Modeling Hydra Behavior Using Methods Founded in Behavior-Based Robotics

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30 Chapter 7. Results and discussiontensity M c = 1 and 2 s duration, presented every 16 s for 3 hours, followed by an absenceof the stimulus for 10000 s, and then repeated presentation every 16 s for 4300 s. Theoutputs of the training data set were reconstructed from [53], and can be seen (later on) inFigs. 7.3 and 7.5.For this model, two different approaches were used: (1) an RNN, and (2) a habituationmodel based on leaky integrators. Both models were optimized, parametrically and structurally,by means of an EA. The fitness measure was, in both cases, taken as f = 1/e,where e is the root mean squared error (RMSE) over the data set during periods ofstimulus presentation 1 :e = 1 ∑√ N (o(i) − y(i)) 2 , (7.3)Ni=1where o(i) represents the i:th measured response, and y(i) the corresponding responsefrom the model. On the occurrence of a stimulus the output from the habituation unit, theresponse strength, s, is related to the probability of a stimulus evoking a response [53].To ensure a valid range of the response probability, p B2 , regardless of habituation model,the following conversion was carried out:⎧⎨ s, 0 ≤ s ≤ 1,p B2 = 0, s < 0,(7.4)⎩1, s > 1.Activation of the AC occurs if M c > 0 and p B2 > X, where X is a random variabledrawn from the uniform distribution, X ∼ U(0, 1). In general, the latency depends onstimulus strength, as described in Section 3.2.1. However, no such information was foundin the literature for Hydra’s response to mechanical stimulus, therefore it was set to beconstant. Reset of the AC occurs at completion of the response, which may be a CP or anLP, as described below. The results from each test case of evolving a habituation unit willnow be described.Test A: Evolving an RNN to represent habituationAs a first experiment it was tested whether an RNN, parametrically and structurally optimizedby means of an EA to fit experimental data obtained in [53], could represent thehabituation to mechanical stimulus. A continuous time RNN was used. After applyingEuler’s method for numerical integration of the network equations, the dynamics of neuroni in the network is governed by the following equation (see also Appendix B):[ ()]y i (t + ∆t) = y i (t) + ∆tn∑m∑−y i (t) + σ b i + w ij y j (t) + w IτijI j (t) , (7.5)i1 Note that no contribution to the RMSE occurs during the recovery period.j=1j=1
7.1. Generation of behaviors 31where b is the bias term, τ the time constant, I the input signal(s), and w and w I are thesynaptic weights from other neurons and input signals, respectively. The integration timestep, ∆t, was set to 0.2 s. The simulation time step (time between two consecutive inputsignals) is 2 s, which gives 10 integration steps between data points used in the calculationof Eq. 7.3. A background to the RNNs used here is given in Appendix B. The RNN wasevolved using an EA with the following properties (see Appendix A for an explanation ofthe terms): explicit encoding, elitism, no crossover, tournament selection, and structuralas well as parametrical mutations. After an investigation of various mutation operators,six different operators were used, as described below. The EA properties are summarizedin Table 7.1.m 1 - Creep mutation: The value of the gene is updated according tow new = w old (1 − 2rc + c), where r ∼ U [0, 1] and c is the creep rate. Since thismutation may generate values outside the allowed range, the gene was scaled intoits proper interval using w → w max if w > w max , and w → w min if w < w min .m 2 - Full-range mutation: The gene is given a new, random value within the allowedparameter interval.m 3 - Add connection mutation: A connection between two units (either between twoneurons, or between an input signal and a neuron) with a randomly chosen synapticweight (within the allowed range), is added.m 4 - Remove connection mutation: Removal of a connection between two units.m 5 - Add neuron mutation: One neuron is added to the RNN (at a randomly chosenlocation). To avoid a macromutation, i.e. a mutation that alters the performance ofthe resulting individual in a significant way, the neuron is added with all weightsset to zero (and with randomly selected bias and time constant). Thus, only thepossibility of new connections is established as a result of this mutation operator.m 6 - Remove neuron mutation: Removal of one randomly chosen neuron and all its incomingand outgoing connections.In Fig. 7.2, the structure of the best evolved RNN is shown. The network consists of threeneurons and, as can be seen from the network parameters in Eq. 7.6, all connections butone input signal connection were established. The evolved RNN performs adequately onthe test data, as can be seen in Fig. 7.3. However, its generalization ability to other ISIsand stimulus intensities is poor, an example of which is also shown in Fig. 7.3. In general,it should be possible to improve this ability by including such stimulus properties in thetraining data set. However, no such data was found in the literature, and it was decided touse another approach rather than creating a new, somewhat arbitrary data set. As a result,a solution based on a model of habituation was investigated, which will be described next.
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Page 11 and 12: Table of Contents1 Introduction 11.
Page 13: Table of ContentsviiB Recurrent neu
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Page 18 and 19: 4 Chapter 1. Introduction1.3 Outlin
Page 20 and 21: 6 Chapter 2. NotationUpper-case let
Page 22 and 23: 8 Chapter 3. Animal behaviorPsychol
Page 24 and 25: 10 Chapter 3. Animal behaviorperiod
Page 27 and 28: Chapter 4Behavior-based roboticsAs
Page 29 and 30: Chapter 5HydraThis chapter presents
Page 31 and 32: 5.1. Hydra as a model organism 17ce
Page 33 and 34: Chapter 6Models and methodsIn this
Page 35 and 36: 6.1. The simulated system 21Contrac
Page 37 and 38: 6.1. The simulated system 23Table 6
Page 39 and 40: 6.3. Constituent behaviors 25Releas
Page 41 and 42: Chapter 7Results and discussionIn t
Page 43: 7.1. Generation of behaviors 29Expe
Page 47 and 48: 7.1. Generation of behaviors 33....
Page 49 and 50: 7.1. Generation of behaviors 35Tabl
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Page 53 and 54: 7.1. Generation of behaviors 39Tran
Page 55 and 56: 7.2. Generation of behavioral organ
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Page 60 and 61: 46 Chapter 8. Summary and conclusio
Page 62 and 63: 48 Bibliography[11] BÄCK, T., FOGE
Page 64 and 65: 50 Bibliography[41] MITCHELL, M., A
Page 66 and 67: 52 Bibliography[69] WATSON, J., Beh
Page 68 and 69: 54 Appendix A. Evolutionary algorit
Page 71 and 72: Appendix BRecurrent neural networks
Page 73: Appendix B. Recurrent neural networ

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