Distributed adaptive control: explorations in robotics and the biology of learning

Tags: MIT press, representations, DACI, learning rule, Neural Networks, adaptive controller, DACII, populations, Thorndike, Hebbian learning, animal learning, Academic Press, Annual Review of Psychology, CS events, A. Germond, distributed adaptive control, Prerational Intelligence, adaptive control, control structure, University of Chicago Press, Journal of Mathematical Biology, G. Indeveri, Cognitive Science Society, P. F. M. J. Verschure, classical conditioning, properties, operant conditioning, nervous system, Verschure Institute for Neuroinformatics ETH-UZ, biological systems, adaptive properties, learning system, target, Journal of Arti cial Intelligence Research, M. Hasler W. Gerstner, environment, DACIII, behavioral pattern, the environment, Oxford University Press
Content: Distributed Adaptive Control: Explorations in robotics and the biology of learning Paul F.M.J. Verschure Institute for Neuroinformatics ETH-UZ, Gloriastrasse 32, Zurich CH 8006, Switzerland www:http://www.ini.unizh.ch/~pfmjv [email protected] Zurich, September 2, 1998 Verschure, P.F.M.J. (1998) Distributed Adaptive Control: Explorations in robotics and the biology of learning, Informatik/Informatique, 1:25-29 1 Introduction biological systems excel in their adaptive properties and the ability to develop appropriate behaviors to novel situations. In 1898 Thorndike reported one of the rst systematic studies on animal learning 18]. A food deprived cat was placed in a so called puzzle box. In order to escape from the box and acquire food it had to manipulate particular aspects of this environment. Only through turning a button, pulling a string, depressing a lever, or pulling a wire loop would the escape latch be opened. Thorndike demonstrated that the time taken to escape from the box rapidly decreased over subsequent trails. In the eld of robotics, despite the enormous advances in the technology used, no devices can be found which can match the behavior of the cats Thorndike studied 100 years ago. This can be interpreted as an invitation to reverse engineer nature. Such an approach has a long tradition. It is only recently, however, that important advances have been made in the study of these forms of behavior and their related brain mechanisms to make it a feasible option. This paper will describe a synthetic approach towards the study of behavior, called Distributed Adaptive Control (DAC), which attempts to model these phenomena from a biological perspective. DAC has been developed using large scale computer simulations of neural models interfaced to real world devices. Before elaborating on DAC some de nitions and clari cations on terminology will be provided. 2 Learning: de nition and terminology Although learning has been intensively studied over the last century no appropriate definition is available. In general, learning designates relatively long lasting changes in the The author thanks Peter Konig for helpful discussions on this manuscript. Part of this project was supported by NSF-SPP 1
interaction between an organism and its environment. Hence, in the study of behavior operational de nitions of learning, tied to speci c kinds of experimental paradigms, are used. Before elaborating on the central components of the de nition of learning a more fundamental question will be addressed; why do biological systems learn? The present investigation assumes that learning expresses aspects of biological systems which allow them to deal with unpredictability 19]. Two types of unpredictability are distinguished: somatic and environmental. Somatic unpredictability results from the variability in the realization of the body plan. For instance, the detailed properties of the optics of an eye will vary over individuals. This property of biological systems constitutes a form of unpredictability which needs to be handled by a nervous system. For the present discussion we will make the assumption that the mechanisms which allow a nervous system to deal with somatic unpredictability are developmental. Environmental unpredictability is derived from the world in which biological systems have to function. This problem will be ampli ed by the extend to which the system under investigation is dependent on distal sensing, which is quite common for many organisms. The response of the organism to this source of unpredictability will be called learning. Even though the distinction between developmental processes and those involved in learning is not very clear, for our present discussion we will only address the issue of learning. Learning will be operationally de ned in terms of the standard paradigms used to investigate its properties; most notably classical and operant conditioning. Classical, or Pavlovian, conditioning 15] refers to learning phenomena where initially neutral stimuli, or conditioned stimuli (CS), like lights and bells, are through their simultaneous presentation with motivational stimuli, unconditioned stimuli (US), like footshocks or food, able to trigger a conditioned response (CR). The success of this learning process is measured in terms of the probability of the occurrence of a CR after presentation of a CS. As to be expected the reality of animal behavior in the domain of classical conditioning is more complicated than was initially anticipated 10]. In order to place the discussed models in a proper context a number of additional properties of this type of learning need to be emphasized. Both at a behavioral and an anatomical level it is appropriate to distinguish consummatory, or speci c, components from preparatory, or non-speci c, ones 8, 