Estimation of moving agents density in 2D spacebased on LSTM neural network

Marsela Polic∗, Ziad Salem†, Karlo Griparic∗, Stjepan Bogdan∗ and Thomas Schmickl†∗University of Zagreb

Faculty of Electrical Engineering and Computing, LARICSe-mail: marsela.polic@fer.hr

†University of GrazArtificial Life Lab

Abstract—As a part of ASSISIbf project, with a final goal offorming a collective adaptive bio-hybrid society of animals androbots, an artificial neural network based on LSTM architecturewas designed and trained for bee density estimation. Duringexperiments, the bees are placed inside a plastic arena coveredwith wax, where they interact with and adapt to specialized staticrobotic units, CASUs, designed specially for this project. In orderto interact with honeybees, the CASUs require the capability i)to produce and perceive the stimuli, i.e., environmental cues,that are relevant to honeybee behaviour, and ii) to sense thehoneybees presence. The second requirement is implementedthrough 6 proximity sensors mounted on the upper part of CASU.In this paper we present estimation of honeybees (moving agents)density in 2D space (experimental arena) that is based on LSTMneural network. When compared to previous work done in thisfield, experiments demonstrate satisfactory results in estimatingsizes of bee groups placed in the arena within a larger scope ofoutputs. Two different approaches were tested: regression andclassification, with classification yielding higher accuracy.

I. INTRODUCTION

This work was conducted as a part of the ASSISIbf project(Animal and robot Societies Self-organise and Integrate bySocial Interaction – bees and fish). The long-term goal of theproject is to create mixed societies of honeybees and robots, aswell as fish and robots, with a very high level of social integra-tion. As a part of the project, specialized static robotic units,CASUs (Combined Actuator-Sensor Unit) have been designed[1] for controlled producing and sensing of a variety of stimulirelevant for honeybee behaviour. By using multiple stimuli ascommunication channels, we hope to achieve effectively onesingle, integrated society, a social cyborg [2]. We expect thatsuch a biohybrid society can collectively perform tasks withgreater efficiency and robustness than the individual biologicaland robotic societies.

The process of machine learning in the project is a keyelement in the whole generation process for biohybrid sys-tems. Basically, an evolutionary adaptation module adaptsthe microscopic rule-sets performed by the robotic part ofthe mixed society until the collective (animals and robotstogether) performs the targeted operation. As this process isnot stopped at runtime, the whole biohybrid system adapts notonly during the design phase, but keeps on adapting duringthe runtime of the system in operation phase. This adaptationtakes place on multiple levels and at multiple places within the

collective system. On the one hand, evolutionary computationadapts robotic behaviour, both individual, as well as thecollective behaviour of society, as a consequence of robotinteraction. On the other hand, the animal components in thecollective systems are (compared to computer systems) verysophisticated learners who also adapt on both individual andcollective level. Finally, animals and machines adapt togetheras a mixed society.

In the imagined experimental setup, an experimental arenais built with multiple CASUs and groups of bees. The twosocieties are to interact through available sensory and actuatingunits, where the robotic part is guided by the developeddecentralized algorithm, and the biological part acts upon thenatural rules of a bee swarm. The CASUs are unaware of theglobal state of the honeybee swarm: their group size, spatialdistribution and dynamics are unknown. However, through thelocal information obtained through their respective sensors,and through the partial communicated information that theyexchange, the robots are supposed to react and adapt toenvironmental states and eventually cooperate on a globallevel both mutually, and with the bee society. Local densityof honeybees is one of the important quantitative measures,which enables realization of such distributed cooperation byproviding the robot behaviour algorithms with a numericalmeasurement of one environmental state.

