Emotion recognition becomes an important aspect in the development of human-machine interaction (HMI) systems. Positive emotions impact our lives positively, whereas negative emotions may cause a reduction in productivity. Emotionally intelligent systems such as chatbots and artificially intelligent assistant modules help make our daily life routines effortless. Moreover, a system which is capable of assessing the human emotional state would be very helpful to assess the mental state of a person. Hence, preventive care could be offered before it becomes a mental illness or slides into a state of depression. Researchers have always been curious to find out if a machine could assess human emotions precisely. In this work, a unimodal emotion classifier system in which one of the physiological signals, an electrocardiogram (ECG) signal, has been used is proposed to classify human emotions. The ECG signal was acquired using a capacitive sensor-based non-contact ECG belt system. The machine-learning-based classifiers developed in this work are SVM and random forest with 10-fold cross-validation on three different sets of ECG data acquired for 45 subjects (15 subjects in each age group). The minimum classification accuracies achieved with SVM and RF emotion classifier models are 86.6% and 98.2%, respectively. Emotion is an important aspect of human consciousness, which drives our mental state even subconsciously. The emotional state ensures mental well-being, as well as our overall health. The human emotional state is a result of chemical changes in the brain which affect the whole body and its overall expression and actions. They affect feelings, which certainly act as an important parameter which differentiates humans from other species. We feel a diverse range of emotions which may be often situational and might be triggered by outside events. A constant state of sadness for a long time causes depression. A state of severe mental illness may also result in physical illness. When a person is angry, the temperature of the body increases and may even lead to shivering. The blood pressure of a person fluctuates in cases of intense happiness and sadness. A state of intense fear results in sweating and an increase in heart rate. The state of disgust and surprise may lead to a reduction in the heart rate. A pleasant activity relaxes our mood and reduces stress which leads to a reduction in heart rate in comparison to a hyper state. The rhythm of the heart changes with emotions. Researchers have tried to correlate various facial features, speech signals, and audiovisual features, as well as physiological signals such as EEG , ECG, GSR , and respiration signals, with changes in emotions. Broadly, human emotion recognition systems are categorized into non-physiological- and physiological-based systems. Non-physiological systems utilize facial expressions, speech, audio, and video of the subject when exposed to elicit emotions through an external stimulus. As these features can be masked, for example, a happy person can pretend to have a serious and sad facial expression, as well as a sad person can pretend to have a smiling face, a physiological-based system is also of merit. This second method utilizes physiological signals such as ECG, EEG, GSR, and breathing signals as feature datasets to classify human emotions. The physiological signals are involuntary in their source of generation, hence they cannot be masked or controlled by the subject. Much work has been reported using non-physiological methods of emotion recognition. Our motivation in this work was to utilize the minor changes in ECG waveform caused by changes in emotional state to classify seven different kinds of emotions. An ECG is a quasi-periodic bioelectrical signal which is an electrical activity of the heart acquired in the form of skin potential. This work reports the design and development of a unimodal (ECG)-based contactless human emotion recognition system. The functional block diagram of the proposed system is shown in With the advancement of technology, healthcare services have become more patient-oriented. The implementation of IoT (Internet of Things) and AI  with ML (machine learning)-based systems enables us to provide the required preventive care. They are widely used to develop smart healthcare systems for biomedical applications. The detection of diseases, from the very dangerous to the least dangerous, is being conducted using ML techniques. Machine-learning models can process a huge amount of patient data, including medical history, from many hospitals very quickly and are used in the detection and classification of diseases. For example, H. Zhu et al. presented an effective Siamese-oriented region proposal network (Siamese-ORPN) for visual tracking, and the authors proposed an efficient method of feature extraction and feature fusion . W. Nie The non-physiological method of emotion classification involves inputs as responses such as speech, audio, video, and facial expressions corresponding to various emotions. K. P. Seng et al. reported an audiovisual feature-extraction algorithm and emotion classification technique. An RFA neural classifier was used to fuse kernel and Laplacian matrices of the visual path. The emotion recognition for seven types of expressions achieved an accuracy of 96.11% on the CK+ database and 86.67% on the ENTERFACE05 database . Facial Researchers have also explored the physiological method of emotion detection. Mainly, EEG and GSR signals have been used to develop classifier models. Even then, unimodal ECG-based human recognition systems offering high accuracy using contactless acquisition of the ECG signal are still not much explored. In contactless systems, ECG data acquisition with minimum artefacts has always been a challenge to researchers. This work proposes an ECG belt system for contactless acquisition capable of acquiring ECG data with high precision and accuracy. The functional block diagram of the ECG data acquisition system is shown in M. R. Islam et al. conducted an extensive review of EEG-based emotion recognition techniques in two categories, deep-learning- and shallow-learning-based models. A very detailed list of features used by researchers for the development of emotion classification models was reported. The paper analyzed the relevance of features, classifier models, and publicly available datasets. The authors minutely identified the advantages, as well as the issues, of each technique reported in the domain and suggested possible methods to overcome them . E. P. TIn this work, our purpose was to investigate a greater number of subjects from a wide range of age groups to develop a highly accurate ECG-based emotion classifier system. The classification accuracies can be enhanced using SVM and RF as achieved in this proposed work, and the comparative study is tabulated in The acquired signal was processed by the signal processing block using MATLAB 2020b software. A total of ten statistical features of the ECG signal were extracted for each subject for all seven emotions in an induced emotional state while watching videos containing specific emotional content. Processing included sampling, normalization, denoising, and the removal of outliers to obtain processed ECG data in .csv file spreadsheets. Finally, the prepared datasets were used to extract features using feature extraction algorithms developed using MATLAB codes. The feature datasets were used for training and testing for the development of emotion classifiers using machine-learning tools. The models were trained and cross-validated to classify different emotions. The emotion classifier models were designed to classify seven types of emotions: Anger, Disgust, Fear, Happy, Neutral, Sad, and Surprise.A hardware system for an accurate ECG acquisition from above the cloth has been designed.Ten statistical features of the ECG data have been extracted using developed feature extraction algorithms.Experiments have been conducted on a total of 45 subjects and seven different categories of emotions using emotion classifier models (such as SVM and RF) developed using MATLAB have been classified.Developed models are capable of classifying human emotions precisely with reasonably high classification accuracies for a contactless unimodal ECG-based emotion recognition system.These models offer higher classification accuracy in comparison to the unimodal physiological-signal-based emotion recognition systems reported earlier. The contactless ECG belt acquisition system offers an accurate, compact, and contactless ECG data acquisition which does not require on-body AgCl gel-based ECG electrodes. So, the proposed system differs from other contactless systems such as radar-based systems which utilize the electromechanical movement of the chest and are usually complex and bulky. The system response is accurate and has the potential to be developed as an end-use product such as a lie detector. The key contributions of the proposed work are as follows:The proposed system includes an efficient wireless ECG data acquisition belt system utilizing capacitive sensing technology , signal processing block  and feature extraction algorithm (F1–F10), emotion classification using classifier models (SVM and RF classifiers), feature selection, and validation. A detailed explanation of each block is included in the later part of the section. The experiment involved human subjects and hence was conducted very cautiously; some of the experimental data took many iterations before being considered in the final dataset. The whole process flow chart is shown in A contactless method of accurate ECG acquisition is in itself a challenging task. The designed hardware acquires ECG from above the cloth of the subject. The noise minimization was achieved using filters designed using low-noise op-amps. The acquired signal was processed in the signal processing module.The stable connection of the Bluetooth module (HC-05) with the PC system was a challenge while acquiring the data. Experiments were required to be repeated in some cases.One of the features (heart rate) extracted for the ECG signal for the corresponding emotion was verified with a Mi Band 5 simultaneously. In some cases, the experiment was repeated.The intensity of any emotion also depends on the diurnal baseline of an individual mood; the baseline was modified as a neutral case for each individual. It can be referred to as calibration before experimentation.The major implementation challenges are listed below:The volunteers who participated in this experimental study were explained the methodology, and the required consent was taken. The volunteers were healthy subjects with no cardiac history.The volunteers were categorized into three different groups based on the age group to which they belonged. The three different age groups selected were 21–30 years, 31–40 years, and 41–50 years, with a male to female of 3:2.The audiovisual stimuli were already prepared in the form of video clips of 60 s length for each of the seven different emotions inclusive of pre- and post-10 s of static image to obtain a baseline. The selection of the audiovisual stimuli was made with the help of the previous literature ,40,41,42A total of 45 volunteers (15 from each of the selected