9]. For instance, in the case of eyelid conditioning, where a tone (CS) is presented with an airpu to the cornea (US), the animal will display a number of responses. Next to the closing of the eye lid, which can be seen as speci c to the US, non-speci c behavioral or autonomic responses can be observed; startle, freezing, withdrawal, changes in heartrate, breathing, or Galvanic skin response. The conditioned occurrence of these non-speci c responses will follow a di erent temporal trajectory than the speci c-responses. Non-speci c responses show a fast acquisition (about 5 to 15 trials), while the development of the US speci c CR takes a much larger number of trials. The CR will ultimately express the timing of the US. A more general interpretation of the behavior revealed in classical conditioning is that it allows behaving systems to learn about correlations between CS and US occurrences. To a certain extend one could speak of the substitution of the US by the CS through learning. This can be seen as a crude approximation of causal relationships in the world through correlative measures 22]. Operant, or instrumental, conditioning describes learning procedures in which the UR is contingent on a particular action displayed by the organism. The earlier mentioned puzzle box experiments of Thorndike can be taken as an example. The distinction between classical and operant conditioning is still debated in the eld of animal learning. In the work presented here we make the assumption that both experimental paradigms address
complementary components of one complete learning system.
3 Distributed Adaptive Control: The working hypotheses
The modeling series of Distributed
Adaptive Control (DAC) 27] explores
the question how biological systems
Reflective Control
acquire, retain, and express knowl-
(DACIII) Adaptive Control (DACII) Reactive Control (DAC0)
edge of their environment. In the evaluation of the di erent models the method of choice was the instantiation of simulated control structures in real-world devices (robots). This
approach is seen as the instantiation
of a research program of synthetic
epistemology. In 21, 23, 24] the
methodological and conceptual arguments for this choice are further elab-
Figure 1: The three levels of control distin- orated.
guished in the design of a complete learning system.
The working hypotheses behind the DAC modeling series (illustrated in Fig-
ure 1) can be summarized as follows:
First, the basic competence of a behaving system to e ectively interact with its envi-
ronment is derived from a reactive control structure. By solely relying on prewired re-
lationships between US events and URs it will re exively respond to immediate events.
The triggering stimuli, USs, are derived from proximal sensors. URs can be given a more
general interpretation as re ecting species speci c behaviors. Second, as an adaptive con-
troller the learning system will on one hand develop representations of states of the distal
sensors which correlate with the events which activate the reactive controller. This element
re ects aspects of the fast non-speci c component of classical conditioning. On the other
at this level of control re exive responses can get further shaped, for instance in terms of
their timing and duration. This aspect of adaptive control re ects the slow speci c com-
ponent of classical conditioning. Third, through forming more general representations of
CS events and their relation to actions the learning system functions as a re ective control
structure. At this level of control \plans" of actions can be formed through developing
sequential representations. A system which comprises of these three components will be
refered to as a complete learning system. It needs to be emphasized that the three levels of
behavioral control are not de ned as independent modules. As will be illustrated with the
examples which will follow each level of control is strongly constrained by the preceding
4 DACI and DACII: Evaluation of the hypothesis on the adaptive control structure
The DAC series started with a model proposed in 25] which was developed to solve some fundamental problems observed in models of so called reinforcement learning (i.e. 7, 17]), which are also widely used in the domain of machine learning (see 6] for a review). This class of models has proven to be very e ective in dealing with a wide range of optimization problems and capture elements of classical conditioning. Their successful application to real-WORLD PROBLEMS, however, has still been rather limited. These models have two distinguishing features. In general, CSs are treated as prede ned discrete sensory states. The actual learning process deals with the association of these prede ned CS representations with particular responses, URs. The development of these associations are under the control of a global reinforcement signal derived from the presentation of a US. DAC, however, makes the assumption that an essential step in the learning process is the acquisition of CS representations based on the assumption of somatic and environmental unpredictability. In other words, the actual properties of the world de ning a particular event have to be distinguished before any change to the behavior can be made. In addition, the global signals employed in order to convey an error measure is considered too strong and assumption. This does allow a formal treatment of these methods in terms of gradient descent methods. Despite their possible role as a heuristic in interpreting brain function 16], however, this assumption cannot be validated presently. DAC makes the more minimal assumption of the strict locality of the learning process.
