4.1 Introduction

Behavior in its most elementary form is purely reactive. The motor patterns produced are caused only by the immediate perceptual state of the animal. In this chapter, we will introduce some basic classes of reactive behaviors and consider what different properties they possess. There are two distinct historical lines that we will follow.

The first historical line has its start in Lewin's topological psychology (Lewin 1936) and his view of behavior as controlled by a force field generated by objects or situations with positive or negative values or valences. The idea was later developed by Hull (1932, 1943, 1952), who used it as the basis for his goal-gradient construction. After having fallen in disregard for many years, the idea has been recently resurrected through Arbib's (1987, 1991) work on motor schemata and Arkin's (1987, 1990) use of potential field methods for robot navigation. The common denominator of all these approaches is their account for the directedness of behavior. They all subscribe to the position of hedonism, that is, the organism is considered to approach pleasure and avoid pain. This leads naturally to a distinction between four types of behaviors: (1) appetitive behavior that is directed toward an object or a situation, (2) aversive behavior that is directed away from an object or a situation, (3) exploratory behavior that relates to objects or situations that are unknown, and finally, (4) neutral behavior that is guided by objects that are known to be neutral, that is, neither appetitive nor aversive.

The other historical line is that of reflexes and fixed motor patterns. The idea of reflexes has a long history, but the word was not used until 1784 when it was introduced by Prochaska (See Shepherd 1988). The concept of fixed motor patterns was suggested by Lorenz (1950). By introducing hierarchies of motor patterns, Tinbergen (1951/1989) made one of the most important contributions to this area. Recently, the development of behavior-based robots moves the idea in a new direction, from a descriptive framework to a foundation for design (See, for example, Brooks 1991a, and Maes 1990). While the first historical line is mainly concerned with directedness, this other line emphasizes coordination and sequences of motions.

The two directions are not at all incompatible, of course. In fact, one of the conclusions of the present chapter will be that a better understanding of reactive behavior must be based on directedness as well as coordination and sequences of behavior. The chapter concludes with an inventory of basic reactive behaviors.

4.2 The Directedness of Behavior

One of the most fundamental aspects of most behaviors is that they are directed. Animals do not just move around at random but are guided by their perception of the world in such a way that their behavior is likely to accomplish something of importance, such as finding food or a mate. It will thus be necessary to consider goal-direction at some length before we can start the construction of an artificial creature. To make the notion of direction precise, we will need to define a language suitable for the task. This language will take its starting point in Lewin's topological psychology. We will tailor it to fit our needs, and as the language becomes more precise, it will gradually begin to look like a theory of behavior.

To make the presentation clearer, we will start with behaviors that are purely reactive and relate to objects in space. This also makes it natural to use spatial concepts to describe behavior. As the theory moves away from reactive behavior, the spatial concepts will gradually be transferred from the external space to the internal space of the animal. In the later chapters, we will try to make a case for the idea that all cognition is based on spatial concepts and that goal-directed thought may merely be goal-directed behavior made internal. Before we can make such broad claims, however, we must first move back in time to the early days of topological psychology.

Topology and Vectors: Lewin's Field Theory

The psychology of 1930 left much to hope for in terms of descriptive precision. It is not hard to understand why the psychologists of the time envied the exactness and conceptual rigor of physics and mathematics. Inspired by the latest developments in pure mathematics, Kurt Lewin tried to developed a formal mathematical language for psychology. The foundations for this language were presented in his book Principles of Topological Psychology (Lewin 1936), which was the first in a series of works that developed his ideas from a topological psychology into a vector psychology where the behavior of a person was explained in terms of forces acting on the individual.

The problem that hampered the development of a formal vector psychology was that it seemed difficult or impossible to define a metric on the psychological space. Without a metric, the concept of psychological vector or force is meaningless. In this respect, vector psychology could never offer more than a metaphorical description of a person. However, as we will see below, for artificial creatures, at least, a precise vector psychology is in fact possible. To make such a vector theory possible, we must first consider Lewin's theory in more detail.

The psychological theory developed in the language offered by topology and vectors is generally referred to as the field theory. The central concept of the field theory is that of a life space that determines the behavior of an individual. The behavior at any moment in time can be described as a function of the life space of the individual. The life space includes the whole situation determining the behavior of an individual, that is, both the person, P, and the environment, E. If we denote the behavior of the individual by B, the field theory can be summarized in Lewin's famous formula,

(Equation 4.2.1)

One of Lewin most important insights is that we should consider the momentary situation of an individual in order to understand its behavior. This contrasted with many of the popular theories at the time, where the causes of behavior were sought not in the present but in the past. This does not mean that the past does not have a role in determining the present situation of an individual. On the contrary, both the experienced past and the expected future, that is, the total life situation, may play a part in determining the immediate situation. But, it is this situation that determines behavior and not the past or the future.

The goal as a psychological fact undoubtedly lies in the present. It really exists at the moment and makes up an essential part of the momentary life space. On the other hand, the content of the goal Š lies as a physical or social fact in the future. Indeed, it may not occur at all. The nature of the expectation and the character of what is expected, in so far as they act as psychological conditions at the moment, naturally do not depend upon whether or not the event comes to pass. (Lewin 1936, p. 36)

Although Lewin did not consider this possibility, the language that he developed makes it possible to talk about all behavior as reactive in a sense. However, since reactions have their causes in the momentary life situation, and not only in the physical environment, the complexity of behavior can go far beyond simple stimulus-response reflexes.

It is in the representation of the psychological environment that Lewin's mathematical concepts reveal their large potential. Like von Uexküll's Umwelt, the psychological environment refers to the environment as it is perceived by the individual and not to the physical environment (See section 2.9). Consider, the following example from Lewin (Lewin 1936 p. 96; figure 4.2.1). A boy wants to become a physician. To achieve this goal, he is required to first pass the college entrance examination (ce), then college (c), and medical school (m), etc. Finally, he will be able to establish a practice (pr) and reach his goal (G).

