtasks) and the curve (Robot=5, Edge=10, Cloud=10). As computing equipment increases, the overall computing power increases. The performance of REC architecture is better than the other two architectures.
We set up task arrive factors and subtasks of different sizes to explore their impact on system utility. We adopt the subtasks of different sizes. Each subtask is set to 25 frames and 50 frames. The task arrival factor (TAF) is 1 when there are 1500 frames in a task queue. If the task queue is not full (TAF<1), we add five subtasks to it each time. Each edge takes one subtask from task queues for calculation per time. In this case, we use different numbers of robots, edges, and clouds to calculate. The experimental results in Fig.7 show that the system utility increases as the subtask sizes (SS) increase if computing resources are not fully utilized. System utility could be improved by increasing the number of edges or subtasks when the communication time cost has little effect on computation time costs. Also, it could divide the more massive part of the computing task into high-performance computing devices to improve system utility. 
Nose ROI was selected to extract the respiration rate signal to compare with existing RR monitoring methods, including DLRRMS without eliminating erroneous peaks (DLRRMS-EEP), Gaussian window (GW) [30] , and frequency domain analysis method (FDAM) [55] .
The width of the Gaussian window was set to be 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150 to process the respiratory signal. The results were shown in TABLE 2. The overall results were the best when the width of the Gaussian window was 130. At this time, their MAE and RMSE were 0.8359 and 1.1734, respectively. 
Also, the Bland-Altman method was used to evaluate the consistency between RR monitoring by DLRRMS and the real respiration rate. The difference between the measurement results is the vertical axis. The average of ground truth and predictive value is the x-axis. The difference between measurement results is the y-axis. We draw a scatterplot and mark the 95% consistency limit. Fig.9 shows that DLRRMS has the best consistency. 
We have done three comparative experiments to evaluate the time costs, accuracy, and consistency of DLRRMS, respectively. In the first comparative experiments, as the number of robots, edges, and clouds increases, the computing resources of architecture increase. We decompose timeconsuming computing tasks into devices with relatively good computing capabilities. In "Robot+Edge+Cloud" and "Edge+Cloud" architectures, the most time-consuming Spatiotemporal feature tracking calculation tasks are placed on edges, and respiration signal extraction and preprocessing tasks are placed on clouds. In "Edge+Cloud" architecture, we put facial feature extraction tasks on edges. Moreover, respiratory signal feature extraction and preprocessing tasks are placed on clouds. In cloud architecture, all computing tasks are placed on clouds. In this case, the overall system effect increases by increasing the number of edges. However, when the number of devices increases to a certain extent, communication delays and communication time costs increase. Communication time costs are mainly consumed by information interaction and resource competition between robots, edges, and clouds. When the communication network is congested, the system utility is reduced.
In the second and third comparative experiments, GW with a fixed width processes the respiratory signal after Butterworth filtering. It is not suitable for peak filtering of any width when the instantaneous breathing frequency changes and may miss some peaks. In addition, the unconscious head movement would produce motion artifacts and bring the noise to the respiratory signal, and it may affect the RR accuracy of FDAM. DLRRMS-EEP calculates RR without eliminating falsing peaks, and it counts more peaks that should not be retained. However, DLRRMS effectively overcomes the defects of the above existing methods by setting an amplitude threshold, and it is verified through the experimental results of TABLE 3 and Fig.9 . Fig.10 shows the plots of GW, DLRRMS, original signal. Both GW and DLRRMS use the same signal preprocessing method, such as detrending, standardization, Butterworth filtering. However, the steps applied to eliminate error peaks are different. The former uses a polynomial Gaussian fitting method, and the latter eliminates false peaks by setting an amplitude peak threshold. Since GW and DLRRMS use the same signal preprocessing method and only use different methods to eliminate false peaks, the experimental results between them are very close. Besides, it could be seen that the correlation of peaks retained between DLRRMS and the original signal is higher than that of GW and the original signal from Fig.10 . This is the reason why DLRRMS proposed is better than GW.
There are many broad application prospects in the medical field. However, due to the imbalance of data and individual differences, we need to collect more data and explore related future work issues. Also, we need to integrate more non-contact and contact physiological parameters into our system to provide a scientific basis for realizing comprehensive health monitoring.
In this paper, the deep learning-based respiratory rate monitoring system using mobile robots and edges is designed. Due to the limited computing resources of mobile robots and the real-time requirements of physiological parameter monitoring in medical scenarios, a three-tier architecture with robot layers, edge layers, and cloud layers is adopted to decompose different computing tasks. We deploy feature extraction tasks, Spatio-temporal features tracking tasks, and respiration signal extraction and preprocessing tasks at robot layers, edge layers, and cloud layers, respectively. This architecture meets the needs of real-time tracking of infrared noses and extracting breathing signals while considering the limitations of mobile robots' computing resources. Compared with "Edge+Cloud" architecture and cloud architecture, our three-tier architecture of "Robot+Edge+Cloud" has better performance in task decomposition. It spends fewer time costs than the other two architectures. In this situation, real-time and effective breathing signals could provide data support for medical staff to make decisions if more physiological data is integrated into the system. In terms of accuracy, compared with current mainstream GW, FDAM, and DLRRMS-EEP, the MAE and RMSE of DLRRMS proposed in this paper are reduced by 5.12%, 5.06% at least, respectively. Besides, the consistency evaluation of DLRRMS is better than other comparison methods. In short, our DLRRMS could not only calculate the respiratory rate in real-time but also ensure the accuracy of respiratory monitoring.
Haimiao Mo is a PhD student at the School of Management, Hefei University of Technology, China. His current research is in the area of noncontact health monitoring, data mining, machine learning, and swarm intelligence algorithm optimization. Vasilakos has served or is serving as an Editor for many technical journals, such as the IEEE TRANSACTIONS ON  NETWORK AND SERVICE MANAGEMENT, the IEEE  TRANSACTIONS  ON  SYSTEMS,  MAN,  AND  CYBERNETICS-PART B: CYBERNETICS, the IEEE  TRANSACTIONS ON INFORMATION TECHNOLOGY IN  BIOMEDICINE, ACM Transactions on Autonomous 