In 25] it was shown that the assumption of the locality
Excitatory Inhibiory
of learning could reliably re ect the acquisition of CS-US
Fixed Plastic
associations, using multiple CS modalities. In a next step,
in order to nd a behavioral validation of this proposal,
a control structure was de ned, called DACI, which was
USIS- Proximal sensors
US+ Proximal
applied to a simulated robot in an obstacle avoidance and
sensors target approach task 27]. Figure 2 summarizes the basic
components of this control structure. In the rst experi-
ments a single CS modality was considered derived from
Distal sensors
a range nder, while the USs were derived from collision
Figure 2: DACI and DACII: subsequent models of adaptive control. See text for explanation
(US?) and an abstract target sensor (US+). The reactive controller was de ned by mapping the occurrence of an US onto a speci c action of the robot, approach in case of an US+ and avoidance in case of an US?. An US event also induced activity in populations of units which re ect
an internal state (IS); called aversive in case of an US?
and appetitive in case of US+. The projections of the proximal sensor to these IS pop-
ulations conserved the topology present in the sensory sheet. Through the prede ned
interactions of the IS populations (indicated with I in Figure 2) preference relationships
were established on order to resolve con icts. Con icts, for instance, occur in case the
robot nds an obstacle in its path while following a gradient dispersed by a target. The
units which ultimately drive the e ectors receive inputs from the IS populations. Through
a winner take all interaction one motor unit, and therefore action, is selected. The system
would resort to its default behavior of moving forward, exploration, in case none of the IS
populations were active. Learning proceeded by changing the connections between the IS
populations and the CS population. In this way associations between events transduced by the distal sensors and internal states could be acquired. In these experiments it was demonstrated that DACI could successfully act in an envi-
0 0 0 0 0 0 0 1 1 1 1 1 1 10 0 0 0 0 0 0 1 1 1 1 1 1 10 0 0 0 0 0 0 1 1 1 1 1 1 10 0 0 0 0 0 0 1 1 1 1 1 1 1 = Avoidance
= Approach
0 0 0 0 0 0 0 1 1 1 1 1 1 10 0 0 0 0 0 0 1 1 1 1 1 1 10 0 0 0 0 0 0 1 1 1 1 1 1 10 0 0 0 0 0 0 1 1 1 1 1 1 1
Target Figure 3: DACI: Emergent behaviors of the adaptive controller ronment containing several obstacles and a single target. In addition, these experiments demonstrated the need for an activity dependent depression term in standard Hebbian learning rules. This rendered a learning rule similar to the well known Oja rule 13] which is able to extract the principal components from its input set. In this case this solution emerged out of the analysis of the performance of a behaving device. In addition these tests demonstrated that the relationship between observed behavioral regularities and the properties of the control structure can in certain cases only be understood in case the properties of the environment, the sensors and e ectors of the behaving system, and the learning history are taken into account. Figure 3 shows some forms of structured behavior displayed by the adaptive controller, such as wall-following and impasse resolution, observed in these experiments. These behavioral patterns, however, are not explicitly represented by the control structure. The adaptive controller is only able to avoid or approach in response to immediate sensory events. It does not have the means to represent sequences of actions. In 1] the optimization technique of genetic algorithms was used to demonstrate the stability of DACI over a wide range of parameters. A next series of tests involved the comparison and validation of the Simulation results using real-robots 12]. In this case it was shown that the learning properties of DACI were independent of the actual distal sensors used. In 30] DACI was further generalized to a larger mobile platform applied to a visually guided block sorting task. In these experiments explicit performance comparisons were made between di erent proposals on rules governing synaptic plasticity. It was shown that so called \value based" learning rules 3] perform rather poorly in these types of tasks as compared to the learning method used in DAC. In subsequent work 28] it was shown that the learning rule employed is prone to overgeneralize the representations it acquires. This is a fundamental problem for any local learning rule. Early CS-IS associations, expressed in the strength of the connections between the respective populations, in many cases would dominate later classi cations. In the earlier described example of wall following these properties of the learning rule could induce an overgeneralization of this behavior; circling around obstacles. It was subsequently demonstrated that this problem could be solved while adhering to the assumption of the locality of learning process. Next to the feedforward path from the CS populations to the IS populations a recurrent inhibitory pathway between these populations was introduced. This extension was called DACII. As opposed to DACI, DACII would modify
the strength of the connections dependent on the deviation between actual CS events, transduced by the distal sensor, and CS events predicted through the IS activity. In 29] it is demonstrated that this extension to the original learning method, called predictive Hebbian learning provided the means to reliably capture CS representations and maintain these representations over extended periods of time in both simulated and real robots.