Figure 4.2.1 The situation of a boy that wants to become a physician. P, person; G, goal; ce: college entrance examinations; c, college; m, medical school; i, internship; pr, establishing a practice (adapted from Lewin 1936).

Figure 4.2.1 illustrates the main components of topological psychology. The situation consists of a number of regions. One of them contains the person, P, and another is the goal region, G. As can be expected, regions can be included in each other. In the figure, the different regions are included in the total situation characterized by the outer oval.

Regions are separated by boundaries. These are considered to resist psychological locomotion to a degree that can vary from nearly none to infinity. Boundaries that offer considerable resistance are called barriers. In this example, psychological locomotion refers, not to bodily motion, but to an alteration in position in the quasi-social life space of the boy. In the boy's conception, the college entrance examinations offer the greatest resistance, represented by thicker lines in the figure. This is probably, as Lewin noted, a false but nevertheless clear picture.

In this example, the track to becoming a physician is represented by a set of spatial regions. Although the artificial creatures we will develop below will not have such high ambitions, it is still possible to use a similar language to describe their behavior since the problems they come across will usually be spatial in a very concrete sense, as well. For example, to obtain food, the creature must move from one location to another. This makes the two-dimensional domain that was introduced in the last chapter ideal for the exploration of topological concepts.

The concept of a life space can readily be used to represent the momentary situation of our creatures as well as the influences on behavior exercised by the past and the expected future. We will see in the next chapter that learning can be seen as a process that restructures the life space in such a way that the resulting behavior is changed. In the more general case, it is also possible to consider concept formation and problem solving as processes of restructuring.

So far, we have deliberately avoided Lewin's vector concepts since we will have reason to discuss them at length below. However, a few simple examples are appropriate here. Figure 4.2.2a shows a child (C) on one side of a barrier (B) and a desired toy (T) on the other. The force field acting on the child is indicated by an arrow. It is obvious that movement in this direction will not reach the desired goal since the barrier is in the way. Figure 4.2.2b shows a restructured life space that would solve the problem. The dotted path shows one of the possible ways around the barrier. In figure 4.2.2c the child finds himself in a situation which contains an aversive object that causes the child to withdraw or retreat.

Figure 4.2.2 Field forces influencing the behavior or a child (C). (a) The desired toy (T) directs the locomotion of the child in its direction. (b) A restructured life space that makes it possible for the child to reach the toy. (c) An aversive object (-) makes the child withdraw.

We see that forces can be either driving, such as forces generated by the desired or the aversive objects, or restraining, such as the force corresponding to the barrier (Lewin 1935). In general, the closer to the generating object or event the person gets, the larger the driving forces become. We will return to the different types of field forces that can be represented in this way below where we outline a modern version of the vector psychology.

When using ideas from physics psychologists have been known to make misstakes from time to time and Lewin is no exceptions. One of them is to confuse the notions of velocity and acceleration. This leads to strange conceptions such as force-fields controlling speed rather than acceleration. This is unfortunate since it makes it impossible to use the terminology of psychology without being in conflict with the use of these terms in physics. Since the terminology has already been established in both fields, some abuse of terminology is thus unavoidable.

Hull's Goal-Gradient Hypothesis

The idea of force fields as the determinants of behavior was also incorporated in Hull's theory in the form of goal-gradients (Hull 1932, 1938). Although stated in somewhat different languages, both Lewin's and Hull's theories make essentially similar prediction in many situations. This is especially true in their analysis of conflict and choice. However, Hull's theory moved beyond Lewin's when it tried to give an explicit account of the process that constructs the goal-gradients. It also tried to explain how the goal-gradient is transformed into movement in the physical world. This is something that Lewin's theory could not explain.

Figure 4.2.3 The stimulus-response dynamics of a simple maze. Behavior is explained with the following ideas: drive stimulus, SD, stimuli in the environment, Si, proprioception, si, reactions, Ri. SS represent the stimuli in the start box and RG the goal reaction. (Adapted from Hull 1932).

Figure 4.2.3 shows the stimulus-response dynamics of a simple maze learning task when the animal has learned it correctly. Suppose there are two possible paths from the start box to the goal box, one long, X, and one short, Y. A process that conditions reactions to the stimuli preceding it sets up a goal-gradient for the environment. All reactions, Ri, are conditioned according to the temporal and spatial proximity to the goal reaction RG. The reaction that directly preceded the goal reaction is most strongly conditioned to its preceding stimuli and the earlier reactions are conditioned progressively weaker.

The upper series of stimuli, Si, represent external stimuli that can be detected in various places in the maze. The SD represents an internal drive stimulus, such as hunger, that persists throughout locomotion in the maze. The small s's represent proprioceptive stimulation that results from the execution of their preceding responses. The dotted arrows represent learned associations set up during the learning phase and the small figures represent the strengths of these associations. As can be seen, the closer an association is to the goal reaction, the stronger it is. Also note that the two sequences have the same start SS.

When the animal is placed in the start box and is under the control of the drive stimulus SD, two reactions are available to it that have previously been reinforced, R1 and RA Since the reaction RA is closer to the goal reaction, both in time and space, the reactive potential is larger for RA than for R1. As a consequence, the animal will chose the reaction RA that will result in the shortest path to the goal, that is, path Y.

The reactive potential of an animal is considered to increase with the proximity to the desired goal, thus making the animal run faster the closer it comes to it. The original formulation of the goal-gradient hypothesis made many unrealistic simplifications. It ignored that an animal has a top speed and that the goal-gradient can, therefore, not be directly reflected in the speed of movement. It is also necessary for the animal to slow down before reaching the goal in order not to collide with it.

Despite these simplifications, Hull developed the force-field concept in a very important way when he made the medium representing the forces explicit. This medium was the set of responses available to the animal. Using the set of responses as a starting point, it is possible to define both the direction and the magnitude of the forces determining behavior. For such a definition to work, however, it is necessary that responses are defined in relation to the animal, as is the case in Hull's theory. This is not possible within a theory that defines responses in relation to the environment as, in Skinner's operants, for example (Skinner 1974).

