Via Giuseppe Moruzzi, 1 - 56124 Pisa, Italy. {Onofrio.Gigliotta,Giovanni.Pezzulo,Stefano.Nolfi}@istc.cnr.it. Abstract. In this study we show how simulated robots ...
Emergence of an Internal Model in Evolving Robots Subjected to Sensory Deprivation Onofrio Gigliotta1,2 , Giovanni Pezzulo3 , and Stefano Nolfi2 1
Department of Relational Sciences, University of Naples Federico II Via Porta di Massa, 1 80113 Naples, Italy 2 Istituto di Scienze e Tecnologie della Cognizione - CNR Via S.Martino della Battaglia, 44 - 00185 Rome, Italy 3 Istituto di Linguistica Computazionale “Antonio Zampolli” - CNR Via Giuseppe Moruzzi, 1 - 56124 Pisa, Italy {Onofrio.Gigliotta,Giovanni.Pezzulo,Stefano.Nolfi}@istc.cnr.it
Abstract. In this study we show how simulated robots evolved to display a navigation skills can spontaneously develop an internal model and rely on it to complete their task when sensory stimulation is temporarily unavailable. The analysis of some of the best evolved agents indicates that their internal model operates by anticipating functional properties of the next sensory state rather than the exact state that sensors would have assumed. The characteristics of the states that are anticipated and of the sensory-motor rules that determine how the agents react to the experienced states, however, ensure that the agents produce very similar behaviour during normal and blind phases in which sensory stimulation is available or is self-generated by the agent itself, respectively. The characteristics of the agents’ internal models also ensure an effective transition during the phases in which agents’ internal dynamics is decoupled and re-coupled with the sensory-motor flow.
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Introduction
The idea that cognitive agents act on the basis of internal models of their tasks rather than purely on the basis of the stimuli they receive from the external environment can be considered fundamental in cognitive science [1],[2],[3]. The structure and functioning of internal models is however much more debated. Traditional theories in cognitive science describe internal models as symbolic mental structures that support higher level cognition and whose representational content is conceptual and is not tied to any sensorimotor modality. The de-emphasization of symbolic representations in cognitive science, and particularly cognitive robotics, has resulted in decreased attention to internal models in favor of a non-representational view [4]. Recently, however, the idea of internal modeling is gaining consensus anew, as numerous researchers in cognitive psychology, neuroscience, and robotics are increasingly reusing ideas originating from the domain of motor control [5,6] into more cognitive domains, therefore reintegrating the idea of internal modeling and representation in an “embodied”, “motor” view of cognition [7,8,9,10,11,12,13]. S. Doncieux et al. (Eds.): SAB 2010, LNAI 6226, pp. 575–586, 2010. c Springer-Verlag Berlin Heidelberg 2010
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Internal models come in (at least) two varieties: inverse models and forward models. The former compute the necessary motor commands to achieve a certain goal given a starting condition, and the latter predict the sensory consequences of those motor commands. Fig. 1 highlights the differences between (a) a stimulus-response system, and (b) one endowed with (multiple pairs of) internal, forward and inverse models, which is inspired by the architecture for motor control described in [14]. In the latter, the internal models (inverse and forward) realize an inner loop, which parallels actual sensorimotor interaction and mimics its input-output properties. Such loops can function on-line with action (b), or off-line (c), that is, detached from the current sensorimotor context. When this last condition holds, sensory inputs are substituted by predicted inputs, and motor outputs are inhibited. This last mode of functioning permits chaining multiple predictions (in principle, for an arbitrarily long number of steps) so to realize long-term lookahead predictions, or “mental simulations” [10,11].