age groups) were shown the audiovisual stimuli in random order but while keeping an average time gap of 10 min between two video stimuli or until the subject returned to their baseline level.While watching the video to elicit a specific emotion, the ECG of the subject from the ECG belt system was recorded and sent in parallel wirelessly to MATLAB using the serial port of the PC.An ECG feature extraction algorithm was developed; a live script ran on MATLAB in which the acquired ECG signal was firstly processed for noise removal and normalization, and then the statistical features were extracted.The subjects were also asked to write down the emotions they felt while watching the audiovisual stimuli; only those cases are considered in which the category of the clip and the emotion felt and mentioned by the subject matched.One of the primary features, heart rate, calculated from the feature extraction algorithm was verified with the heart rate acquired using the PPG sensor of a Mi Smart wrist Band 5. The experiment was repeated for the case in which the heart rate using the algorithm and smart band varied by more than 3–5 bpm.The ECG data for all seven emotions for the selected age groups and the corresponding feature datasets in the form of three different sets  were prepared as final feature datasets.The datasets were used individually to train classifier models using SVM and RF classifiers with a 10-fold cross-validation technique with PCA enabled.Two principal components were selected for each set of data to avoid overfitting problems. The significant features were selected using the wrapped method.The hyperparameters were tuned using the Bayesian optimization technique using optimizable classifier learners for both of the designed models to recommend the best hyperparameters.The classification accuracy obtained was validated and compared with available techniques.The experimental steps followed in this study are as follows:The ECG data was acquired using a non-contact capacitive ECG belt system. It is a 2-lead ECG system with a reference electrode attached to the wrist. The belt was wrapped around the waist above the cloth only. It can acquire the ECG of a person above a cloth of thickness up to 100 microns. The subjects under investigation were exposed to video clips of 40 s length for 7 different emotions: Anger, Disgust, Fear, Happy, Neutral, Sad and Surprise. The data acquisition system hardware included a signal processing block containing an instrumentation amplifier implemented using INA128P for signal amplification and filters using low noise op-amp LM324N to remove noises such as motion artefacts, etc. The overall accuracy of the 2-lead ECG belt system was compared with a 12-lead Holter monitor, which is quite high (up to 96%), and it was found very suitable for non-contact ECG acquisition . To miniThe signal processing block was connected to an Arduino controller which controls the sensing application and data acquisition. The acquired data were transferred using a Bluetooth module to the PC for further processing and feature extraction. The block diagram of the data acquisition system is shown in For each set of data, the ECG signal corresponding to induced emotions for 15 subjects was recorded and analyzed. Each person was shown all 7 video clips containing 7 different emotions, and the normal state was ensured by keeping a gap of 10 min between the videos. Three sets of data, named Set A, Set B, and Set C, were prepared. Set A was acquired for the subjects within the age group of 21–30 years, Set B for the 31–40 years age group, and Set C for the 41–60 years age group. The male-to-female ratio was 3:2. The subjects volunteered and were explained the experimental procedure, and the required consent was taken. The demographic details of the subjects are included in The ECG data were obtained for all 15 subjects in .csv format with a gain of 100 and a sampling frequency of 256 Hz. The data were recorded for 60 s including pre- and post-ten seconds of normal state value for the baseline. To ensure the base value, a static image of natural scenery was shown. The subject was exposed to video clips of 40 s length, hence the ECG data for that period were taken out for feature extraction and emotion classification. The data were processed to remove any noise using the denoising application of the signal processing tool in MATLAB R2020b; one of the cases is shown in The main idea behind the development of a unimodal ECG-based emotion recognition system is the potential of the physiological signals to have information that can be used to classify the emotional state of a person as is claimed in much of the reported literature. The ECG signal is a quasi-periodic bioelectrical signal of low amplitude and frequency. The minor variation in the amplitude of the signal will majorly constitute the emotional contents. The contactless method was utilized in this work, and the ECG signal was processed properly to minimize the impacts of motion artefacts and any other system noises. Theoretically, the statistical features selected represent those minor variations in the ECG signal. Experimentally, the partial dependence plots were plotted to interpret the models’ classification dependency on a particular feature. It was found that each model had statistical ECG features with an average contribution of 8%, except for heart rate which contributed 15% on average. The minor fluctuations in the ECG signal can be expressed in terms of the statistical features of the ECG data to train emotion classifier models.For 40 s of ECG data sampled at 256 Hz, for one emotion and a single subject, there was a total of 10,240 data points. The parameters were extracted for each sampling interval, hence for one subject and one emotion; the feature set was of a 40 × 10 array. For 15 subjects, each feature dataset had a size of 4200 × 10, corresponding to the ECG dataset of 1,075,200 data points as tabulated in A total of 10 statistical time-domain features (F1–F10) of ECG signals were calculated. The features  were extracted from .csv data files of the recorded ECG signals for the various emotional states of the subjects. The parameters and their mathematical expressions are tabulated in The extracted features for all selected emotional states were prepared with the corresponding emotional response allotted to them. The features were calculated using ECG data used to classify the emotional state of a person in this study. The datasets were prepared using features as input and emotional responses (seven categories) as output. The dataset was analyzed using various classifiers available in MATLAB R2020b. The data for each set were disjoint for the training set, and no data from other sets were used to train models except in one case when the combined data of all three sets were used to train the models separately.SVM is one of the most efficient supervised classifier learners. It divides the data into support vectors and keeps one vector of the data at a time for validation, trains the rest of the vectors, and this process repeats till the learner finds the most suitable decision boundary (hyperplane) to classify the data precisely and accurately. In this study, an SVM classifier with a quadratic kernel function was used to develop the emotion recognition models. To tune the hyperparameters, Bayesian optimization techniques with multiclass methods one-vs-one and one-vs-all were used. Different kernel functions in SVM optimizable  were used in this research work to recommend the best hyperparameter. Moreover, to avoid overfitting the problem, principal component analysis (PCA) with a 95% variance level was enabled, and it selected 2 principal components.Random forest was one of the robust techniques used to classify the data more accurately and precisely. Ensemble bagged tree and, to tune hyperparameters, the ensemble optimizable  were the classifier learners used from this category. The ensemble bagged tree divides the data into subsets randomly with replacement to train and reduces the variance of the decision tree. It bags various models in one to enhance classification accuracy. Each subset is used to train the collection of decision trees and provide benefits for all decision trees. Hence, it is an ensemble of many decision trees operated on randomly divided subsets and bags the average response from all the decision trees to arrive at the most efficient classification models. Random forest, an extension of ensemble bagging, uses a random selection of features also to grow trees.Classifiers used in this research work are SVM, RF, and their optimizable forms. SVM quadratic and ensemble bagged tree were the two machine-learning classifiers used for training and testing. Both of the techniques support classification as well as regression. In SVM, each parameter was correlated with other parameters individually and collectively to assess the correlation of features with the emotional response of the subject. It selected the best decision boundary, also called a hyperplane. RF contains multiple decision trees which combine to arrive at a single answer. A 10-fold cross-validation technique was used for each case. Optimization in both cases utilized 30 iterations to recommend hyperparameters and selected the best one.The three ECG feature datasets were prepared out of three different raw ECG data (acquired using an ECG belt system hardware) for three different age groups. They have been used to develop models capable of classifying human emotions quite precisely and accurately. The experimental setup with a subject under investigation (permission granted to publish the photograph of the subject) is shown in To analyze the performance metrics of the developed classifier models, the true class, the predicted class, the true positive rate (TPR)  and the The hyperparameters were tuned using the Bayesian optimization technique for the multiclass method , and four models of SVM optimizable with individual datasets and combined datasets were trained and developed. The confusion matrices and classification error plot with 30 iterations of optimization using the Bayesian method are shown in The confusion matrices for the random-forest-based classifier named ensemble bagged tree classifier developed for each dataset and the combined are shown in The ensemble optimizable models were also trained and validated to obtain the most suitable kernel function offering minimum classification error and recommended the best hyperparameter. The confusion matrices and classification error plots with 30 iterations of optimization using the Bayesian method are shown in The designed system with reported classification accuracy was obtained experimentally for the emotion recognition of 45 healthy subjects of three different age groups. Further experimental analysis is needed to claim the generalization of the developed models for patients with cardiac issues. This work will be extended further in the future to analyze the emotions of patients with CVDs.The ROC and AUC curves for all the models were analyzed, and they were found to be quite close to the ideal case. The ROC–AUC curve for the SVM model with the quadratic kernel function trained and tested using the Set A feature dataset (youngest of the age groups taken) is included in The training time and prediction speed for all the training models used in this research work are tabulated in The overall performance of the random forest ensemble bagged tree classifier was found to be even better than the highly efficient SVM quadratic in the case of the models being designed using the same dataset, and the same goes for the optimizable classifiers of both classes. The designed system is a simple, economical, unimodal ECG-based emotion classifier system. A comparison bar graph showing the classification accuracies of all the developed emotion classifiers is shown in The ECG signal containing the emotional contents of 15 subjects from each of the three different age groups was acquired using a non-contact capacitive ECG belt system. The signal was processed, and a total of ten features were extracted for each sample interval of the final sampled ECG signal datasets. The emotion classifiers were developed using SVM- and RF-based machine-learning techniques. The data were analyzed set-wise as well as subject-wise. The overall average classification accuracy achieved is very promising and sufficiently high. The proposed system and selected features are very suitable to detect the emotional state of a person using an ECG signal. The system is simple, very fast, and highly reliable. The response of the system was compared with available systems reported in the literature as tabulated in