The responses available to the animal determine the directions of the forces influencing its behavior in a self-centered coordinate system. The reactive potential of these responses gives the magnitude of the forces controlling the animal. Given a certain stimulus situation and a complete description of the animal, we can potentially calculate the forces acting on the animal and predict its behavior.

The responses are similar to the boundaries in Lewin's topological psychology, but instead of viewing them as resistance, we may identify them with a certain amount of effort. Thus, the resistance of a boundary is equal to the effort required to execute the reaction that moves the animal through the boundary. Using this odd but important identification, the situation in figure 4.2.3 can be redrawn in a Lewinian flavor as shown in figure 4.2.4. This representation of the situation could be enhanced by including vectors that would represent the strength of the force field, that is, the same information as the reactive potentials in the Hullian analysis.

Figure 4.2.4 The dynamics of the simple maze using a Lewinian representation. Each stimulus is contained in a region of the life space. To pass from one region to the next, an animal must cross a boundary, that it, it must perform some action. The boundary in the middle is assumed to resist any attempt to cross it. Thus, there are only two paths from the start to the goal.

Potential Fields and Motor Schemata

Both Hull and Lewin used a physical language to talk about psychological phenomena. This is even clearer in Köhler's version of the field theory. He used the analogy of electromagnetic force fields to describe the dynamics of behavior. This approach is highly holistic since it emphasizes the role of the whole field as a determinant of behavior. A single stimulus can, thus, not be considered as the cause of behavior until it has been incorporated in the whole.

In the use of potential fields methods for robot control, the parallelism to physics is made even more explicit. The robot is considered to be an electrically charged particle in an electric field generated by the various objects in the environment. Obstacles are assigned negative potentials while the goal is considered positive. If the robot follows the gradient of the electric field, it will successfully reach the goal and avoid obstacles in most environments.

The method was introduced by Khatib (1985), but is primarily known through Arkin's (1987) work in the area. He has combined the potential field method with the concept of a motor schema introduced by Arbib (1991, 1993). A motor schema is a representation of a certain motor activity with respect to every location in the environment. Figure 4.2.5b shows the motor schema for the action move-to-goal of the environment in figure 4.2.5a. The arrows shows that the direction of movement at each location in space is in the direction of the goal point.

Figure 4.2.5 Two motor schemata and their combination. (a) The environment. (b) The motor schema move-to-goal, (c) The avoid-wall schema, (d) The behavior of a creature using the combined schema.

This particular motor schema could have been generated by the potential field method since the direction of movement coincides with the attracting force of the electrically charged particle at the goal point. For an environment with no obstacles, this motor schema is sufficient to navigate toward the goal. In a more complex environment, more schemata are needed. Figure 4.2.5c shows the motor schema avoid-wall considered as a field generated by the wall. The robot is supposed to move away from the wall.

If the wall and the goal are located in the same environment, the action of the robot can be calculated by adding the two force fields together as shown in figure 4.2.5d. Note that the picture shows the path preferd by the robot rather than the sum of the two vector fields. By following this combined motor schema, the robot can reach the goal without colliding with the obstacle. The most important aspect of this control method is that it generates stable control strategies. It does not matter if the robot is accidentally moved off course since the gradient field will automatically compensate for this and get it on the right track again. Another nice property of the method is that the different motor schemata controlling the robot can be calculated independently and then simply combined, either by adding them or by taking the maximium of them. For instance, the processes that calculate the move-to-goal schema do not communicate with the avoid-obstacle process at all. The potential field method is, thus, very well suited for parallelization (See also section 4.3).

Although this method has many merits, there are a number of important problems; the most noticeable being that it very easily generates local maxima in the gradient landscape at other places than at the goal. One possible solution to this problem is to add noise to the motor schemata, but this is not entirely satisfactory (Arkin 1990). Another problem is that it is location based. This means that, in general, the location of the robot must be known before the force vectors can be calculated. Potential fields may also give rise to strange behaviors, such as avoidance of objects behind the robot (Connel 1990).

Despite these problems, the idea of motor schemata is very attractive as a way to represent the latent behavior of an agent. In many respects, it is similar to Lewin's vector fields, but instead of showing the direction of movement in an internal psychological space, it shows the direction of movement in the physical space. If we keep the state of the agent constant, we can, potentially, move the agent to all possible locations in space and record its movement. This record is essentially an image of the psychological environment of the agent and we have, thus, found a way to make the notion of a psychological space precise. This is one of the central ideas that we will use in the next section as we try to outline a modern field theory.

Toward a Modern Field Theory

Though in theory, one should be able to measure all the parameters controlling an animal in a given situation, this is not possible in practice. With artificial creatures, however, the situation is different. The problem here is not to keep track of all the parameters, but rather to make sense of them. The modern version of the field theory that we will outline in this section is intended to describe very complex behavioral dispositions and internal representations in a way that relates directly to the behavior they may potentially cause.

Like Lewin's topological psychology, the concepts put forward below are initially intended as a language and not a theory in itself. They are, however, highly interwoven with the theory we will develop. We also believe that this language will aid the presentation in the rest of the book since it allows a common description of many different perceptual and behavioral phenomena. The language will be approached by a number of progressively more complex examples.

Figure 4.2.6 A discrete environment. See the text for an explanation.

Let us first consider the discrete environment shown in figure 4.2.6a. It consists of 25 distinct regions. One of them contains the creature, C, and another contains the goal, marked by a black dot in the figure. The arrows show the four possible directions of movement the creature is able to perform. Like in Lewin's topological psychology, the boundaries between the different regions offer a resistance to locomotion. Let us assume that the strength of this resistance is 1. This means that the effort, or cost, required to pass through the boundary is also 1. We let the function c(a, b) denote the minimal cost of moving from location a to b. Note that this cost function does not need to commute as it does in the example, that is, it is not necessary that c(a, b) = c(b, a).

The reward obtained at each region is shown in figure 4.2.6b. As we can see, the creature receives a zero reward at all locations except for the goal. The values shown in this figure consitute the reward, or goal, function for the environment.

