Modeling Hydra Behavior Using Methods Founded in Behavior-Based Robotics

34 Chapter 7. Results and discussionTest B: Evolving a habituation model based on leaky integratorsOne way of modeling habituation is to use cascaded leaky integrators, as proposed e.g. in[62], and illustrated in Fig. 7.4. With the stimulus input as Y 1 , the equations for unit j ina cascade of n integrators becomeV j (k + 1) = a j V j (k) + b j Y j (k), (7.7)Y j+1 (k) ={Yj (k) − V j (k), Y j+1 (k) > T j0, otherwise.(7.8)Here all thresholds, T j , were set to 0. The response strength, s, is taken as the output fromthe last (N:th) unit, Y N+1 , on the occurrence of a stimulus, as proposed in [62]. An EA wasused to evolve the size (N) and parameters {a 1 , a 2 , ...a N , b 1 , b 2 , ...b N } of a habituationmodel on this form to fit the data previously described. For the EA, chromosomal realnumber encoding was used, with genes taking values in [0, 1]. Two-point crossover 2 andtournament selection was used, as well as two mutation operators, m 1 and m 2 . Carryingout parametrical mutations, m 1 assigns a new (random) value to a gene. Mutation operatorm 2 adds or removes, with equal probability, two genes (corresponding to one integratorunit), to an indidivual. The EA properties, along with the performance of the obtainedmodel, are shown in Table 7.2 and Fig. 7.5, respectively.T ✲ ✓✏ 1 TI 1✲ ❡✲ σ1 ✲ ✓✏ 2Y 1 V 1 Y 2 VI 2✲ 2 Y❡✲ σ2 ✲ 3-✻ + ✒✑ -✻ + ✒✑+✲ b j✲ ❡ ✲ z −1 ✲I j + ✻a j ✛Figure 7.4: Habituation model based on leaky integrators. The top panel shows two cascadedunits in compact form. Here, σ j is a threshold unit with parameter T j . The bottom panel showsthe contents of each integration unit, I j .2 Since each integrator unit is represented by two genes, a valid individual consist of an even number ofgenes. To avoid generating individuals with odd number of genes, the crossover points were restricted toevery two genes.