Transportation authorities have adopted more and more incentive measures  to reduce the use of private cars by combining them with public transit. However, such measures remain difficult to assess with traditional transport models. This article proposes a different approach: an agent-oriented model. To reproduce realistic applications in an urban context (a metropolis), we investigate the preferences and choices of different agents based on utilities and focus on a modal choice performed through a multinomial logit model. Moreover, we propose some methodological elements to identify the individuals’ profiles using public data (census and travel surveys). We also show that this model, applied in a real case study , is able to reproduce travel behaviors when combining private cars and public transport. Moreover, we focus on the role played by park-and-ride facilities in this context. Thus, the simulation framework makes it possible to better understand individuals’ intermodal travel behavior and assess its development policies. PT). They generally consist of adjusting public transport pricing [Faced with the issues of global warming and the high cost of living, political actors are increasingly looking at collective and less polluting transport systems  to provide solutions that are both inexpensive (for the customer) and ecological. These policies, for the most part, aim to reduce the use of private cars in favor of soft modes of transport  and public transport  [PVPT policy [In France, for example, such policies are included in the mobility orientation strategy, which aims to strengthen the transport supply by (1) rebalancing the modal shares in favor of public or active modes , 2) strengthening the shared use of individual transportation modes (carpooling and car sharing), and 3) encouraging multi-modality and inter-modality. Inter-modality can be defined as the combination of several transportation modes during a single trip [ strength encouragPV+PT) . It ofteT policy .agent-based model (ABM), describes a system as a set of agents interacting with each other. The ABM is particularly distinguished by the study of the decision-making processes underlying the behaviors, because there is a natural relation between the individuals (from a transportation system) and the agents (from our model). To our knowledge, the inter-modal behaviors within these tools are not very well defined or are even missing [Therefore, it is essential to think carefully about decisions to promote this practice. To evaluate their policies, mobility and transport stakeholders often use software for traffic simulations . Differe missing ,13.PVPT), which requires park-and-ride facilities (PR). The modal choice is defined by a multinomial logit (SI-MNL) model coupled with the simulation tool MATSim/eqasim [Our approach describes a multi-agent simulation to reproduce inter-modal trips from publicly available mobility data. The type of inter-modality studied concerns the combination of private cars and public transport  in France. After calibrating and validating the simulation with household travel survey data, we evaluate the use of the PR facilities and study the agents’ behavior using this alternative. The simulation shows that some PRs located at the entrance to Lille are overloaded during peak hours. The simulation framework proposed can thus be used as a tool to explore actions aimed at promoting the combination of private cars and public transport, such as the construction of new PRs and free access to public transport subscribers.The developed simulation framework is applied to the European Metropolis of Lille . PVPT). Then, MEL) and validates our approach. Finally, The remainder of this article is organized as follows. First, we describe the data and how they can be used today to simulate travel demands for a region . Then, wABM mobility demand. They can be grouped into two categories based on the acquisition method. Thus, we distinguish the active approach, where data from surveys are gathered through questionnaires addressed directly to individuals  surveys.In France, the main data sources on mobility come from the census and household travel . In France, these data characterize EMD is the unique survey providing mobility practices. The survey considers the detailed reasons (primary and secondary activities), the number of trips, the intermediate trips, and the transportation mode actually used. The data also contain some main users’ socio-economic characteristics . These are often used to establish public mobility policies.Based on a census  and floating car data (FCD). FMD are obtained either by triangulation or by the inter-cellular transfers and the relay antennas of the operators during travel. FCD are generally obtained from vehicle location data (GPS). They can also be obtained via the locations of phones when they are switched on in a vehicle. These data provide better knowledge of the O/D flows than data from standard surveys, as the information is more detailed and more recent for users’ travel routes due to the frequently updated location system. These data are handy for calibrating the model [FCD and FMD are obtained through their use.Massive mobility data are mainly derived from he model  and estihe model . FCD andThe authorities organizing mobility are deploying more and more devices (sensors) to control user access to public transport and parking facilities by validating tickets and subscription cards or capturing Wi-Fi signals. The volume of captured data provides crucial information for sizing the transport offer according this demand. Thanks to ticketing data, it is possible to build travel O/Ds , performThe main limitation for their processing and use is the lack of trip data . They can also come from the operator’s facilities (telephone or satellite and card readers), but they may not represent the global population .EMD provide information on inter-modality behaviors through the description of journeys and the different transport modes during the trip. Ticketing data could also provide information on the combination of public transport with other modes, particularly the private car (through relay car parks) or shared modes such as bicycles and electric scooters. However, to extract such information would require an in-depth analysis of these data.Among all these data sources, only ABM. Finally, we focus on the modal choice supporting the utilities for the agents  [The individual practices consider the motivations and the different activities for all their trips (from and toward his or her home). In contrast to a traditional (macroscopic) model ,26,27, tailable) ,29.ABM by considering the modal choices.In addition, the activity-based model allows, through synthetic population generation techniques, evaluating different mobility policies in a more straightforward fashion than with a macroscopic model. Combining activity-based and agent-based models is a way of reproducing the interactions between the individuals during their performed daily activities . Thus, tABM simulators was already proposed in [MATSim [SUMO [MATSim reproduces the inter-modal behaviors better through an activity-based approach and the notion of utility for the agent’s decision process  with shared micro-mobility (bike) services. However, our study focuses on the combination of private cars with PT through the use of park-and-ride facilities.Earlier, a comparative study of the seven most popular posed in . The wor [MATSim  and SUMOim [SUMO  are partcess see . MATSim g MATSim . This inTransportation demand is typically derived from a synthetic population. It is a collection of agents with attributes such as home location, age, gender, socio-professional categories, and ownership of transport data . The transportation demand includes the activities and trips performed by the agents. It includes elements such as the types of activities and their locations, the beginning and ending times for these activities, and the trip mode. Thus, it is possible to create more refined analyses by considering the agents’ individual characteristics.open source synthesizers for different case studies are available [To the best of our knowledge, there are no normalized data for the population or transport demand. Demand generation must be performed by the modeler or researcher based on the available data. Some vailable ,33. Nevei has for an alternative m (transportation mode in our case study) [Several factors related to the individuals  and the transportation mode  have been identified as impacting the modal choice . Mathemae study) . This ututility-based agent [The notion of utility allows for a model that is more realistic for the individuals’ travel behaviors . Individuals will choose a transportation mode or a combination of modes, maximizing their utility. The modal choice can thus be easily taken into account by the agents. This naturally leads to considering the approach described by the ed agent . ThroughMATSim platform  software [eqasim) [MATSim. Each individual (agent) has a daily plan of trips and activities. Agents’ initial daily plans are then represented by the initial demand with the transportation supply . The plans of all agents are defined through the mobility micro-simulation module QSim, generating the associated flows and also different phenomena such as traffic congestions and emissions. The plans are then evaluated by a score based on the performed activities and the utility provided by the transportation mode. At each iteration, a subset of the agents can modify their plans to improve their score by changing either the transportation mode, the route, or the departure time (Re-planning). Each agent, in turn, will have the possibility to optimize his or her daily mobility plans. A co-evolutionary algorithm is used to reach an equilibrium state where no improvement