Figure 4.2.6c shows how much it is worth to be in each of the different regions. These values are called the potential reward, G, of each location, that is, the reward the animal will obtain if it follows the path that offers the least resistance to the goal. If R(g) is the reward obtained at the goal location, g, and z is the current location of the creature, the potential reward function is defined as,

(Equation 4.2.2)

This suggests a definition of psychological distance between two regions as the psychological, or perceived, effort required to move from one region to the other using the path with least resistance. For psychological distance between a and b, we will use the notation, . This measure will be formally defined in chapter 5. Note that psychological distance does not in general define a metric on the life space since the psychological distance from A to B may not be the same as that from B to A. This non-commutativity of psychological distance is a well known fact from psychological experiments (See, for example, Lee 1970).

If we want an artificial creature to behave optimally, it should be designed in such a way that its psychological distance coincides with the actual cost function of the environment. In the next chapter, we will consider a set of learning mechanisms that have as their function to establish approximations of appropriate measures of psychological distance.

Figure 4.2.6d shows the direction of maximal growth of the potential reward. To receive the maximal total reward the creature should follow these directions as closely as possible, that is, choose the path with the shortest psychological distance. So far we have only discussed what the creature should do. To see what it really does, we need to observe its behavior in the environment.

Figure 4.2.6e shows one possible outcome of placing the creature in each region and recording its action. Since diagonal locomotion is not possible, the creature has to choose randomly in some regions. Note that we do not need to make any assumptions about the internal workings of the creature to make a record like this. However, it does require that we can somehow keep the internal state of the creature constant. For an artificial creature, this simply means that we temporarily turn off any learning abilities it might have.

Given a result like that in figure 4.2.6e, what can we say about the creature? We may consider the actions selected as an approximate record of the life space of the animal. To get a better picture, we could place the creature in each region many times and calculate its average direction of movement. Let us assume we received the set of directions shown in figure 4.2.6d, that is, on the average, the creature followed the direction of maximal growth of the potential reward. From this, we would conclude that the goal is represented in the life space of the creature. We also see that the environmental representation of the animal must agree, to some extent, with that in figure 4.2.6c.

This conclusion, however, requires that we first establish the base case for the behavior of the creature. In the following, we will assume that its behavior is random when no objects are perceivable in the environment. Random behavior will be marked with a black dot.

Let us now introduce a barrier in the environment as shown in figure 4.2.7a. Figure 4.2.7b, c and d show three possible outcomes if we repeat the procedure above in the new environment. The different records make us draw different conclusions about the life space of the creature. In the first case, 4.2.7b, the creature obviously knows the location both of the barrier and the goal and can choose the optimal path. What the field does not tell us, however, is how the creature knows the optimal path. The historical cause of the behavior can be excessive training in the environment. However, it is also possible that the creature can directly perceive both the barrier and the goal and can make the sufficient inferences about the optimal path. It may even have some form of innate knowledge of the world.

In the situation in 4.2.7c, the barrier hides the goal which makes the creature move at random at places where the barrier is in the way of the goal. In figure 4.2.7d, the goal is perceived by the creature but the barrier is not. Its movement is identical to that in the previous example. The result of this representation is that the creature will get stuck at the barrier if it starts on the wrong side of it. If it selects actions at random, it may get away eventually, however.

Figure 4.2.7 A discrete environment with a barrier.

This example shows that it is possible to represent perception in terms of action. In figure 4.2.7b, where the creature acts on both the barrier and the goal, we may say that it has somehow perceived them both. In figure, 4.2.7d, on the other hand, the creature has perceived the goal but not the barrier.

This view of perception emphasizes its active nature and its relation to action. Something is perceived if it can be acted on, that is, if it changes the life space of the animal. Remember that all the arrows in each of the figures above do not represent actual movement, but rather potential movement that will be executed only when the creature is placed in that particular region of space. Perception is, thus, not identical to action, but rather to latent action (See chapter 7).

In the examples above, we have made many simplifications, the most important being the use of a discrete set of regions and actions. To make the ideas presented above more realistic, we must make the transition to continuous spaces. For this, we first need to define some mathematical concepts. Given a fixed coordinate system, with points , a scalar field is described by a function, say, f, that assigns a scalar value to every location in space. From a differentiable scalar field we may derive a gradient field, -f, that gives the direction of maximal growth of the scalar field for all locations in the space. The operator - is pronounced Œdel' or Œnabla', and in n dimensions it is defined as:

(Equation 4.2.3)

A gradient field is, thus, a special type of vector field, that is, a function that assigns a vector to each point in space. In physics, gradient and vector fields are used to describe force fields of the type that Lewin used to describe the life space of a person. It should, thus, come as no surprise that the concept of vector fields will be of great importance throughout this book.

Figure 4.2.8 The relation between the reward function, the potential reward function and the gradient. (a) The reward (or goal) function. (b) The potential reward function. (c) The gradient generated by the potential reward function. The lower figures show cross sections of the three functions.

We can use these mathematical concepts to develop a field theory for continuous spaces in the following way. A goal, g, is placed at the location marked by a dot in figure 4.2.8a. When the animal reaches this location, it receives a scalar reward, Rg. As above, the environment can be described with a reward function R(z), that assigns a reward to every location in the environment z. In this simple example, R(z) = Rg, if z=g and R(z) = 0 otherwise. When reward is received only at the goal locations, the reward function will sometimes be referred to as the goal function. From the reward function, we may derive a second function describing the potential reward at each location in space. At the goal point, the potential reward is equal to the actual reward Rg. At other places the potential reward is given by the reward at the goal minus the minimal effort, or cost, required to move from that location to the goal. The cost of moving from a to b will be called c(a, b). Figure 4.2.8b shows a potential reward function generated around the single goal in 4.2.8a. The optimal direction of locomotion is given by the gradient field derived from the potential reward function, -G as shown in figure 4.2.8c. The relation between cost and the potential reward function, G for a goal g, is thus given by the following formula,

(Equation 4.2.4)

The functions depicted in figure 4.2.8 are defined in terms of the environment. It is obvious that the environment must first be perceived by the animal before it can influence behavior. To give a picture of the life space of an animal, the vector fields must be defined in terms of the animal and not in terms of the environment. Keeping this in mind, we can now formally define our equivalent of Lewin's formula.