Previous attempts have been done to estimate the densityof agents using machine learning algorithms. Salem andSchmickl [3] used RULES-4 algorithm (RULe ExtractionSystem version 4) [4], an incremental classification machinelearning algorithm. In this work, bristlebots were used insteadof bees as agents. The bristlebots represent a very simple formof electrically driven mobile robots, making use of moderndevelopment in low-mass motors and batteries. These mobilerobots have the property of random movement, and with asize and speed comparable to the one of bees, can act asreplacement in case of a lack of bees in some experiments, e.g.during the winter season. The data was collected based on themeasurements of the six proximity sensors of the CASU. Thealgorithm generated a set of rules able to predict the number ofbristlebots in the arena based on the CASU’s sensor readingswith satisfying accuracy within a learned range (up to 10 bees).

In this work, another approach was taken on the same

problem, both with respect to the algorithm deployed, andthe agents in focus. Taking into consideration the nature ofdata and time variance of underlying function, an algorithmwith memory and ability to handle time series was sought.A recurrent neural network (RNN) based on Long Short-Term Memory (LSTM) architecture is proposed and trainedon experimental data.

We successfully applied the algorithm to the problem ofestimating the number of young honeybees in an experimentalsetting similar to the described previous work [3]. The algo-rithm yielded satisfactory results in estimating sizes of beegroups placed in the arena within a larger scope of outputswhen compared to previous work done in this field. Twodifferent approaches were tested: regression and classification,with classification yielding higher accuracy.

II. BIOLOGICALLY INSPIRED EXPERIMENTALSETUP

Study of the young honeybees (Apis mellifera L.) is inthe focus of ASSISIbf project. These recently emerged socialinsects, up to 24 hours old, are used as moving agents inexperiments, with description of underlying processes of a beeswarm and formation of a biohybrid society as a final prospect.This society would consist of bees, fish, and robotic devices,which should all interact, adapt and enable intelligence emer-gence from a set of cognitively simple individual agents.

A. Experimental setup

The biohybrid society to be formed, inspired by the naturalformation of a swarm, should represent a decentralized systemin which collective intelligence emerges from a set of simpleagents of a lower individual intelligence level in combinationwith a simple set of rules governing their behaviour. Instead ofusing a central sensing unit (e.g. camera, laser), a decentralizedapproach was chosen through deployment of a large numberof distributed, simple and inexpensive sensors. In addition,the distributed approach also results in increased robustnessand removal of spatial constraints on the experimental site(ease of deployment in different places). These sensors areboth small and inexpensive, which makes them convenientfor application in large amounts. Their small size results inreduced energy consumption, but on the other hand also limitstheir performance, enabling them only to be used in short-distance sensing. However, they are easily replaceable in caseof malfunction or deterioration over time. One of the mostimportant virtues of a system relying on this kind of sensorysetup is the robustness with respect to the sensor imperfection.The simplicity of these units enables the system to adapt tothe inherent changes, such as malfunction of several of itscomponents, even during the runtime, which is one of themain advantages of a decentralized system as opposed to theone relying on a central master component.

The technical part of the system was therefore imagined asa network of static robot units with limited capabilities andaccess to only local information. The robots designed as apart of the project, CASUs (Fig. 1), consist of a set of simple

Fig. 1. CASU isometric view with labeled main parts.

Fig. 2. CASU in interaction with bees.

sensors and actuators that enable them to sense and respondto the changes in the environment based on the behaviouralgorithms built by the evolutionary adaptation. Even thoughthe CASUs have the ability to influence the behaviour ofbees (Fig. 2) through different stimuli (attraction, repulsionand “freezing”), in this experiment they were only used asobserving agents in the arena setting, through their infraredproximity sensors readings. The six proximity sensors areplaced on the top of the CASU, and can detect obstacles upto approximately 3 cm distance from the sensor surface. Theircircular placement on the CASU top enables detection in afull 360◦ range. In the experiments conducted in this work,a single CASU was used for honeybee detection and densityestimation. The idea is to gain an insight of the sensor activityand undelying features in a rudimentary setup, which can laterbe used with slight modifications to estimate honeybee densityaround different CASUs placed in a bigger arena.