is possible.This work is based on the Multi-Agent Transport Simulation (software  coupled [eqasim) . Figure eqasim, the initial decision-making module is replaced by a discrete choice module (DMC). Therefore, eqasim allows better behaviors by focusing on the modal choices using a discrete choice model and does not enable other replanning strategies. The simulation produces new trips captured by a Variables component  for the modal choice module. These new values, resulting from interactions between agents, may vary from one iteration to another . Estimators compute the utility of different modes based on their variables and parameters.In MATSim/eqasim requires as input the origin/destination (O/D) coordinates of the activities for the agents’ plans. However, to avoid indirect identification of persons in the surveys, the areas  of residence, their activities, and the O/D locations of their trips are deleted. Moreover, the data on inter-modal practices are not directly usable without preprocessing. We show how to rebuild these data without compromising the privacy and how to extract the information on inter-modality.The current version of We detail the rebuilding for the O/D coordinates  and inteSurvey data are commonly based on predefined zones, (drawing sectors) to maintain the anonymity of individuals. No information on the municipalities of residence or activities  is thus provided. However, these sampling areas must be consistent with the administrative divisions while ensuring scaling of the results for population of this area. The information on the municipalities is necessary for the generation of the synthetic population in order to have observations from the studied area.QGIS and ArcGIS.To define the municipalities of residence and activities, we superpose the shapes of the drawing sectors  on those of administrative divisions . The drawing sectors, which are generally smaller, will thus appear for the corresponding municipalities. This task can be realized with software for geographical data processing, such as In addition, the O/D coordinates of trips are necessary to estimate the discrete choice model and also for the creation of the activity plans for each agent. Thus, we aim to redefine consistent coordinates from the O/D drawing sectors and Euclidean distances provided in the survey. We propose a method which can be defined by two steps: (1) generating random points . The person file provides information on characteristics such as age, occupation, and driver’s license ownership. The trip and leg files provide information on the sequence of the transportation mode used, trip purpose, departure time, and distance. It is possible to recover the inter-modal trip information based on the trip file. Note here that we consider, as an inter-modal trip, the combination of several mechanized transportation modes , even if some studies also consider the combination of walking  and public transport as an inter-modal practice [PT) modes  is an inter-modal trip [practice . Thus, tdal trip ,38.trip and leg). In addition, the modelings consider the following transportation modes:PT mode. This aggregation of PT modes is needed to enforce this alternative compared with the other transportation modes . In addition, we currently focus on an inter-modality combining public transport with other individual transportation modes (car and bike). The public transport modes, therefore, are merged to facilitate identification of the combinations with the car and the bicycle and to have enough observations of this practice to carry out the simulations.All public transport modes  are represented by a single PV). For example, a driver taking a private vehicle and then public transport will be considered as PVPTPTPV (a similar way for PVPTPTPV).The car mode, as the driver or a passenger, is considered as a private vehicle .For the inter-modal combinations with public transit, we consider all PVBike or PVBikePT. We also do not consider the combination of PT (PTPT) modes in this study.It is also assumed that we do not consider combinations that are too unrepresentative, such as To rebuild the inter-modal trips, we identify all trips for each trip by merging these two files  should be performed through infrastructures, particularly park-and-ride (PR) facilities, as illustrated in The combination of private car and public transport (car_pt for the outward journey and (2) pt_car for the return journey. The car_pt alternative (shown in red) is defined by a private vehicle (as the transportation mode) from the home to the PR (first trip) facility. The second trip is performed by the PT mode  from the PR to the destination, or more precisely to the nearest station, followed by an egress of walking. The same process is performed for the return trip, using the alternative called pt_car (blue). In this case, the first trip is made by public transport from the previous destination to the same parking facility used for the outward journey. In the second trip, the individual returns home using the same vehicle left at this parking facility.We propose two new complementary transportation modes: (1) PVPT alternative, we define four constraints, which are presented as follows:PVPT alternative.Only agents owning a car and a public transport ticket can use the PR facility must be used in the outward and return journeys.The same PT. In this case, the car must be picked up and dropped off at the agent’s home.The home must be the origin (destination) of the trip performed by car_pt and pt_car, are only considered during the modal choice process.The chain of alternatives, including the modes In order to ensure a consistent generation of possible cases for the MATSim assumes that the transportation mode’s routing process must be defined explicitly. Otherwise, users using these modes will be directly moved to their final positions. Moreover, the current version of MATSim/eqasim cannot simulate the combination of a private car and PT via PR. car_pt and pt_car modes depends only on the used park-and-ride (PR) facilities. Therefore, the PR choice must be achieved before the routing. The choice of park-and-ride facilities is then defined as the decision to select one among a set of PRs located close to the agent’s house. The process of searching for a parking space and the capacity of the PR are not taken into account for the moment to propose a straightforward model. In addition, the choice of using the PR closest to the individual’s home is also relevant under current mobility policies and aims to favor public transport rather than private cars. This modeling choice is also justified by the unavailability of PR usage data to identify individual preferences when considering elements such as the search times, the parking costs, and the walking times [PR. Then, it performs PT routing from the PR to the closest public transit stop (station) for a given destination. The rest of the trip is performed by walking to reach the destination . We propose a travel routing algorithm for PVPT as follows:1.PR closest to the agent’s home.Identify the 2.PR using the routing module proposed by MATSim.Perform routing by car between the home and 3.PR and the destination using the public transport routing module. This can be also achieved by using the routing module.Carry out the routing between the 4.For the return journey, the analysis is similar but with a starting time for the trip by public transport.ng times . The rouPVPT receives the following information: the characteristics of the agent  performing the trip, the O/D of the trip, and the location of the park-and-ride facility (provided by the PR search module), which are necessary to calculate the route.Thus, during the simulation, the routing module of car_pt and pt_car) representing the inter-modal choice (PVPT) have the same characteristics for the trip, except for the routing, as mentioned above. A multinomial logit model (MNL) called the simple inter-modal MNL (SI-MNL) is used to design the modal choice.The two transportation modes . Therefore, we suppose that the modal choices are independent, and the error terms are without correlations. The hierarchical structure of the model is presented in PV and PT functions  and the alternative’s attributes .alternative specific constants (ASC) define the variation of choice not explained by the known attributes exclusively.The The r set-up ,40. Thesquations  and 3),,MNL is jIn the following section, we present the results of different experiments performed to validate our approach.This section presents an application of the developed framework. We describe the studied area and the simulation set-up details , as wellMEL is composed of 95 municipalities with 2. As in most European metropolises, we observe that the population is gathered in Lille (the main city), while the rest of the metropolis is weakly populated. Note that the number of vehicles per household is higher in these peripheral areas, whereas around The PR facilities, corresponding to 5005 parking spaces. For our study case, we use the EMD , carried out in 2016, which informed us of the recent mobility practices of the people. The vehicle (PTPT trips).The public transport network includes two metro lines  [n modes) .SI-MNL) was statistically significant, with an initial log likelihood (LL) equal to SI-MNL model shows that the explanatory variables introduced were significant. The significance of the estimated model was also confirmed by the rho square equal to PT  calibration was then carried out to reproduce the reference situation according to the household travel survey.EMD, public transit supply, and the park-and-ride facilities) to carry out the simulation are publicly accessible on the open data site of the MEL. Due to computational time-saving reasons, ® core™ The initial travel demand (including the agents’ daily plans) and supply were generated by adapting the synthesizer pipeline, initially developed for Ile de France . All thePVPT alternative  are presented on the ordinate axis, while the Euclidean trip distances are on the abscissa. This representation allows a better appreciation of the modal distributions. For example, we can see that the walking share was very large for short distances and close to zero for long distances, corresponding to our intuition. Case 4 (selected for the following results), with _pt=1.25 d, producPVPT alternative) from the household travel survey.EMD. However, there was a slight variation between the simulated and observed travel times. This difference can be explained mainly by the reference data, where the travel times were rounded values (the times were multiples of five) rather than exact ones. The distribution of distances and times underlined the modal shares, with an almost uniform distribution between short trips (less than 2 km) performed on foot and for long trips (more than 2 km) mainly made by car. These last results validate our approach to reproducing mobility behaviors for our study case. Then, we evaluated the use of the park-and-ride (PR) facilities and the user profiles combining private cars and public transports.The distances and durations from the simulation corresponded thoroughly with the observed data from the PRs are the infrastructures required to combine private cars and public