Let us assume that the location and posture of an animal can be described by a set of values . Any action that the animal can perform can be represented as a change in z. The momentary behavior of the animal is thus given by the quantity,

(Equation 4.2.5)

To calculate this quantity, we need a number of interrelated concepts. The momentary sensory environment, s(t), picked up by the sensory apparatus of the animal at time t, is a function of both the physical environment, e(t), and the current location in space, z(t). The immediate sensory environment should be contrasted with the potential sensory environment given by the set of all sensory signals that could potentially reach the animal if all possible positions where assumed. The potential sensory environment is, thus, a concept related both to von Uexküll's Umwelt and Gibson's ambient optical array (Gibson 1979).

The internal state of the animal is described by the vector, . This state changes as a function of time and the momentary sensory environment. When the internal state of the creature is independent of time and is only a function of the momentary sensory environment, the creature is said to be reactive.

This definition of a reactive creature is an idealization, since it assumes that there is no time lag between sensory input and actuator output. In reality, no animal can be reactive in this sense, but the definition is, nevertheless, useful since it allows us to discuss reactive behavior in a stringent way. It would, of course, be possible to define the momentary sensory environment as a function of an interval of time instead, but this would make the mathematical presentation unnecessarily complex.

The internal state is used to calculate the momentary actuator output, a, of the animal. For a purely reactive creature, the actuator output is given directly by its location in space. Note that the momentary actuator output is different from the momentary behavior. The actuator describes what the creature tries to do, and the behavior is what it can be observed to do when the actuator output has been transformed by the mechanics of the body and the laws of physics. This lets us keep the ordinary meaning of the word behavior.

The momentary behavior is calculated from the momentary actuator output, the location in space, and the properties of the environment, together with the physical laws governing that environment. Thus,

(Equation 4.2.6)

Figure 4.2.9 shows the different components of the creature and its environment and their relations. Note that the location and posture of the animal must be considered a property of the environment since its alteration depends on the actuator output as well as the environment.

Figure 4.2.9 The interaction of the creature, c, and its environment, e. An actuator output changes the location of the creature, z, which in turn changes the momentary sensory input, s. The sensory input changes the internal state, x, of the creature which in turn produces a new actuator output. The internal state of the creature and the environment may, of course, also change on their own regardless of each other.

This equation will be our version of Lewin's B=f(P, E). There is one important difference however. In our formulation, the concept of a life space is not merely metaphorical. Given that we know the internal state of the animal, it is possible to draw a picture of its life space. Especially in the case of a purely reactive creature, this can easily be done in a way analogous to the discrete situation presented above. For a fixed time, t, we estimate the average vector field and take this as the life space of the creature. When the behavior of the creature is entirely deterministic, the life space is given directly as a function of z:

(Equation 4.2.7)

This suggests that we view the creature and its environment as a dynamical system (Kiss 1991, Thelen and Smith 1994). In the rest of this chapter, we will take a closer look at this function and characterize some different classes of reactive behaviors in terms of the life spaces they generate.

Behavior in Relation to a Single Object

We now put the definitions above to work and investigate the basic classes of directed behavior and the minimal artificial nervous systems that can generate them. Throughout the presentation, we will use the nervous system in figure 4.2.10 as an example. This network can generate all of the behaviors described in the text. (Figure 4.2.11 summarizes the appropriate connection weights for the different behaviors.) Behavior in relation to a single object in space can be characterized by whether the object is appetitive, aversive, neutral or unknown, which gives us the four classes of behavior that will be presented below.

In the animal learning literature, the different types of behavior listed in table 4.2.11 are usually defined in terms of learning (See, for example, Gray 1975). Here, we will try to make definitions that are entirely independent of any learning abilities that the animal may have and are thus applicable in many more situations.

Figure 4.2.10 Nervous system that can generate the different behaviors discussed in the text. Olfactory sensors at the top linearly excite or inhibit the motor neurons at the bottom to produce the desired behavior. Inter-neurons with semi-linear output functions make the avoidance gradients steeper than the approach gradient. (See text for explanations).

Behavior in Relation to an Appetitive Object In order to eat, an animal is usually required to move away from its present location and toward the location of food. Once the food source is reached, the food-seeking behavior is followed by eating. This is an example of the two main components of behavior in relation to an appetitive object. In many cases, both appetence and consummation may consist of a whole set of behavior patterns with varying degrees of complexity and adaptability (Lorenz 1977, p. 57; Timberlake 1983).

Figure 4.2.11 Summary of the different behaviors discussed in the text. The right part of the table shows connection weights that should be used for the nervous system in figure 4.2.10 to produce the various behaviors. The values a and b are arbitrary constants with 0 < b < a and c > 0 is the resting activity of the motor neurons. Blank table entries indicate that the corresponding connections are missing or have zero weights.

Here we will consider the dynamic properties of the appetitive situation as they appear in the spatial domain when only one goal object is present. In the next chapter, we will study how different learning methods are involved in the appetence and the consummation phase, and in chapter 6, the role of time varying valences will be investigated.

Appetitive behavior can be divided into the two classes of goal-directed and non goal-directed or wandering. To distinguish the two, we will present a definition of goal-directed behavior and consider behavior that does not fit this definition as non goal-directed.

We want to propose that the following definition captures the essential properties of goal-directed behavior. Let g be the location of a goal, G. A behavior, f, is goal-directed, with respect to a stationary goal G, if it has the following properties:

(GD1) The location of the goal influences the behavior, that is, f is a function of g.

(GD2) The distance to the goal in psychological space decreases with time, that is,

Given this definition, it is neither necessary nor sufficient that the animal reach the goal. This definition of goal-directedness is, thus, primarily concerned with the striving of the behavior and not with its result. Also note that goal-directedness in this sense is a momentary property of a behavior. Since goal-directed behavior can alternatively be characterized as approaching the goal, this type of behavior can also be referred to as approach behavior. This does not mean that all behaviors which approach a goal necessarily are goal-directed. It is quite possible for an animal to approach a goal without utilizing an approach behavior.