The proximity sensor consists of two LEDs: the emittingand the receiving one. The emitting LED produces an electro-

magnetic beam in the infrared spectrum, which then reflectson a nearby object, and travels back to the sensor surface. Thereceiving LED then produces output voltage depending on theintensity of the reflected beam. The output of the proximitysensor is then a measure of amplified output voltage on thereceiving LED. Since the direction of the beam cannot bedistinguished, there is no information of the distance from thesensor to the obstacle. Therefore, a form of sensor fusion isneeded in order to obtain a useful information about the stateof the CASUs near surrounding.

B. Method

In this work, the goal was to estimate the number of thehoneybees in a circular arena surrounded by plastic wall withdiameter of (d = 12.5cm). The data for estimation is producedby proximity sensors, and then fed to a machine learningalgorithm. The experimental setting consisted of a singleCASU at the centre of the arena, and a set of different beespopulation sizes. Fig. 3 gives an overview of the experimentalsetup.

Fig. 3. Overview of the circular arena with 30 honeybees

In the initial stage, we record the infrared readings for oneminute with an empty arena (no honeybees). This recording islater used as an overview of the idle state of sensors for controlpurposes. After this initial tuning experiment, we place thehoneybees in the arena and let them walk on the wax aroundthe centered CASU for 30 minutes.

We conducted the experiments with three different sets ofhoneybee population sizes. In the first set of experimentsthe honeybee population size varied from 1 to 42 bees withincrease of 3 (1 bee, 4 bees, 7 bees, etc.). In the second setthe populations varied from 3 to 30 bees with increase of 3.In the final set the population varied from 1 to 32 bees withincrease of 1. The final result of experiments is CASU log filecontaining the infrared readings for the six proximity sensors.The samples are collected every 0.1 sec. The readings arevaried based on how close are the honeybees to the infraredsensor. Table I shows data set sample with 30 bees moving in

TABLE IDATA SET SAMPLE OF 30 BEES, WHERE: F=FRONT SENSOR, FR=FRONT

RIGHT SENSOR, BR=BACK RIGHT SENSOR, B=BACK SENSOR, BL=BACKLEFT SENSOR, FL=FRONT LEFT SENSOR. DATA REPRESENTS

UNPROCESSED SENSOR OUTPUTS OF PROXIMITY SENSORS, WITH VALUESWITHIN RANGE [0, 65529], ROUGHLY CORRESPODING TO THE

PERCENTAGE OF EMITTED INFRARED BEAM REFLECTED TO SENSORSSURFACE.

F FR BR B BL FL1 10910 13076 12679 15040 15106 158342 10923 13067 12681 15039 14846 158253 10923 13067 12681 15039 14846 158254 10912 13073 12683 15041 15109 158245 10912 13073 12683 15041 15109 158246 10917 13072 12677 15034 14846 158217 10919 13074 12681 15037 15105 158248 10919 13074 12681 15037 15105 158249 10921 13077 12678 15046 15104 1582510 10916 13078 12679 15042 14847 15829

the arena surrounding the CASU. The values in the table areraw sensor values, i.e. a digital representation of the amplifiedoutput voltage on the receiving infrared LED. The table showschanges in the infrared readings for the Back Left sensor dueto honeybees within the range of detection. Activity of thissensor is shown in a schematic in Fig. 4.

Fig. 4. One active sensor state corresponding to the data sample in Table I

These data will be the used for input to the machineleaning algorithm discussed in the following sections. Asshown in Fig. 5, the continuous values are first binarized byoffset removal. The offset is calculated from the initial tuningmeasurement in the empty arena. As shown in the figure, thistuning measurement is removed from the data set, because ofambiguity of such sequence with respect to target values whenbinarized. Upon offset removal, the data series is compared toa threshold defined as a percentage of the offset value, whichfinally produced a binary input sequence.