transport. Therefore, the choices of their location, capacity, and cost of use are key elements for this inter-modal practice. Based on the number of entries, we assess the capacity of PR facilities to absorb PVPT transport demand. PR entries during the morning peak hours for the departures from home. The capacity of each PR (provided in parentheses) gives an idea of their filling rate.PRs  and Tourcoing (Gare de Tourcoing and Pont de Neuville). Apart from the particularity of being located in the main towns, these PRs have parking spaces (only 100 places on average). This small size is undoubtedly a strategy for developing PRs around primary cities to better manage flows for this area. However, the simulation shows that these PRs cannot contain the transport demand. Due to a lack of usage data, we cannot check this situation.During the peak hour, seven  bold in  were ovePVPT alternatives during their travels are also interesting. PV and PT and their trip purposes.The profiles of individuals using PVPT users from the simulation and observed data were between 18 and 54 years old. This result is consistent with the age required to obtain a driver’s license and acquire a car. However, the simulation failed to reproduce the people aged between 18 and 24 years old well. This use rate of the PVPT alternative is mainly explained by the low motorization (car ownership) for this category of agents in the synthetic population. Contrary to the reference situation, the simulation showed that men used the inter-modality more than women. In terms of professional status, the results of the simulation matched perfectly with the reference data. Workers practiced the inter-modality more. This result can be explained by the professional trips from the peripheral areas (characterized by car ownership) toward Lille (the main activity area) in particular. We also note a good result concerning the trip purposes: work, leisure, and other . The educational motivation did not really give the desired result in the simulation, while that for shopping was overestimated. This was also justified by the motorized observations of the 18–24 year old group in the simulation.The majority of the PVPT for the distances, durations, motivations, and socio-professional categories. The limitations of the simulation and the lack of data for PR uses will now be discussed.The simulation successfully reproduced the observed behavior with The anonymized data from different surveys  and the BD TOPO, BPE, or OSM) to generate a fixed set of O/D coordinates corresponding to potential activity locations . The determination of the points thus generated would allow quickly inferring the pairs of coordinates by reducing the computational times.Our methodological approach aims to simulate realistic transportation scenarios from anonymized open data. The good results obtained by our algorithm in building the O/D coordinates depended on the area size and the number of points to be generated randomly. The larger the size of the drawing sector, the more random points should be generated to have a better chance of approximating the Euclidean distances. Therefore, the calculation times for searching for pairs of synthetic O/D points becomes very high, preventing other possibilities from being explored. One solution to this problem would be to use geographic databases . Thus, the utility function of PVPT alternatives could be defined in terms of three components [PV characteristics between home and the PR;The PR, taking into account its own characteristics;The specific utility of the PT characteristics between the PR and the destination.The Another point of discussion deals with the modeling of the choice for mponents :The PV cIn addition, specific survey data on inter-modality could enrich the synthetic population with user behaviors and their trip purposes . UnfortuABMs remains a difficult problem. For example, usage data for PR facilities can be useful for calibrating the simulation model. The data can be obtained through the installation of access control devices for these different PRs . In addition, the user’s sociodemographic data  can come from card IDs. Such data  can also be used to perform real-time simulations where agents update their decisions by considering the current traffic .As mentioned above, one of the main limitations for the inter-modal agent-based simulation is the quality of the available data. The data concerning these inter-modal practices are based on a few data sources. Reproducing more realistic simulations for ABM and provide a generic framework to simulate the inter-modality from open data. In this context, we focused on the inter-modal combination of a private vehicle with public transport (PVPT). The agent-based approach is suitable for studying these mobility behaviors, particularly the inter-modality. The modal choice for each agent was thus performed by a multinomial logit (SI-MNL) to select an alternative. This approach requires disaggregated data (census and household travel surveys) to generate agent-based transport scenarios and to reproduce travel behaviors as faithfully as possible.In this paper, we proposed studying the inter-modal travel behaviors from the perspective of the MATSim/eqasim simulation tool. We described the changes proposed for the definition of these new transportation modes and the inter-modal routing through the park-and-ride facilities . Our model was also applied to an urban context (MEL). After the calibration and validation of the simulation to reproduce the inter-modality practices , we evaluated the use of the park-and-ride facilities (PR) by evaluating the number of entries and their capacities. We showed a consistency between the simulation outputs and the actual use of different PRs, particularly during peak hours. Due to the absence of data for the PRs, it was difficult to compare the simulation results with a reference situation. We also studied the user profiles and their motivations for inter-modal trips. The simulations reproduced the shares of individuals practicing inter-modality, such as for persons aged from 18 to 54 years.This model was subsequently integrated into the well-known PRs) and coercive (urban toll) constraints. The exploitation of data from certain typical modes may improve the results obtained by our approach, such as bus management [As part of future work, we will plan to study the traffic congestion for the city center of Lille. The objective will be to investigate the travel behaviors under incentive (free access to nagement  or bike-nagement .


In this paper, we investigate the algorithms for traversal exploration and path coverage of target regions using multiple agents, enabling the efficient deployment of a set of agents to cover a complex region. First, the original multi-agent path planning problem (mCPP) is transformed into several single-agent sub-problems, by dividing the target region into multiple balanced sub-regions, which reduces the explosive combinatorial complexity; subsequently, closed-loop paths are planned in each sub-region by the rapidly exploring random trees (RRT) algorithm to ensure continuous exploration and repeated visits to each node of the target region. On this basis, we also propose two improvements: for the corner case of narrow regions, the use of geodesic distance is proposed to replace the Eulerian distance in Voronoi partitioning, and the iterations for balanced partitioning can be reduced by more than one order of magnitude; the Dijkstra algorithm is introduced to assign a smaller weight to the path cost when the geodesic direction changes, which makes the region division more “cohesive”, thus greatly reducing the number of turns in the path and making it more robust. The final optimization algorithm ensures the following characteristics: complete coverage of the target area, wide applicability of multiple area shapes, reasonable distribution of exploration tasks, minimum average waiting time, and sustainable exploration without any preparation phase. Autonomous unmanned systems, which can replace humans in dangerous or inaccessible workspaces, are currently a popular research topic, and many results have been achieved in related control synergy methods. A fundamental problem in autonomous unmanned systems is to determine an optimal path that passes through all points of a given region of interest, while avoiding specific subregions . In the scientific literature, this problem is often referred to as the coverage path planning problem (CPP), but it can also be referred to as sweeping, complete geographic search, area patrol, etc. Typical applications are the work of detection and rescue cameras ,2, grounNowadays, multi-agent systems improve the performance of individual agents through information sharing and communication collaboration, such as task execution efficiency, robustness, flexibility, and fault tolerance, resulting in distributed decision-making, formation control, area coverage, and other related applications. The mCPP problem discussed in this paper, aims to plan optimal paths for each agent. The paths will form a path coverage of the global target region for the purpose of protecting or supervising this region, while minimizing the total coverage time.In order to cope with the corner case of narrow or near-enclosed areas, geodesic distances are used for initial area assignment, which greatly improves the efficiency of the next iterations;Dijkstra algorithm is applied to dynamically assign weights in calculating geodesic distances, optimizing the shape of the subregion, reducing path turns, and improving energy efficiency;The characteristics of paths generated by RRT-based methods are improved by selecting the most suitable among different weight schemes when building spanning trees.Using a complex indoor scenario as an example, the full-flow solution of this paper is applied for simulation implementation, and the performance of the planned path scheme is quantified and evaluated.Although numerous solutions for generating coverage paths in general polygonal environments already exist, these implementations are either not publicly available, computationally unsuitable for large and complex environments, have realistic application flaws in the planned paths, or lack complete system integration. In this paper, we propose a strategy that can quickly generate full-coverage paths for multiple agents in non-convex regions, based on recent multi-agent traversal algorithms ,5,6, extThis paper is organized as follows. Coverage path planning in a known environment, also known as repetitive sweeping or region traversal, can be formulated in detail as follows: given a target area and a sensor model, a feasible path is planned for mobile robot that provides complete actual access to the target area while minimizing some cost metric , under the premise of the motion model and spatial constraints . The basOne of the simplest exact unit decomposition techniques that can generate complete coverage paths is the trapezoidal decomposition method ,14. For The methods mentioned above can be classified as offline methods. Acar and Choset ,20 have In general, single-agent CPP, as an early control problem, has mature strategies available after years of research and validation. The use of multiple