The definition should be compared with the one presented by McFarland and Bösser (1993) which requires that the goal is explicitly represented and is used to guide behavior over time. The differences between their notion of goal-directedness and the one we present here are very subtle, but it appears that their definition is slightly more restrictive. Condition (GD1) appears to be weaker than the requirement for explicit representations and condition (GD2) does not require that the difference between the desired state of affairs and the current state is explicitly used as feedback to control behavior, as they suggest. In the ethological literature, approach behaviors, as defined above, are usually referred to as topic responses or taxes.

Common to all these taxes, the simplest and the most complex alike, is the fact that the creature turns directly, without any process of trial and error, in the direction most favorable for its survival. In other words, the size and the angle through which it turns is directly dependent on that formed by the creature's longitudinal axis and the direction of the impinging stimulus. This Œangle-controlled' turning is characteristic of all taxes. (Lorenz 1977 p. 52)

The mechanisms that control taxes are called servo-mechanisms (Gallistel 1980). They are, thus, canonical examples of teleological behavior (Rosenbleut, Wiener and Bigelow 1943). To model goal-directed behaviors we will elaborate on the idea of potential reward functions. We have already seen how a potential reward function can be defined around a goal. To describe the dynamics of the appetitive situation, some further functions of a similar kind are needed. We will call these goal-gradients in agreement with Hull's use of the term (Hull 1932). The goal-gradient around an appetitive object describes the strength of the approach tendency at every distance from it. The size of the goal-gradient is considered to be reflected in the speed of movement at different distances. The concept of a goal-gradient is, thus, related to the potential reward function described above.

In our artificial creatures, the smell gradients picked up by the olfactory sensors generate signals that have the desired properties of a goal-gradient. Taking this into consideration we see that there are four possible types of goal-directed approach behaviors (See figures 4.2.10 and 4.2.11). The first will be called accelerating. A behavior of this type becomes more vigorous as the psychological distance to the goal decreases. The opposite behavior is also possible and will be called decelerating. A behavior of this kind will typically cause the animal to stop at the goal. The behaviors of real animals usually show a combination of these two types. Up to a certain distance from the goal, the speed of movement increases until it reaches its top speed. After this point, the speed decreases instead and nears zero at the goal. This will be called a combined approach behavior. Note that a combined approach behavior can be generated by combining either an accelerating approach and an accelerating avoidance behavior or by combining two decelerating behaviors.

Miller (1944) suggested that the combined approach behavior is the result of desired objects being both appetitive and aversive, thus generating both an approach gradient and an avoidance gradient. This corresponds to the idea that a goal object may be dangerous if the animal collides with it at high speed. Since the slope of the avoidance gradient is considered to be steeper than that of the approach gradient, the sum of the two gradients will yield an approach behavior that increases in speed as the animal gets closer to be goal but then drops off to zero when the goal is reached. Schmajuk and Blair (1993) have shown that if these ideas are combined with an appropriate physical model, the speed of movement generated closely follows that of a real animal in a runway.

Finally, a creature can show orienting behavior. Such a behavior moves the animal closer to the goal in the sense that it directs its sensory apparatus toward the goal. Table 4.2.11 shows the different types of goal-directed behavior, and in figure 4.2.10 a nervous system that can generate the different behaviors is shown.

Figure 4.2.12 shows computer simulations of the three types of approach behaviors using the type of smell cues described in the previous chapter. Accelerating approach causes the creature to move toward the goal. When the goal is reached, the locomotion of the creature starts to oscillate around the goal point (4.2.12a). Decelerating approach makes the creature move more slowly the closer it gets to the goal. In the simulation in figure 4.2.12b, the creature stops before it reaches the goal. Finally, in figure 4.2.12c, a combined approach behavior is simulated. The resulting path shows an abrupt change at the distance from the goal where the approach and the avoidance gradient are equally strong. At this point, the creature starts a circular locomotion around the goal point. The distance from the goal to this circle depends on the relative strengts of the approach and the avoidance gradients. While the nervous systems simulated here were explicitly constructed, behavior similar to that shown in the figure has also been automatically evolved using simulated evolution (Beer 1992). Very similar architectures have also been discussed by Braitenberg (1984).

Figure 4.2.12 Computer simulations of four classes of approach behaviors. (a) Accelerating approach followed by oscillations around the goal. (b) Decelerating approach: the creature stops before it reaches the goal. (c) Combined approach: the creature is attracted to a circular path around the goal. Note that in all these simulations, the creature does not stop when it reaches the goal.

In the combined approach behavior, the approach tendency is inhibited by what will be called an active avoidance tendency that increases as the animal gets closer to the goal. On its own, this active avoidance tendency would make the animal move away from the goal, as we will discuss further below in relation to aversively motivated behavior. Animal studies suggest that there also exists another avoidance tendency, usually called passive avoidance (Gray 1975, Mowrer 1960/1973). The role of this avoidance gradient is solely to inhibit another behavior, in this case the approach behavior. To do this, it should not be directed. Thus, it can not be used to move away from an object. In figure 4.2.10, a central node, qp, is included that allows behavior to be inhibited in this way. Following the suggestion of Gray (1975, 1982), this system will be called a behavioral inhibition system (or BIS), and the behavior it produces will be called passive avoidance. This is a system of great importance that we will return to many times below. Here, we will only consider its role in slowing down the creature before it reaches the goal.

A creature using a passive avoidance gradient in a combined approach strategy must have a correct estimation of the distance to the goal if it wants to approach it successfully. If the estimated distance to the goal is too short, it will stop before the goal is reached, and if it is to far, the creature will either run passed the goal or get hurt while colliding with it. To behave optimally, the creature should stop exactly at the goal; that is, the approach and avoidance gradients should be equal at the goal location.