Fig. 1. Comparison between purely stimulus-response systems (b) and those endowed with anticipatory capabilities, which run an “internal loop” on-line with action (b), or off-line (c)
In other words, since internal models support the anticipation of action consequences, they can be used as “inner worlds” to try out actions, such as walking or reaching, internally rather than in the external environment. This novel view of internal modeling, which incorporates control-theoretic ideas and an embodied view of cognition, is clearly synthesized in the emulation theory of representation proposed by [9, p. 1]: in addition to simply engaging with the body and environment, the brain constructs neural circuits that act as models of the body and environment. During overt sensorimotor engagement, these models are driven by efference copies in parallel with the body and environment, in order to provide expectations of the sensory feedback, and to enhance and process sensory information. These models can also be run off-line in order to produce imagery, estimate outcomes of different actions, and evaluate and develop motor plans. In this paper we investigate whether internal modeling could spontaneously arise in living organisms for the sake of effective motor control. More specifically, in
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this paper we investigate whether artificial embodied agents, that are trained for the ability to exhibit a given behavioral skill, develop and use an internal model that allows them to anticipate forthcoming stimuli to overcome the problems caused by the fact that sensory stimulation is temporarily missing. From a computational point of view, artificial organisms faced with a navigation problem in the presence of sensory stimuli will most likely develop a reactive, stimuli-based behavioral strategy (which can involve dynamical aspects, see later). The rationale behind our task design is that, when the environmental conditions change so that stimuli become temporarily unavailable, the artificial organisms have two options: either developing brand new behavioral strategies for dealing with the absence of stimuli, or learning to self-generate stimuli, so to reuse their already established behavioral strategy. Our study then aims to verify if this second option actually happens during neural evolution (and with which frequency) and if the ability to self-generate stimuli could create the adaptive conditions for the development of an internal model in an embodied and situated agent even in absence of any explicit reward for prediction. Note indeed that the simple self-generation of stimuli is not a guarantee that an internal model has been developed. Indeed, we are interested in differentiating the case of (self-) triggering of stored motor routines from the case of self-sustaining behavior through an on-line prediction of action effects—only the latter being, in our definition, an instance of internal modeling. The fact that biological organisms can overcome the problem caused by the temporal lack of sensory information has been demonstrated, for example, in the experiment carried out in [15]. In this work a group of blindfolded human subjects were asked to perform a series of task (e.g. walking to a given marked location, avoiding obstacles, and throwing objects toward different location of the room) after having been asked to observe the room in which they were located and to direct their attention toward specific objects and markers. The fact that the subjects were able to accomplish these tasks rather well and almost as accurately with respect to a control situation in which they were not blindfolded clearly indicates that they are able to compensate the lack of visual information through some form of internal process, for example through an internal model that allows them to generate the required information by internally anticipating the consequence of their actions. In a series of studies, Ziemke and collaborators have attempted to verify whether an artificial agent trained for the ability to accomplish a given task in normal and blind conditions could manage to overcome the problems caused by the lack of sensory information [16,17]. In the first work, the authors evolved a population of simulated wheeled robots for the ability to move along a square corridor in normal and blind conditions. The robots’ sensors included only a linear camera able to detect four visual landmarks located at the four corresponding edges of the corridor itself. The analysis of the results obtained in this study demonstrates that, in some cases, the evolved agents display an ability to keep navigating within the environment also during blind phases. The analysis of one of the best individual indicates that the behaviour produced by the agents during blind phases always converges