agents for regional complete coverage is a recent challenge for researchers. Puig  utilizedSariel  treats tMaza  proposedIn unknown environments, intelligent swarms require dynamic mapping using the sensors of each agent, while data sharing and real-time communication among robotic agents typically require a distributed algorithm. Recent research ,30 has pThe focus of many studies on the mCPP problem has been on the task partitioning, while a simple “Z” pattern of coverage path is adopted for the decomposed units. Li  and TorrThe grid-based method uses grid cells of uniform resolution for a decomposed representation of the target region. This representation using grids was first proposed by Moravec and Elfes . HoweverThe literature ,28 handlIn our work, we re-examined the grid-based regional decomposition method and analyzed the cause of the “blind spot” where obtaining an effective sub-region division is difficult. We propose to use geodesic distance instead of general Euclidean distance, which enables faster convergence to a satisfactory solution for corner cases. Moreover, with a consideration for energy efficiency in practical applications, the number of turns in the path is effectively reduced by optimizing the shape of the sub-regions and the generation of the spanning tree, resulting in a more reasonable coverage for the target region.In this paper, the term “coverage” implies that individual intelligences must actually visit the corresponding regions. An effective multi-agent coverage algorithm should generate a covering path for each agent, so that the union of all paths can produce full coverage of the region while minimizing the average waiting time. Initially, the target region is described based on a grid, and subregions are divided based on the number of agents and their initial positions. In subsequent stages, the exact path for each agent within its exclusive region is planned through a spanning tree.x, y), and then discretely represented as equal grid cells with a certain resolution. The centers of the cells are represented by nodes:The discrete grid, due to its simplicity and flexibility, is one of the most commonly used forms of plane and surface representation in the field of computer graphics . By gridThe precision of grid discretization is dependent upon the scanning density The target polygon and each obstacle can be described with a sequence of grid nodes to represent its boundaries:A grid map can easily be represented as an array or matrix where each element expresses the occupancy status of a grid, including the location of the smart body, the status of its occupancy by obstacles, and whether it is a planable free grid. Define a i. The explorable area is labeled as 0, while the remaining area is labeled as −1.A complete representation of the tagged grid for the target region is shown in The set of free cells, excluding the cells outside the boundary and the cells occupied by obstacles, is defined as the explorable domain Definition 1:Adjacent nodes and are defined as follows:i-th agent. Furthermore, to ensure that the region can be explored cyclically, the planned path must be a closed path. In other words, This means that adjacent nodes must have common edges, which is in accordance with the physical constraints of the movement of the agents. Thus, the planned path for each agent is a sequence of adjacent cells:i-th multi-agent is denoted as We assume that the agents can accurately locate themselves within All the paths of the agents should completely cover the region;The area should be filled without overlapping paths, while avoiding all obstacles;No preparation stage, and the agents can start traveling from their initial position;Considering the constraints of the agents’ motion model, the trajectory should be simple and easy to control .It has been noted that a multi-agent system does not yield N-fold productivity due to various factors. First, the spatial limitations of the environment can force the agents to move together. Second, mutual interference among multiple agents has been reported . Third, Combining the previous discussions, the grid-based mCPP problem can be described as follows:Knowing the inputs Equations (1), (4), (5) and (9), plan the path Given the aforementioned condition 1, if our strategy can further ensure that there is no overlapping between the paths of the agents, then in the region Definition 2:The equivalence conditions required to establish a sub-region optimal solution are summarized as follows:;is connected The first condition ensures that the exploration paths among the agents do not overlap with each other, which is conducive to the generation of the optimal solution. The second condition ensures complete coverage of the free regions. The third condition ensures a balanced assignment of tasks, thus ensuring the minimization of the maximum waiting time among the agents. The fourth condition means that the assigned cells are directly accessible to the agents. This ensures that the exploration of sub-regions is a continuous and ordered operation, avoiding the additional cost of traversing non-connected regions . The last condition can ensure that there is no preparation stage for the agents to reach the responsible subregion before executing the exploration task.When deploying a set of agents, it is crucial to consider task assignment and coordination for enhancing system gain. Region division is the key to accomplish regional traversal using multiple agents, and it solves the mCPP problem by dividing it into several single-agent CPP problems. We continuously correct the distance matrix through an iterative process to construct an assignment matrix, labeling all cells to their corresponding unique agent. The feasibility of a balanced partitioning is explained in , where iFor the agent That is, each cell is assigned to the agent with the lowest travel cost. Then the region Adopting the above assignment strategy can fulfill the 1st, 2nd, and 5th conditions defined in Definition 2.i-th agent records the distance between each cell in i-th agent, and the update formula for each iteration is:i-th agent. If each agent has the same exploration capability, then:i-th agent is smaller than the equilibrium share i-th agents during the construction of the assignment matrix The distance matrix etail in .x, y] is in Since the target region is non-convex and there may be obstacles or no- entry areas inside, the above iterative procedure, although easier to converge, does not guarantee the continuity of the subregions (condition 3 in Definition 2). For the noncontiguous subregions, we introduced the correction matrix Ultimately, to keep the assignment matrix In summary, the region partitioning algorithm uses the distance matrices from cells to each agent’s position as the measure. The results of the region allocation are continuously modified through a process of iterative correction factors to satisfy the conditions outlined in Definition 2. The correction factors include both balance correction factors and connectivity correction factors. The flow of sub-region assignment is shown in After sub-region assignment, each agent is assigned a specific part of the grid to cover. Exclusively sub-regions ensure non-intersecting paths, allowing multiple agents to operate safely and simultaneously while avoiding potential collisions among them.The key feature of this algorithm allows the gradual incorporation of cells at any arbitrary location into the sub-regions. To be more specific, the algorithm temporarily violates the connectivity constraints of the assignment matrix in order to escape from local minima. Subsequently, the algorithm gradually eliminates the presence of unconnected regions and the connectivity of the sub-region In Appendix A of , three iAs shown in We believe that the attribution of the initial grid has a crucial impact on the number of iterations. Taking the case of 80% isolating proportion in The concept of geodesic distance originated from the field of geodesy in earth physics and is also referred to as geodesic or short-range line. It is mainly used to determine the local shortest path between two points in a curved space. In this paper, it is used to represent the cost of paths that bypass obstacles in a non-convex environment.The geodesic algorithms on the surface include graph methods, partial differential equation methods, and optimization methods . The divThe proposed algorithm primarily modifies its current state based on the globally optimal state, not solely by evaluating current information and candidate states. The algorithm approximates the behavior of gradient descent algorithms, possessing the capability of efficient search and reaching global optimality, even in the presence of multiple local minima.The robustness and fault tolerance of the region coverage is highly unfavorable if there is a situation where sub-regions are connected by the width of only one or two cells. The “Future Work” section of  also menInspired by the Dijkstra algorithm , we enhaHowever, it is noteworthy that, unlike the Dijkstra algorithm, which searches based on known global cost, this paper assigns weights to the path cost dynamically and locally. As shown in The improved Dijkstra algorithm replaces BFS, and dynamically introduces the turning weight to calculate the shortest path tree. The specific steps are shown in Algorithm A1 in Applying the assignment algorithm in A spanning tree path covering method with complexity given in . It starIn this method, the target area is discretized into square cells of size refer to a. A minirefer to b. Then, refer to c.Additionally, the number of turns is one of the major factors affecting travel time and energy consumption. It is believed that the choice of the initial spanning tree has a profound impact on coverage efficiency. If the shape of the spanning tree can be properly constructed to minimize turns in the in the closed path of the agent, it can greatly reduce the coverage time in practical applications. To address this issue, this paper appropriately assigns weights to edges in the grid undirected graph and uses this feature to control the connection of nodes in each sub-region’s spanning tree, generating a spanning tree shape that is inclined to follow a specific coordinate direction, thereby affecting the shape of the coverage path.The user-defined region of interest, The sub-regions of the polygon representing obstacles/no-entry zones, The required scan density The number of agents The initial positions The mCPP algorithm proposed in this paper solves the problem of planning paths for multi-agents that participate in a complete traversal of the region, given:As the output of the proposed algorithm, the corresponding coverage path It should be noted that although the final paths Recursive algorithms may have certain limitations and potential challenges in highly complex regions. First, recursive algorithms may be affected by computational resource constraints, as new memory space needs to be constantly created and freed during the recursion process, which requires the processing power and storage capacity of the computer. Additionally, the recursive algorithm may not perform well in some highly nonlinear and non-stationary problems, and may encounter problems