In figures 4.2.10 and 4.2.13, the connection weight m represents the slope of the approach gradient, and n is the slope of the passive avoidance gradient. The intersection of the avoidance gradient with the abscissa is given by the threshold, qp, of the interneuron whose transfer function is assumed to be semi-linear. The creature will stop when the positive and negative goal-gradients are equal. At this location, g, the smell intensity, s, is given by,

(Equation 4.2.8)

For optimal speed, n, m and q should be chosen to satisfy this condition. Even so, we still need to make one change in the approach behavior to make the speed optimal.

Figure 4.2.13 The approach and avoidance gradients around a goal.

If G(z) is the potential reward function around G, and G is stationary, we see that a behavior is optimal, with respect to G, when . None of the approach behaviors described so far are optimal with respect to the potential reward function of the situation. As we have discussed above, the creature should try to follow the gradient of this function if it wants to reach the goal with the least possible effort. This corresponds to movement along a straight line from the start to the goal, but the creature can only move in this way when it is already heading in the correct direction. An optimal behavior could thus be constructed if the creature could be made to first orient itself toward the goal and then start its approach behavior.

If we let behavior be controlled by both an accelerating and a decelerating approach tendency at the same time, the creature will easily orient itself toward the goal (figure 4.2.10 and table 4.2.11). Since the two motor neurons will always receive equally large signals but of opposite sign, we know that the creature will not move toward or away from the goal but will only turn on the spot. If the left and right sensory signals are different, the creature will turn until these are equal and the goal is in front of it. As we have already seen, this means that the orienting behavior is an approach behavior since the psychological distance to the goal decreases, allthough the physical need not do so.

We also need a mechanism that can change between the orienting and the approach behavior. Figure 4.2.14a shows a hierarchy of behavior modules that can do this. In figure 4.2.14b, the corresponding neural network is shown and a simulation can be found in figure 4.2.15.

Figure 4.2.14 Combining orientation and approach for optimal behavior. (a) A subsumption hierarchy with three interacting behavior modules. The lower module makes the creature move ahead, the approach module moves the creature toward the goal object and the orienting module orients the creature toward the goal if it is not sufficiently straight ahead. (b) A nervous system that generates the combined orientation and approach behavior. A comparator neuron (=) detects if the olfactory signals from the two receptors are approximately the same. In this case, the inhibitory synapses representing the decelerating approach gradient are inhibited. This will make the creature approach the goal. When the two sensors give different signals, the orienting behavior is disinhibited and the creature will start to orient toward the goal. Connection weights are set as illustrated in table 4.2.11.

The behavior of the creature in figure 4.2.14 is similar to that of a flatworm which orients itself toward a current that carries the scent of food. When both tips of its head receive equal stimulation, it begins to crawl upstream (Lorenz 1977). The nervous system in figure 4.2.14 is optimal for approach to a goal object if it is the only one in an environment. In more complex situations it is not sufficient. In fact, it is not even very good since the creature will orient itself toward the average location of all goal objects in the environment. This is exactly what the flatworm does in such a situation. In section 4.4, which deals with orienting behavior, we will return to this problem and suggest a solution. However, it should already be clear that we have constructed a neural circuitry that can be used as a base for stimulus-approach association.

Figure 4.2.15 Orienting behavior followed by an accelerating approach. As can be seen, this type of behavior is more effective than the approach behaviors in figure 4.2.12.

The combined approach behavior described above is our first example of an attractor in the life space of the artificial creature. An attractor is a set of points in the life space that has the following properties

(A1) Once the creature has reached the attractor, it will not leave it again.

(A2) Given that the creature is sufficiently close to the attractor, it will eventually end up in it.

Attractors will play an important role as we further develop the field theory. An obvious application is to characterize a goal. When a goal is an attractor for the locomotion of the creature, we know that the goal will be reached if the creature starts out sufficiently close to it. The set of points for which attraction is sure is called the basin of attraction for the attractor. This suggests the definition of goal-reaching behavior. Such a behavior is generated when,

(GR1) The goal is an attractor, and,

(GR2) the creature is located in the basin of attracton of the goal.

We see that for goal-reaching behavior, the attractor coincides with the goal. Note that the definition of goal-reaching behavior depends on both the psychological environment of the creature and its physical environment. Like the goal-reaching behavior, orienting behavior also ends up in a point attractor. This is an attractor of another type, however, since it is independent of the location variables of the creature. For our example creature, only the posture but not location is influenced by the orienting behavior. This means that for the orienting behavior, the attractor is of lower dimensionality than the action space z; that is, regardless of where the creature is located, it will turn toward the goal stimulus, but will not move away from its current location.

Behavior in Relation to an Aversive Object To survive, an animal must avoid situations that are dangerous. In general, there are two classes of aversive situations that must be avoided. The first type, including events such as jumping down from a high tree or eating poisonous food, does not usually require that the animal performs any specific action. To avoid these situations, all the animal has to do is to refrain from doing something. This is passive avoidance that we discussed in the previous section.

The other type of aversive situation requires that the animal take some action; for example, when it is confronted with a predator or a hostile member of its own species. In these cases, the appropriate action is often to escape. This kind of behavior is also called active avoidance. Like approach behavior, active avoidance can be performed with different intensity at different distances from the aversive object. For example, it may be adaptive to start out an escape slowly to avoid the attention of a predator and run fast only at a certain distance from the predator. In other cases, it may be more adaptive to run fast when the predator is close but slow down when the distance is larger. A usual strategy is to freeze to avoid the attention of the predator when the distance to it is great and only run when the pretador gets closer.

The different types of active avoidance behaviors parallel the approach behaviors presented above. The difference is, of course, that behavior is directed away from the aversive object and not toward it. Let h be the location of a stationary aversive object, H. A behavior, f, consists of active avoidance, with respect to H, if it has the following properties:

(AA1) The location of the aversive object influences the behavior; that is, f is a function of h.