III. NEURAL NETWORK

Machine learning has become a mature technology thatis being applied to a wide range of computational problems[5]. It has been dramatically propelled forward by impressiveempirical successes of artificial neural networks, which cannow be trained with huge data sets and large-scale computing

Fig. 5. Sensor output binarization process. The upper subplot shows rawreadings from the sensor (blue), along with the DC-filtered raw readings (red).First one minute of the recording is averaged and subtracted from the rest ofthe raw values in order to remove offset. The first, tuning minute of therecording is then clipped out of the data series, which is shown in the figureby moving the red recording backwards in time relative to the original series.Lower subplot shows the final binary data series obtained by comparison ofa continuous series (red) to a threshold (black).

[6]. Neural network for agent density estimation problemwas built taking into account the nature of input data. Theraw data, collected from six infrared proximity sensors ineach experiment, consisted of six time series of continuousvalues, which were dichotomized into binary values, denotingpresence of a bee, or lack thereof. This format of data implieddeployment of a time-variant algorithm.

A. Choice of neural network

It has been proven that conventional feedforward deepneural networks can approximate any continuous function of nreal variables with mild conditions on its activation functions[7]. However, this only relates to the static processes, anddoes not provide the network with more than only limitedtemporal modeling ability by operating on a fixed-size slidingwindow of input sequence. Recurrent neural networks (RNNs),on the other hand, contain cyclic connections that enable themto model long-term dependencies in the sequence data [8].Among many different recurrent networks, a Long Short-TermMemory (LSTM) neural network was chosen for this problem.

LSTM network was developed in order to solve the opti-mization problem of conventional recurrent networks duringbackpropagation. Depending on the size of weights, the errorsignal travelling backwards through the network tends to eitherblow up or vanish during network learning. In the first case,the error increases during backpropagation, similar to signalpropagation through a positive feedback loop. Because thenetwork weights are tuned based on the error signal, theparameters values oscillate and diverge. In the second case,the error signal diminishes through propagation, which causes

Fig. 6. Memory block schema, from [10]

parameters to change too slowly, yielding a suboptimallytrained network. In order to solve this problem, a structurecalled memory block was introduced. The memory block tendsto enforce a constant (as opposed to exploding or vanishing)error flow through network [9]. A schematic of a memoryblock is shown in Fig. 6.

Initially, the memory block consisted of a cell with arecurrently self-connected linear unit called the ”ConstantError Carousel” (CEC), an input, and two multiplicative gatingunits: input and output. The CEC, whose activation is calledthe cell state, is the part that enforces constant error flow [11].Input and output gating units are responsible for protection ofCEC from activation and noise, and backpropagation error,respectively [12]. These are nonlinear summation units whichcontrol the activation of the cell via multiplication [10]. Theiractivation function, denoted f in Fig. 6 is usually the logisticsigmoid. Block input activation function g is usually tanh orlogistic sigmoid, while output activation function h can beany of those, or a linear function [10]. Later modificationsof the initial proposal include the forget gating unit [12], andpeephole connections [11]. The forget gate was introducedinstead of a constant recurrent connection of the cell to solvethe saturation problem by enabling the LSTM to reset itsstate [13]. The peephole connections enable the gating unitsto observe their direct effect on the CEC [11].

Two different approaches were deployed: regression andclassification. Network architectures for both approaches wereoptimized independently. The first approach was a regressionneural network, which had three hidden layers. The first hiddenlayer consisted of a single LSTM block. The second hiddenlayer had 20 artificial neurons (McCulloch-Pitts neurons) with

TABLE IIINPUT ATTRIBUTES DESCRIPTION

Attribute no. Description1 A single sensor active2 Two sensors active3 Three sensors active4 Four sensors active5 Two neighbouring sensors active6 Two semi-neighbouring sensors active7 Two opposite sensors active8 Three neighbouring sensors active9 Four neighbouring sensors active

tanh activation function. The third hidden layer consisted of10 McCulloch-Pitts neurons with linear activation function.Finally, the output layer was a single neuron with reluactivation function. We used backpropagation for networktraining, with RMSprop as an optimizer, and mean squareerror as an objective function. Two means of regularizationwere used: dropout technique, and early stopping.