5 DACIII: Evaluation of the hypothesis on the complete learning system
DACIII 20] was de ned in order to explore the prop-
Reflective control
erties of re ective control. It constituted a rst step
towards the speci cation of a complete learning sys-
tem. In 29] a more elaborate description of DACIII
is provided, including evaluations using both sim-
ulated and real robots. The adaptive controller
Sense Matching
Competition Act
used in DACIII is similar to DAC II. The re ec-
tive controller modeled by DACIII consists of sev-
Adaptive control
eral components (see Figure 4). The rst component
Reactive control
is a transient memory bu er (Short Term Memory,
Figure 4: DACIII: an approximation of a complete learning system. See text for explanation
STM) in which CS representations and their associated CRs are stored. Storage is conditional on the activity of an IS population. CS and CR representations are provided by the adaptive control struc-
ture. Each segment of STM contains one CS-CR
pair. Conditional to the occurrence of a rewarding event, such as nding a target, the
contents of STM are stored in a permanent Long Term Memory (LTM). CS representa-
tions, stored in LTM, are matched in parallel against ongoing sensory events. Matching
LTM segments engage in a winner take all competition. The winning LTM segment trig-
gers the next action, and reinserts itself in the STM bu er. In addition it will enhance the
probability that the subsequent segment will match with future sensory events, in order
to achieve chaining of subsequent LTM segments. This enhancement, however, is only
The performance of DACIII was compared to that of DACII using a simulated robot simi-
lar to the one used in the rst evaluation of DACI. In this comparison between DACII and
DACIII the environment contained four targets each placed in a corner of a secluded space
(Figure 5A). The gradient they dispersed only persisted over a short range. When a target
is found by the robot it disappears from the environment. A new target will reappear in
its place as soon as another target is found. The system could explore this environment
for 10000 time step. The gradients dispersed by the targets were removed after 7000 time
steps. After this time the system could nd targets through either coincidence or the use
of acquired behaviors. In this comparison DACII found 34 targets while accumulating 106
collisions. For DACIII this score was 53 and 73 respectively. The traces of the subsequent
locations visited re ects the behavior of DACII and DACIII during the period that the
target gradient was absent. The most salient aspect of the behavior of DACIII is its ability
to acquire a stable behavioral pattern (Figure 5C). DACII, does not display this type of
structuring of its behavior and visits all locations in the environment. These experiments
demonstrated that the complete learning system as implemented by DACIII is able to rst, acquire appropriate representations of CS events, retain sequential representations of CS-CR couplings, and express these representations in order to successfully negotiate its environment.