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on a sequence of actions that is very similar to those that are produced during normal phase (in a control conditions in which collision with walls are disabled). During the initial phase in which sensory stimulation is no longer available, however, the behaviour produced by the robot might differ significantly from the behaviour that is exhibited in normal conditions in the same circumstances and might thus lead to collisions between the robot and the walls. In other words, the best evolved individuals often fail to appropriately handle the transition between normal and blind phases. Moreover, contrary to the expectations of the authors, the evolved agents did not rely on an internal model or an ability to internally generate the simulated experience of the stimuli that are temporarily missing. The lack of sensory information in fact was not compensated by an ability to internally generate states that are identical or similar to those that would have been experienced in normal conditions but rather through the development of two different strategies that are executed depending on whether sensory information is available. Indeed, during normal phases the robot accomplished the task by moving forward while turning slightly toward right when the robot visually detecting a landmark and by turning right otherwise. The former elementary behaviour allows the robot to lose visual contact with the landmark toward the end of each corridor and then trigger the latter behaviour (as soon as the landmark is no longer in sight). The latter elementary behaviour allows the robot to negotiate the corner and then trigger the former behaviour (as soon as the robot visually detects the next landmark). During blind phases, instead, the robot solved the problem by executing the same two elementary behaviours described above for a certain time duration (approximately 30 and 5 time steps, respectively) by keeping track of the time spent executing the current behaviour in their internal neurons and by switching behaviour as soon as the appropriate time duration was reached. This study is particularly interesting since it indicates that stimulus prediction and internal modeling strategies do not spontaneously evolve by just forcing the system to act blindfold. Therefore, another goal of paper is to identify the conditions (i.e. the characteristics of the task/environment and the agent control system) that represent a pre-requisite for the emergence of such an internal model. So far the idea of internal modeling has been mainly explored in a control-theoretic perspective, and numerous a-priori assumptions have been made such as the fixed time span of prediction, the specific arrangement of mechanisms (for instance, a comparison mechanism that “matches” real and predicted feedback so to calculate prediction error), and the fact that sensory predictions should be extremely close to “real” sensory input. On the contrary, our study employs a much simpler neural architecture where minimal design constraints were introduced, with the aim to analyze the specific solutions found by the evolutionary algorithm to answer basic questions such as what exactly is predicted in the internal forward models, what is the time scale of prediction, how accurate the predictions should be to be advantageous for an agent, to what extent the internal model can compensate the lack of sensory stimulation, etc. (see [18,19,20,21,22,23] for related studies using various computational modeling techniques).
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Finally, from a technological perspective, our study aims to develop a methodology that can be used to synthesize artificial embodied agents (robots) able to operate effectively in uncertain conditions.
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Methods and Scenario
To achieve the objectives described in the previous section, we set up an experimental scenario in which an embodied and situated agent should develop an ability to display a simple behaviour and keep producing it also when the sensory information is temporarily missing. The agent consists of a simulated eye provided with a single photoreceptor located in front of a 500x500 pixel image generated by the combination of a blue and red gradient ranging continuosly from 0 to 255 along each axis (see fig. 2, left). Each time step, the photoreceptor detects the intensity of the blue and red in the pixel corresponding to the current position of the eye. The agent is also provided with two motors that allow it to move left-right and/or top-down, with respect to its current position, up to a maximum of ± 5 pixels along each axis.
Fig. 2. Left: The environment consists of a screen displaying an image composed by the combination of a blue and red gradient distributed along the left-right and bottom-up axis. Center: The image has been divided into 36 sectors. Right: The architecture of agents’ neural controller.
The task of the agent is to navigate on the image by turning around the center of the image at a distance of at least 130 pixels. For the purpose of measuring the agent’s ability to exhibit such behaviour, the image has been ideally divided into 36 sectors located around its center (see fig. 2, center). The agent’s controller consists of an artificial neural network (see fig. 2, right) with two sensory neurons, eight internal neurons, two motor neurons, and two additional internal neurons (Rr and Br) that are used to replace the state of the sensory neurons when visual information is missing. The internal neurons receive connections from the sensory neurons and from themselves. The motor neurons receive connection from the internal neurons. The two sensory neurons (B and R) encode the intensity of blue and red colour currently perceived by the photoreceptor of the eye. The two motor neurons (M1, M2) determine the