The classification neural network also had three hidden lay-ers: five LSTM cells in the first hidden layer, three McCulloch-Pitts neurons in the second layer, and two in the third. Allof the McCulloch-Pitts neurons had tanh activation function.The output layer in this network consisted of two neuronswith softmax activation function. Again, backpropagationwas used, with RMSprop optimizing binary cross-entropy.Both dropout and early stopping were used for regularization.

B. Data preprocessing

Binarized sensor outputs were additionally preprocessedbefore feeding them into the network. The preprocessingwas conducted as a hyperoptimization process through cross-validation. The first hyperoptimization parameter was numberof attributes. Instead of a timeseries with six attributes (sensorreadings), new attributes were formed similar to [3]. Throughcross-validation, a neural network with 9 attributes (describedin Table II) was chosen among networks with 6, 9, 10and 11 attributes. The choice of the attributes is related tothe expected and experienced bee swarm behaviour, namelythe tendency of swarming, which results in dense honeybeegroups which become relatively large when compared to thesensor size, and trigger the activation of multiple sensors on aCASU simultaneously. The differentiation was made betweenactive neighbouring, or non-neighbouring sensors because ofa possibility of multiple neighbouring sensor activation bya single bee in certain positions, while activation of, e.g.two sensors on opposite sides of a CASU corresponds to atleast two different bees in the CASU close surroundings. Theadditional attributes forming sets of 10 and 11 attributes wererelated to more than 4 active sensors. However, the activity ofthese attributes was very low, resulting in unnecessary increaseof input dimension of the networks without an expected benefitof differentiation between 0 and 5 or 6 active sensors.

The experiments were conducted in order to collect datalasting around 30 minutes. These recordings were split intoshorter samples (lasting 200 s, i.e. 2000 time steps) for several

reasons. First of all, it is easier for the network to generalizeand extract useful information from a shorter input series(less noise). In addition, splitting data into shorter samplesgenerated a larger data set for training and validation. Finally,deployment of (trained) network in experiments was taken intoconsideration. Namely, training a network on shorter samplesenables it to also run on and categorize shorter samples online,producing estimates more frequently during an experiment.The splitting of the recordings resulted in 719 examples.

Because sample time in the experiments is at least anorder of magnitude faster than the dynamics of bees, attributevalues were averaged over time. Number of average valuesof attribute per 200 s (2000 samples) was the second hyper-optimization parameter. Through cross-validation, 40 averagevalues were chosen as input length. In this way, every 5 s ofa 200 s long experiment was represented with one averagevalue.

IV. RESULTS

Neural networks based on LSTM architecture were trainedon a set of 719 examples. The data set was split into trainingand test sets in ratio 9:1. Additionally, 20% of the examplesin the training set were randomly split into a validation set ineach training epoch. The networks were trained in maximum10000 runs, with early stopping set to interrupt training after400 runs of non-decreasing loss function on validation set.The algorithms were trained for 100 times with initial weightssampled from the uniform distribution, as proposed in [14].The main characteristics of the used optimizer, i.e. RMSprop,can be described with the update equations eq. 1-3 for epochk, where g is the gradient of the objective function w.r.t. tothe neural network parameters, E is the exponentially decayingaverage of squared gradients, ρ is the momentum parameter, ηis the learning rate, and parameter ε is solely a smoothing termto avoid division by zero. RMSprop optimizer parameters wereset as follows: initial learning rate was set to 0.003, momentumparameter to 0.9, learning rate decay factor to 0.001, and ε to10−8.

g = ∇θJ(θ) (1)