A: Environment 000000000000011111111111110000000000000111111111111100000000000001111111111111000000000000011111111111110000000000000111111111111100000000000001111111111111000000000000011111111111110000000000000111111111111100000000000001111111111111000000000000011111111111110000000000000111111111111100000000000001111111111111000000000000011111111111110000000000000111111111111100000000000001111111111111000000000000011111111111110000000000000111111111111100000000000001111111111111000000000011111111110000000111111100000000000001111111111111000000000000011111111111110000000000000111111111111100000000000001111111111111000000000011111111110000000111111100000000000001111111111111A00000000000001111111111111000000000000011111111111110011000000000000011111111111110000000000111111111100000001111111C00000000000001111111111111000000000000011111111111110000000000000111111111111100110000000000000111111111111100000000001111111111T0011000000000000011111111111110000000000000111111111111100000000000001111111111111a001100000000000001111111111111001100000000000001111111111111r0000000000000111111111111100000000000001111111111111g001100000000000001111111111111001100000000000001111111111111e00000000000001111111111111000000000000011111111111110011t0000000000000111111111111100110000000000000111111111111100000000000001111111111111000000000000011111111111110011000000000000011111111111110000000000000111111111111100000000000001111111111111010011000000000000011111111111110100000111110000011111000001111100000111110011000001111100000111110011010011G0011010011r001101a0011d0011010011i01en01t 01010000111100110101000011110011010000111100110100001111001100001111O0011b0011sta0000000000001111111111110011000000000000111111111111c0000000000001111111111110000000000001111111111110011le000000000000111111111111000000000000111111111111000000000000111111111111000000000000111111111111001100000000000011111111111100000000000011111111111100000000000011111111111100000000000011111111111100110100000000000011111111111100000000000011111111111100110000000000001111111111110000000000001111111111110100000000000011111111111100000000000011111111111100110000000000001111111111110000000000001111111111110100000000000011111111111100000000000011111111111100000001111111DR0000000000001111111111110000000000001111111111110100000000000011111111111100000000000011111111111100000001111111B00000000001111111111o000000000000111111111111000000000000111111111111b000000000000111111111111000000011111110000000000001111111111110000000000011111111111o000000000000111111111111000000000000111111111111t000000011111110000000000001111111111110000000000001111111111110000000000011111111111000000000000111111111111000000000000111111111111000000000000111111111111000000000000111111111111000000000000111111111111000000000000111111111111000000000000111111111111000000000000111111111111000000000000111111111111000000000000111111111111000000000000111111111111000000000000111111111111000000000000111111111111000000000000111111111111
B: Trajectory DACII
C: Trajectory DACIII
Figure 5: DAC: A comparison of DACII and DACIII during the recall period.
6 Conclusion The DAC series of models is by no means complete. For instance the properties of the speci c learning system, and many elements of a re ective learning system have been neglected and are in the focus of our present activities. So far, however, DAC has shown that the basic assumptions behind this program su ce to de ne adaptive control structures which can capture aspects of advanced forms of behavior using strictly bottom-up principles. DAC has established a bridge between both the behavioral paradigms used in the study of learning and the neuroscienti c explorations of these phenomena. In addition, it has made a number of suggestions which have shown to be of relevance to the elds of robotics 14], ethology 11], arti cial intelligence 2, 4], and cognitive science 23]. In our current research of DAC we have focused on two additional themes. On one hand the development of more appropriate technology to construct behaving devices, especially through the use of more biologically realistic distal sensors (neuromorphic retinae) 5]. On the other more biologically realistic models of the brain mechanisms involved in the processing of distal sensors have been developed 26]. These e orts were undertaken in an attempt to facilitate a further validation of DAC at both the behavioral and the neuroscienti c levels.
References 1] N. Almassy and P. F. M. J. Verschure. Optimizing self-organizing control architectures with genetic algorithms: The interaction between natural selection and ontogenesis. In R. Manner and B. Manderick, editors, Proceedings of the Second Conference on Parallel Problem Solving from Nature, pages 451{460. Amsterdam: Elsevier, 1992. 2] W.J. Clancey. Situated Cognition: On human knowledge and computer representations. Cambridge: Cambridge UNIVERSITY PRESS, 1996. 3] G.M. Edelman, G.N. Reeke, W.E. Gall, G. Tononi, D. Williams, and O. Sporns. Synthetic neural modeling applied to a real-world artifact. Proceedings of the National Academy of Sciences of the USA, 89:7267{7271, 1992.