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amplitude of the eye movement along the left-right and top-down dimension within a range of [-5,5] pixels. Internal neurons are leaky integrators (i.e. neurons that hold a certain amount of the previous activation)[24]. The internal and motor neurons are updated on the basis of a standard logistic function. The architecture of the neural network is fixed. The connection weights and biases and the time constant of the internal neurons are encoded in free parameters and evolved [25]. The initial population consists of 100 randomly generated genotypes which encode the free parameters of 100 corresponding individuals. Each parameter is coded with 8 bits and is normalized in the interval [-5.0, +5.0] for the biases and the synaptic weights, and in the interval [0.0, 1.0] for the time constants. Each subsequent population is obtained by selecting the best 20 individuals of the previous population. Each selected individual is allowed to produce 5 offspring that are generated by duplicating the genotype of the reproducing individuals and by applying mutations (with 2% probability of flipping a bit). Each individual is tested for 20 trials. At the beginning of each trial the eye is placed randomly in one of ten possible positions around the center of the image. The agent is then allowed to interact with the environment up to 4000 time steps. For each time step, the state of the agent’s sensory neurons is updated on the basis of the current position of the eye, the state of the internal and motor neurons is updated, and the agent’s eye is moved on the basis of the current state of the motor neurons. The agent experiences a succession of phases in which sensory information is available (normal phases), and phases in which it is missing (blind phases), according to the following rules. During the first half of each trial (i.e. during the first 2000 time steps) the agent always has access to the sensory stimulation coming from the environment (normal phase). During the second half of the trial, instead, the agent experiences a phase in which the sensory information is available (normal phase) followed by a phase in which sensory information is unavailable (blind phase), and vice versa. The length of both phases varies linearly during the 20 trials so to expose the robot to a progressively larger amount of sensory deprivation. On average, the percentage of sensory deprivation during the second half of the trial is 16%. During all the normal phases, the state of the two sensory neurons is set on the basis of the colour of the current portion of the image perceived by the agent, otherwise is replaced using Rr and Br outputs. The performance (fitness) of the individual has been evaluated by computing the number of subsequent sectors of the image visited by the eye (see fig. 2, left). In particular, for each new visited sector(i.e. when current sector is different from the previous) the fitness F of the individuals is updated by adding dF : |D −130| 1− t100 if 30 ≤ Dt ≤ 230 36 (1) dF = 0 otherwise where Dt represents the distance between the point of the image observed by the agent at time t from the center of the image and 36 corresponds to the number of
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sectors. Trials are terminated before the limit of 4000 time steps when the agent move in the wrong direction so to visit a sector already visited recently. The total performance of an individual is obtained by averaging the performance obtained during the 20 trials. The evolutionary process is continued for 1600 generations and replicated 40 times with randomly generated initial conditions.
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Results
By analysing the behaviour of evolved individuals we observed that in 17 out of 40 replications of the experiment, the best individual succeeded in circling around the center of the image both in normal and blind phases. These individuals manage to compensate the lack of sensory information by self-sustaining their internal dynamics in two substantially different ways. Agents belonging to the first “family” (13 out of 17) solve the problem by developing two qualitatively different strategies for normal and blind phases, and trigger the first or the second strategies during the two corresponding phases. Interestingly, although almost all these agents anticipate incoming stimuli during the normal phases with their neurons Rr and Br, their dynamics are different during the blind phases (like in [17], see below). Agents belonging to the second “family” (4 out of 17), instead, keep reacting to the experienced sensory states in similar ways during normal and blind phases and compensate the lack of sensory information with the self-generation of equivalent information and by anticipating how the state of the sensors would vary as a result of the execution of the planned action. That is, the agents use a predictive strategy based on internal modeling. Now we will discuss in more detail the nature of the solution evolved by the second family of succesful individuals. By observing the behaviour displayed by the best individual belonging to the second (internal modelling) family during
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Fig. 4. Top: State of the sensors and self-generated outputs during a normal phase. The dark and left lines indicate the state of neurons R and Rr, respectively. Similar results were obtained for neurons B and Br (not shown). Center: State of outputs neurons over time. The dashed and dotted lines indicate the state of the neuron Rr during a normal and blind phase, respectively. Similar results were obtained for neuron Br (not show). Bottom: Cross-correlation over time between the states of the two output neurons and the states of the two corresponding sensory neurons. Analysis performed on the data collected for 1000 time steps during normal phase. The position of the peek along the x-axis indicates the extent of the anticipation (for value below 0) or of the delay (for value above 0) of the state variation of the output neurons at time t with respect to corresponding sensory neuron at time t+1. The peak is at -1, indicating anticipation of 1 time step.