E[g2]k = ρ · E[g2]k−1 + (1− ρ) · g2k (2)

θk+1 = θk − η√E[g2]k + ε

gk (3)

TABLE IIIACCURACY OF NEURAL NETWORK TRAINED FOR REGRESSION

Set Training set Test set OverallAccuracy [%] 62.13 72.22 63.14

The accuracy of the regression neural network is shown intable III. A sample of 100 network outputs along with theirtargets is shown in Fig. 8 on the training set, and in Fig. 9 onthe test set. The accuracy of regression network was defined

Fig. 7. Distribution of regression network output error

as a percentage of correct network estimates, where correctwas defined as in eq. 4, i.e. when the network output is within±5 range around the target output. As can be seen in Fig. 8and Fig. 9, the network could not distinguish the outputs largerthan 30, and classified them as 30. It could also not distinguishthe outputs smaller than 5. The distribution of error on thewhole data set is shown in Fig. 7.

correct =

{1, |y − y| ≤ 50, else

(4)

The neural network for regression implied that it should bepossible for an RNN to distinguish between larger and smallergroups of bees. Because of the distribution of available data,with a possible future application in mind, a threshold of 15bees was decided as margin between larger and smaller group.The classification network managed to separate input data intotwo categories (smaller vs. larger group of bees) with accuracyof 88.41% on the training set, and 80.56% on test set.

TABLE IVACCURACY OF NEURAL NETWORK TRAINED FOR CLASSIFICATION

Set Training set Test set OverallAccuracy [%] 88.41 80.56 87.62

TABLE VCLASSIFICATION NEURAL NETWORK

Category Precision Recall F1≤ 15 0.7568 0.8485 0.8000> 15 0.8571 0.7692 0.8108average 0.8056 0.8100 0.8053

The results obtained on the network trained for classificationare shown in table IV. Fig. 10 and Fig. 11 show networkclassification of examples in training and test set. Again, onlya sample of 100 examples on training set is shown. The target

categories, shown as output value 0 or 1, denote classificationinto category ”15 bees or less”, and ”more than 15 bees”,respectively. Network output has been rounded to a closerinteger to gain a clearer view of (mis)classification, as thisrepresentation directly shows network classification decision.As can be seen in table V, the average F1-score is more than0.8, which is a satisfactory result for the intended usage.

V. CONCLUSION

In this paper we presented a method for estimation ofhoneybees (moving agents) density in 2D space based onLSTM neural network as a part of generation process for bio-hybrid ICT systems. The goal is to adapt robotic behaviour,both individual, as well as the collective, as a consequenceof robot interaction with animals. Agents density estimationis the key for achieving this goal as it provides better fitnessfunctions for evolutionary formation of biohybrid society. Forthat purpose we build specialized static robotic units, calledCASUs, that are equipped with six proximity sensors placedon the top part of the unit. The raw data, collected fromthose sensors in each experiment, consisted of six time seriesof continuous values, which were dichotomized into binaryvalues, denoting presence of a honeybee, or lack thereof.This format of data implied deployment of a time-variantalgorithm based on LSTM neural network. Binarized sensoroutputs were additionally preprocessed before feeding theminto the network. The preprocessing was conducted as ahyperoptimization process through cross-validation. We con-ducted the experiments with three different sets of honeybeepopulation sizes and two different approaches were tested:regression and classification. When compared to previous workdone in this field, experiments demonstrate satisfactory resultsin estimating sizes of bee groups placed in the arena withclassification yielding higher accuracy.

ACKNOWLEDGMENT

This work is supported by: EU-ICT project ASSISIbf -Animal and robot Societies Self-organise and Integrate bySocial Interaction bees and fish, no. 601074

Fig. 8. Results of regression neural network on training set.

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Fig. 9. Results of regression neural network on test set.

Fig. 10. Results of classification neural network on training set.

Fig. 11. Results of classification neural network on test set