such as numerical instability. To address these limitations and potential challenges, we can consider expanding or replacing the recursive algorithm with other methods. For example, more efficient optimization algorithms such as deep learning can be explored to better handle highly complex problems. Moreover, different decomposition and merging strategies can be explored to enhance the robustness and reliability of the algorithm.In the previous analysis, we have considered differently shaped regions, including concave polygon  and rectHere, the mCPP process for the given area with 4 agents was analyzed. The iteration process for subregion assignment was plotted in The path coverage planning for the indoor region is performed with four agents, and the process is shown in In practical applications, the detection range of sensors carried by the agents is typically circular, with a coverage diameter of In general, the terms Considering the sensing redundancy of each cell, there should be The original algorithm and the proposed optimization solution are quantified using the performance metrics listed in The optimization scheme has the same index of coverage (PoC) since the grid description of the target region is the same. The optimization scheme dynamically assigns weights to the path cost by an improved Dijkstra algorithm, making the sub-region assignment more reasonable (increased cohesiveness). Combined with the selection of different weighting schemes for the spanning tree, the number of turns in the coverage paths and the repeated sensing regions are both significantly reduced, resulting in an improvement in all types of metrics. To be more precise, the sub-region cohesion optimization method reduced the number of turns by 22.85%, the percentage of overlapping decreased by 22.17%, significantly reducing the wasted resource of redundant scanning in the execution of the operation.(1)In terms of region assignment, we introduce geodesic distances to cope with the problem that Euclidean distances are not directly accessible in non-convex regions. This method optimizes the Voronoi partition for the initial state and is effective for narrow regions and near-closed regions. In addition, we noticed that the partitioned sub-regions may have narrow “bridge” areas, due to the initial positions of agents and the obstructing effect of obstacles. It can be detrimental to the stability of the exploration process if the connectivity of the sub-regions is too dependent on some “bridge” cells. Therefore, this paper also optimizes the shape of sub-regions through a modified Dijkstra method to assign weights to step distances. So that the grid attribution is more reasonable and the robustness of the mCPP strategy is stronger. It is worth noting that the more “cohesive” sub-region division can plan paths with fewer turns and save turning energy.(2)For path planning, we describe the RRT algorithm for sub-region coverage paths. By appropriately assigning weights to edges in the grid graph, the shape of the generated tree is appropriately constructed, thereby affecting the shape of the coverage path, minimizing the turns in the closed-loop path of the agent.(3)In addition, we have built a simulation experimental platform for multi-robot systems in Gazebo and performed the application of the scheme in non-convex scenarios with indoor holes and strong partitions.When using multiple agents for cyclic exploration of a target region, it is important and critical to balance the assignment of tasks for each agent and to plan the corresponding paths within their respective regions. In this paper, we investigate the algorithms related to the grid description of the environment, sub-region assignment and shape optimization, and path planning within a subregion, and the main results and innovations achieved can be summarized as follows:The algorithm of regional path coverage proposed in this paper has been verified by simulation experiments to be feasible and provides new ideas and tools for the engineering field. There are still some problems worthy of further exploration, and future research work can be carried out in the following directions.(1)As the area to be covered grows linearly, the memory required by the grid-based method grows exponentially in finding the optimal paths, which is not suitable for large areas with small sensing ranges . Grid-ba(2)In the process of region division, geodesic distance is introduced to express the path cost in non-convex environments. In fact, geodesic line is a highly intrinsic quantity on a surface and has far-reaching significance in fields such as computational geometry and industrial production. Therefore, we may attempt to extend our task to surfaces (or complex terrains) to meet the demands of applications such as 3D scanning.(3)According to Galceran , the mCP


Periodic torque ripple often occurs in permanent magnet synchronous motors due to cogging torque and flux harmonic distortion, leading to motor speed fluctuations and further causing mechanical vibration and noise, which seriously affects the performance of the motor vector control system. In response to the above problems, a PMSM torque ripple suppression method based on SMA-optimized ILC is proposed, which does not rely on prior knowledge of the system and motor parameters. That is, an SMA is used to determine the optimal values of the key parameters of the ILC in the target motor control system, and then the real-time torque deviation value calculated by iterative learning is compensated to the system control current set end. By reducing the influence of higher harmonics in the control current, the torque ripple is suppressed. Research results show that this method has high efficiency and accuracy in parameter optimization, further improving the ILC performance, effectively reducing the impact of higher harmonics, and suppressing the torque ripple amplitude. The permanent magnet synchronous motor (PMSM) has superior performance and advantages in terms of efficiency, power density, torque-to-inertia ratio, and reliability. However, factors such as cogging torque and harmonic flux in the motor can cause distortion in the control current, resulting in periodic fluctuations in the motor output torque. This fluctuation is known as torque ripple in the motor. This phenomenon can cause mechanical vibration, speed fluctuations , and acoThe PMSM is a multi-variable, strong-coupled nonlinear system, whose periodic torque ripple involves various elements of the motor, such as harmonics, cogging torque, current identification error, phase imbalance, etc. . CurrentWith the widespread application of the PMSM in industrial production in recent years, torque ripple suppression methods based on control strategies have been intensively studied. Chen et al.  suppressThe slime mold algorithm (SMA) is a new meta-heuristic algorithm proposed by Li et al.  in 2020,Therefore, this paper proposes a torque ripple suppression method with a forgetting factor for an open-closed-loop iterative learning control to address the periodic torque ripple generated during the operation of a PMSM. The electromagnetic torque output by the system is used as a feedback signal to track the output current of the speed loop. The difference between the reference signal and the output signal is compensated in real time to the q-axis current reference terminal through an iterative learning control algorithm, and the iteration is repeated continuously to reduce the error. The chaos-mapped SMA is used to optimize the PID control parameters and forgetting factors in the iterative learning controller, improving the tracking accuracy and convergence speed of the torque error. This method does not rely on the system’s prior knowledge and motor parameters, and can adapt to the target motor, reducing manual debugging of parameters. It improves the optimization speed, avoids local optima, achieves better suppression effects, and further improves the torque ripple suppression effect. Simulation experiments were performed in the MATLAB/Simulink platform. The reduction in the number of iterations required for adaptive iteration obtained from simulation, as well as the reduction in torque ripple coefficient and torque ripple, all indicate that this method can further improve the performance of iterative learning control and better suppress the amplitude of torque ripple.Therefore, this paper proposes a torque ripple suppression method of an open-closed loop iterative learning control with forgetting factor for the periodic torque ripple generated when a PMSM is working, and optimizes and tunes the control parameters in the ILC using the SMA after chaos mapping to improve the optimal-searching speed and avoid local optimum, thereby further improving the torque ripple suppression effect. Relevant simulation experiments were conducted on the Simulink platform, and the simulation results showed that this method can further improve the performance of iterative learning control and suppress torque ripple amplitude.In the vector control system, neglecting the saturation of the magnetic circuit and core loss, as well as the effect of leakage flux and eddy current effect, the voltage equation of a PMSM in the synchronous rotating coordinate system is:In the equation, Among them, If further assumed that the PMSM used is a surface-mounted motor without salient poles and p represents the number of pole pairs of the motor and In Equation (3), The main causes of torque ripple include cogging torque and flux harmonic distortion; among which, cogging torque is the circumferential torque generated by the interaction between the rotor permanent magnet magnetic field and the cogging of the stator core, achieving suppression through the optimized design of the motor body , while mAmong them, In the equation, An iterative learning control (ILC) is a control method for trajectory tracking systems that perform repeated movements , which gIn this paper, the author designs a PID iterative learning controller for the speed loop of the PMSM vector control system, which uses the electromagnetic torque output by the system as a feedback signal, tracks the output current of the speed loop, and compensates the q-axis current set end in real time with the difference between the reference signal and the output signal through the ILC algorithm, repeating the iteration to reduce the error. Through this method, the controller can adjust the current in real time to control the output torque of the motor, achieving the torque ripple suppression effect.The ILC iteratively calculates the error α can be between 0 and 1. When the value of α is larger, the error of the system output decreases as the value increases. However, when the value of α approaches 1, the forgetting factor gradually fails. Therefore, the value of the forgetting factor needs to be determined based on actual engineering conditions to consider the convergence speed and robustness of iterative learning.The value of the forgetting factor q-axis current An open-closed loop PID type ILC algorithm with a forgetting factor is used to suppress the periodic torque ripple of the PMSM. From Equation (3), it can be seen that the electromagnetic torque of the motor is proportional to the Among them, An SMA  is a