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a test in which the agent experiences a blind phase lasting 1000 time step after the first half of the trial (fig. 3, left), we can see how, during the blind phase, the agent keeps producing the same quasi-circular trajectory while slowly drifting toward the top-right part of the image (this process continues until sensors R and B are recovered). Moreover, by observing the trajectory produced by the agent during the successive normal phase (fig. 3, right), we can see how the agent manage to quickly recover from the drift as soon as the sensory stimulation become available again. These results demonstrate that the agent succeed in mastering also blind phases in which sensory information is temporarily missing. Moreover, the obtained results suggests that the lack of sensory information can be tolerated only for a limited amount of time since small differences between the behaviour produced in normal and blind conditions tend to cumulate over time during blind phases. Finally, this analysis shows that the agent is able to handle the transitions between normal and blind phases and vice versa by continuing to produce the desired behaviour. The fact that the state of sensory neurons (R and B) at time t+1 and the state of the additional internal neurons (Rr and Br) at time t differ significantly during blind phases (fig. 4, top) indicates that the agent does not operate by predicting the exact state that the former neurons would assume at time t+1 in a normal condition. However, the cross-correlation analysis of the state of the two sets of neurons indicates that the variations of the output neuron at time t are in phase with the variations of sensory neurons at time t+1, during blind phases (fig. 4, bottom). In other words, it anticipates a property of how sensory states vary over time. It is worth noting that this is sufficient for behaving adaptively. Indeed, that despite the differences in the input signal profiles, the output signal profiles are very close in the two phases. The comparison of the dynamic of variation of the output neurons (Rr and Br) during a normal and a blind phase (fig. 4, center) indicates that the state of the neurons vary over time in a rather similar way independently from the fact that the sensory neurons are fed with actual data collected from the environment or with self-generated data, despite the two data differ significantly.
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Discussion
Our study shows that a simulated robot trained with a genetic algorithm in a navigation task can develop an internal model of the robot/environmental interaction, and rely on it to fulfill the same task adaptively even when the robot is temporarily “blindfolded”. The robot’s internal model has several key characteristics: (1) It is autonomously developed depending on the demands of the agent-environment interactions rather than externally designed (the robot is not rewarded for anticipating the next sensory states or the way in which sensory states will vary). (2) It is primarily driven by its own dynamic properties, and can be triggered by both external and internal, self-generated inputs. That is, it is self-sustained, in the sense that the agent can endogenously (re)generate it by using self-produced rather than external stimuli, and “detachable” from the
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sensorimotor loop. (3) It is of an anticipatory nature, since it correlates with future stimuli more than its past or present stimuli, and can be self-sustained while “real” sensory stimuli are missing.
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Conclusions
Theoretical studies suggest that internal models could have originated in living organisms for the sake of adaptive behavior, not for cognition, and were therefore exapted for advanced cognitive and social operations [9,12]. Unfortunately, little effort has been devoted to the verification of this hypothesis–something that is admittedly very complicated to do empirically, but is more feasible by using the methodology of evolutionary robotics, which we adopted in this study. The central hypothesis that motivated our design methodology is that a (temporary) deprivation of external stimuli can make it favorable, from an evolutionary perspective, the development of a robot’s internal model even in the absence of any explicit reward for prediction. Indeed, once the robot has learned a reliable behavioral strategy and an associated dynamical representation of its task, it could be favorable to maintain the same strategy, and at the same time learn to self-maintain the same dynamics via self-generated inputs, rather than evolving two separate strategies to deal with the presence or absence of external stimuli. Our study is part of a more general initiative in cognitive science that aims to draw a naturalized, embodied view of cognition by tracing it back to sensorimotor learning and motor control, some of which maintaining a representational perspective [9,12], and some others not [26]. Most studies mentioning internal modeling tend to frame the problem in control-theoretic terms; for example, [9] describes internal modeling loops in terms of Kalman filters. On the contrary, in our experiment we make fewer a-priori assumptions, for example about prediction and its time-scale, or the similarity between external and self-generated stimuli. By analyzing the best architectures selected by neural evolution, we observe that certain characteristics of the evolved internal models are actually close to abstract control-theoretic models; for example, one-step predictions emerge under appropriate environmental conditions. At the same time, the evolved internal models have certain characteristics that can hardly be studied from an a-priori perspective; for example, as illustrated in fig. 4, self-generated stimuli are different in amplitude and more regular than external stimuli. Overall, our experiments can be considered a further step in the clarification of this novel and multifaceted view of embodied cognition.
Acknowledgements The research leading to these results has received funding from the Europeans Community 7th Framework Programme under grant agreements ITALK (ICT214668) and HUMANOBS (ICT-231453).
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