4] H. Hendriks-Jansen. Catching Ourselves in the Act. Cambridge Ma.: MIT press, 1996. 5] G. Indeveri and P. F. M. J. Verschure. Autonomous vehicle guidance using analog VLSI neuromorphic sensors. In M. Hasler W. Gerstner, A. Germond and J-D. Nicoud, editors, Proceedings Arti cial Neural Networks-ICANN97: Lausanne, Switzerland, pages 811{816. Lecture Notes in Computer Science. Berlin: Springer, 1997. 6] L.P. Kaelbling, M.L. Littman, and A.W. Moore. Reinforcement learning: A survey. Journal of Arti cial Intelligence Research, 4:237{285, 1996. 7] A.H. Klopf. The Hedonistic Neuron: A theory of memory, learning and intelligence. Washington D.C.: Hemisphere, 1982. 8] J. Konorski. Integrative Activity of the Brain. Chicago: University of Chicago Press, 1967. 9] D. G. Lavond, Kim J. J., and Thompson R. F. Mammalian brain substrates of aversive classical conditioning. Annual Review of Psychology, 44:317{342, 1993. 10] N.J. Mackintosh. The Psychology of Animal Learning. New York: Academic Press, 1972. 11] D. McFarland and T. Bosser. Intelligent Behavior in Animals and Robots. Cambridge, Ma.: MIT press, 1993. 12] F. Mondada and P. F. M. J. Verschure. Modeling system-environment interaction: The complementary roles of simulations and real world artifacts. In , editor, Proceedings of the Second European Conference on Arti cial Life, pages 808{817. Cambridge, Ma.: MIT press, 1993. 13] E. Oja. A simpli ed neuron model as a principal component analyzer. Journal of Mathematical Biology, 15:267{273, 1982. 14] O. Omidvar and P. Van der Smagt. Neural Systems for Robotics. New York: Academic Press, 1997. 15] I. P. Pavlov. Conditioned Re exes. Oxford: Oxford University Press, 1927. 16] W. Schultz, P. Dayan, and P.R. Montague. A neural substrate of prediction and reward. Science, 275:1593{1599, 1997. 17] R. S. Sutton and A. G. Barto. Toward a modern theory of adaptive networks: expectations and prediction. Psychological Review, 88:135{170, 1981. 18] E.L. Thorndike. Animal Intelligence: an experimental study of the associative processes in animals. Number 8 in The Psychological Review Series of Monograph Supplements. New York: Macmillan, 1898. 19] P. F. M. J. Verschure. Taking connectionism seriously: The vague promise of subsymbolism and an alternative. In Proceedings of the Fourteenth Annual Conference of the Cognitive Science Society, Bloomington, Indiana, pages 653{658. Hillsdale, N.J.: Erlbaum, 1992. 20] P. F. M. J. Verschure. The cognitive development of an autonomous behaving artifact: The selforganization of categorization, sequencing, and chunking. In H. Cruze, H. Ritter, and J. Dean, editors, Proceedings of Prerational Intelligence, pages 95{117. Bielefeld: ZiF, 1993. 21] P. F. M. J. Verschure. Formal minds and biological brains. IEEE expert, 8(5):66{75, 1993. 22] P. F. M. J. Verschure. Minds, brains, and robots: Explorations in distributed adaptive control. In A.B. Soares, editor, Proceedings of the Second Brazilian-international conference on Cognitive Science, 1996. 23] P. F. M. J. Verschure. Connectionist explanation: Taking positions in the mind-brain dilemma. In G. Dor ner, editor, Neural Networks and a New Arti cial Intelligence, pages 133{188. London: Thompson, 1997. First presented at ZiF workshop Mind and Brain, 1990. 24] P. F. M. J. Verschure. Synthetic epistemology: The acquisition, retention, and expression of knowledge in natural and synthetic systems. In Proceedings World Conference on Computational Intelligence 1998, Anchorage, pages 147{153. IEEE, 1998. 25] P. F. M. J. Verschure and A. C. C. Coolen. Adaptive elds: Distributed representations of classically conditioned associations. Network, 2:189{206, 1991. 26] P. F. M. J. Verschure and P. Konig. Modulation of temporal interactions in cortical circuits. In H-M Gross, editor, Proceedings of SOAVE97, pages 77{88. Dusseldorf: DVI, 1997. 27] P. F. M. J. Verschure, B. Krose, and R. Pfeifer. Distributed adaptive control: The self-organization of structured behavior. Robotics and Autonomous Systems, 9:181{196, 1992.
28] P. F. M. J. Verschure and R. Pfeifer. Categorization, representations, and the dynamics of systemenvironment interaction: a case study in autonomous systems. In J. A. Meyer, H. Roitblat, and S. Wilson, editors, From Animals to Animats: Proceedings of the Second International Conference on Simulation of Adaptive behavior. Honolulu: Hawaii, pages 210{217. Cambridge, Ma.: MIT press, 1992. 29] P. F. M. J. Verschure and T. Voegtlin. A bottom-up approach towards the acquisition, retention, and expression of sequential representations: Distributed adaptive control III. Neural Networks, page In Press, 1998. 30] P. F. M. J. Verschure, J. Wray, O. Sporns, G. Tononi, and G.M. Edelman. Multilevel analysis of classical conditioning in a behaving real world artifact. Robotics and Autonomous Systems, 16:247{ 265, 1995.

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