mathematical model that simulates the behavior and morphological changes of slime molds during their foraging process in nature. When the slime mold approaches a food source, the biological oscillator generates a propagation wave through the veins, increasing the cytoplasmic flow . The higM represents the population size of slime mold, and W represents the quality coefficient of slime mold, and its equation is:Among them, Among them, er areas .The search range of the SMA can be further expanded by using logistic chaotic mapping to initialize the population instead of random values. With a simple structure, logistic chaotic mapping can show balance in the phase space through a reasonable control parameters selection. By using logistic mapping during population initialization, the search range can be effectively expanded, and the efficiency of subsequent algorithms can be improved. Its iteration expression is:q-axis current.This paper selects four key parameters of iterative learning, A periodic trigger is incorporated to this process, with the rotor rotating once as a period, and the rotor position signal collected by the system is used to replace the time signal to control the operation of the ILC, thus effectively preventing the deviation of the compensation position corresponding to the current compensation value.In slime mold algorithms, fitness In this equation, The specific steps for an ILC parameter optimization based on the SMA are as follows.N and the population size M.Step 1: Initialization. Use logistic chaotic mapping to initialize the slime mold population positions in the four dimensions of Step 2: Assign the positions of Step 3: Update the current optimal individual and its fitness value.Step 4: Calculate the slime mold mass coefficient W according to Equation (15).Step 5: For each slime mold individual, update the parameters Step 6: If the algorithm reaches the set maximum iterations, output the optimal PID control parameters ; otherwise, return to Step 2.Step 7: The algorithm ends.M = 24, dimension In Matlab, the function m is used to write the chaotic initialization SMA, and a PMSM double closed-loop vector control (foc) model based on iterative learning compensation torque ripple suppression is built in Simulink to control the four parameters in the ILC for iterative optimization, whose value ranges are The target parameters are optimized through the SMA and compared with the optimization results of the PSO, to obtain the optimal parameters shown in In To further verify the effectiveness of this method, the data of torque suppression effect after ILC-SMA optimization is compared with the data from the system without a suppressor, and the data after being suppressed by the ILC and ILC-PSO methods:The torque ripple coefficient In this equation, Combining the simulation results of several suppression methods in To further verify the above conclusion, the fast Fourier transform (FFT) is performed on the torque ripple in the above figure, and the following harmonic analysis comparison chart is obtained.It can be seen from the harmonic analysis results in In summary, this article discusses the suppression of torque ripple in permanent magnet synchronous motors and proposes a torque ripple suppression strategy based on SMA optimization iterative learning parameters. In traditional dual closed-loop FOC control systems, the iterative learning deviation value is used to compensate for the speed loop q-axis torque current to reduce periodic torque ripple.The simulation results show that the SMA-ILC method has a better performance than the PSO-ILC method in terms of torque ripple suppression. Compared with the PSO-ILC method, the standard deviation and torque ripple coefficient of the SMA-ILC method are reduced by 19.1% and 26.3%, respectively, and the high-order harmonics after FFT analysis are reduced by 18.43% and 17.52%, respectively. The results show that the SMA-ILC method has a more effective torque ripple suppression effect for permanent magnet synchronous motors. This scheme can be used in industries with high requirements for low-speed stability of motors, such as the sports equipment industry. It can be used in treadmills to reduce speed fluctuations at low speeds and reduce the vibration felt by the foot. The SMA-ILC algorithm improves efficiency, but does not solve the dependence of this type of control method on torque sensors or torque observers. In future research, deep learning technology can be introduced to consider the non-electric factors affecting torque ripple, further improving the accuracy of torque ripple.


The study of wave-like propagation of information in nonlinear and dispersive media is a complex phenomenon. In this paper, we provide a new approach to studying this phenomenon, paying special attention to the nonlinear solitary wave problem of the Korteweg–De Vries (KdV) equation. Our proposed algorithm is based on the traveling wave transformation of the KdV equation, which reduces the dimensionality of the system, enabling us to obtain a highly accurate solution with fewer data. The proposed algorithm uses a Lie-group-based neural network trained via the Broyden–Fletcher–Goldfarb–Shanno (BFGS) optimization method. Our experimental results demonstrate that the proposed Lie-group-based neural network algorithm can simulate the behavior of the KdV equation with high accuracy while using fewer data. The effectiveness of our method is proved by examples. Nonlinear science is an interdisciplinary research field that spans a wide range of scientific domains, including life science, mathematical science, spatial science, and geographic science. In recent decades, the study of solitons has become increasingly important and widespread. Solitons are relevant in many fields of science, including fluid mechanics, quantum mechanics, biology, ocean engineering, and more. Therefore, the solution of soliton equations is theoretically and practically critical and has become an important area of theoretical and application-based research. The investigation of soliton equation solution techniques has not halted since the soliton theory was first put forward. Numerous equations have verified several mature solution techniques, including the Painlevé analysis , the BacThe ability to answer such scientific computing issues in conjunction with numerical analysis has significantly improved with the development of machine learning . The mosRecent advancements in deep neural networks have enabled researchers to solve differential and partial differential equations (PDEs) with fewer data points while maintaining high accuracy, making deep learning techniques an increasingly popular alternative to traditional numerical methods. In the beginning, Lee et al.  employedWhile neural networks have been used to solve PDE problems, the development of efficient algorithms that utilize minimal resources whilst still effectively addressing the underlying properties of solutions remains an ongoing issue. In this paper, we propose a novel approach that utilizes a Lie-group-based neural network algorithm for solving the KdV equation. Our new method boasts good learning performance, which we affirm by comparing its numerical results with those obtained from the true solution. Specifically, inspired by the unique form of Lie group theory for solving first-order differential equations, we developed a novel method to address PDE problems by constructing a solution consisting of a neural network function and a Lie-group-based solution. In our approach, the sum of these two parts approximates the solution of the differential equation. To effectively apply this approach to PDE problems, we first convert the PDEs into an ODEs. We observed that constructing the solution in this manner eliminates the need to increase the initial value item in the loss function whilst still fully satisfying the initial value. Moreover, using only a small number of neural network parameters can improve fitting ability, all thanks to the Lie-group-based solution. Our proposed approach is highly efficient since the Lie-group-based solution captures the nonlinear characteristics of the KdV equation well before training the neural network. As a result, the cost of the subsequent neural network calculations is reduced. Our approach not only delivers precise predictions but also highlights essential characteristics of the KdV solution such as the constancy of solitary waves over time. By leveraging our method, we can better understand and analyze complex physical phenomena described by the KdV equation, a feat that has remained challenging using other techniques. The ability to capture these key features is crucial in advancing our understanding of nonlinear dynamics and provides a significant boost to the predictive power of our model.Encouragingly, our investigation revealed that this new method can efficiently and accurately capture complex phenomena in nonlinear waves. We developed all implementations using PyCharm The remainder of this essay is structured as follows. The algorithm presented in this paper and its precise steps are shown in Consider the general form of PDE as follows:x, t, the solution u to be solved, and the partial derivatives of u with respect to the space variable x make up the nonlinear function N. The equation is subject to boundary or initial conditions.The independent variables x or t and u in 𝓛.Our study focuses on the restoration of the dynamic behavior of the KdV equation using a Lie-group-based neural network algorithm. Compare with the existing PINN learning method, experimental findings demonstrate that our proposed method can accurately restore the dynamic behavior of the KdV equation with high accuracy and fast convergence under a small number of parameters and a simple network structure. In addition, a deep study is done for our proposed algorithm, and the accuracy is improved when the number of hidden layers increases with the number of neurons contained, but the time cost spent is also relatively high.To confirm the accuracy and reliability of our proposed algorithm, we searched for other solitary solutions of the KdV equation. In the study presented in , an evalNotably, the success of our approach depends on capturing the mathematical substance of the equation solutions, which is often overlooked in machine learning techniques used for numerical solutions of differential equations. Recent research has shown that more implicit information about the solutions could be ignored when using these approaches. However, our proposed algorithm overcomes this limitation with only a shallow neural network model and limited data. Through our validation process, we have shown that our proposed algorithm performs effectively, producing highly accurate predictions for solitary solutions of the KdV equation. Our approach offers a new avenue for accurately predicting complex nonlinear solutions of PDEs and lays the foundation for future studies into other similar problems, which motivates us to study models in other interdisciplinary fields, such as finance or medical biology. The future work requires more research on optimization techniques to improve performance in addition to addressing parameter constraints or initial value constraints encountered in appeal problems.