(AA2) The distance to the aversive object in psychological space increases; that is,

Condition (AA2) suggests that direction of optimal avoidance is given by the gradient of the potential reward function around H. Thus, active avoidance is optimal if , where H(z) is the potential reward function that is typically negative with its minimum at h. In analogy with approach behavior, it is easy to construct creatures that show the different types of active avoidance behaviors (See figure 4.2.10). Two computer simulations of accelerating and decelerating active avoidance behavior are shown in figure 4.2.16.

Figure 4.2.16 Computer simulations of two types of active avoidance behaviors. (a) Accelerating active avoidance. (b) Decelerating active avoidance.

Behavior in Relation to a Neutral Object Most elements of an environment are neither very useful nor very dangerous for an animal. Such elements will be called neutral objects. In our example world, the only neutral objects are walls and objects that give off neutral smells, but in the real word most objects are of this type. Of course, this does not mean that neutral objects cannot become attractive or aversive at another point in time (See chapter 5). In this section, we will consider objects that are not interesting in themselves at the moment and whose only function is to be in the way of the animal. Such objects are similar to the barriers in Lewin's field theory in that they hinder psychological and physical movement. However, they are also different in that they may take on aversive properties in certain situations.

Let us first consider the case of simple collision avoidance. In this type of passive avoidance, the animal needs to move around an object in order to reach a goal object. A situation of this type has already been shown in figure 4.2.2. Had it not been for the obstacle, the optimal path would be in a straight line from the current location of the animal to the goal. If we assume that the animal is sophisticated enough to perceive both the goal and the barrier at a distance, and that the influence of the goal is such that the animal is not able to move around the barrier, how should the speed of movement be changed near the barrier if the creature is to avoid colliding with it at high speed?

To avoid collision, the animal must obviously slow down before it reaches the barrier. It seems appropriate to assume that the creature should try to move as close to the goal as possible. It should therefore move the whole way up to the barrier before it stops. This means that its speed must be zero at the barrier, and thus, the speed of movement must be changed in such way that it is positive everywhere along the path but decreases to zero exactly at the barrier.

Since the speed of movement depends on the attractiveness of the goal, the force generated by the barrier cannot be independent of the goal object. The most natural way to make the opposing force of the barrier dependent on the goal is to consider it a function of the speed of movement of the creature, or alternatively of the approach gradient. Let g(z) be the behavior of the creature when the barrier is removed, and let b be the point of intersection between the path to the goal and the barrier. A behavior, f, is called neutral avoidance if it can be written on the form,

(Equation 4.2.9)

where represents the psychological distance between z and b, and n(x) is a scalar function with the following properties:

(Equation 4.2.10)

(Equation 4.2.11)

(Equation 4.2.12)

The expression n(Y(z,b)g(z) sets up a neutral avoidance gradient. In Hull's analysis of the above situation, he concluded that the barrier should be considered as an aversive object with an avoidance gradient of a practically vertical degree of steepness (Hull 1952, Theorem 90). In light of the previous presentations, it seems that his conclusion is invalid for animals that do not have negligible mass. Since the animal must slow down before it reaches the barrier, the normal passive avoidance depends both on the speed of movement and the mass of the animal, that is, on its momentum. This cannot sensibly be considered as a property of the barrier. The same problem faces a potential field account of the situation.

Figure 4.2.17 shows the simplest nervous system that is able to stop the creature in the desired way. When the creature comes into contact with a wall, its speed is reduced in such a way that it will stop just before the wall. Since the whiskers of our creature are relatively short, the avoidance behavior will not start until the creature is fairly close to the obstacle. This type of avoidance is, thus, more effective if some other type of sensors are used that react at a longer distance.

The previous discussion of neutral avoidance assumes that there is only one barrier in the environment. Since this is not usually the case, we need some way to combine avoidance gradients from different barriers. Above, we saw that two ways to combine gradients are to sum them together or to take the maximum of them.

Figure 4.2.17 Neutral avoidance. The signals from the two whiskers suppress the signals from the smell sensors to make the creature stop before it collides with an obstacle.

When the potential field method is used for path planning, obstacles are considered as aversive objects with a very steep avoidance gradient, as in Hull's classical analysis. Avoidance gradients from different obstacles are added together to yield the behavior of the robot. This scheme has the disadavantage that the robot will avoid two obstacles twice as much as a single obstacle. A larger collection of obstacles may even generate active avoidance behavior, that is, it seems as if the robot is afraid of obstacles. If the neutral gradients are added together, the same problem can occur. We can, thus, conclude that neutral avoidance gradients should not be composed using addition. What mechanism should be used instead? It turns out that a selection of the maximal avoidance gradient does a better job. When many obstacles are present, only the one closest to the animal will have any effect. This will also be discussed in section 4.3.

Behavior in Relation to an Unknown Object The most interesting class of objects are those that are unknown. There is an inherent conflict in the behavior that should be directed toward such object. Since an unknown object could be dangerous, it should not be approached. However, the object may be appetitive and should, thus, be approached. An unkown object is a typical case of an approach-avoidance conflict (See section 4.3). The solution to this conflict is to approach the object but with caution.

This behavior varies according to how much is known about the object. The creatures that will be described here use the strategy of approaching the unknown object from a distance but avoiding it when they come closer. This makes it possible for them to learn about the object while still being able to avoid it if it is dangerous. When learning is included in the nervous system, the avoidance tendency decreases over time if the animal is not hurt, until it is able to approach it all the way.

Figure 4.2.18 Combined active avoidance. The creature uses an approach strategy at a distance, but avoids the object at a closer range.

Figure 4.2.17 shows how a combined active avoidance behavior can be used to investigate an unknown object. In chapter 7, we will see how exploratory behavior is generated using a combination of behavioral inhibition, orienting behavior, and the combined active avoidance behavior. A sequence of these behaviors will be called an orienting reaction or orienting response. (See also section 4.4.)

This concludes the discussion of behavior directeded toward or away from a single object. Below, we will see examples of more complex behaviors that cannot be considered as directed in the sense that they cannot be generated by a composition of potential fields. First, however, we must investigate how an animal can behave in relation to multiple objects.

4.3 The Coordination of Behavior

In chapter 2, we saw that many behaviors are generated by innate releasing mechanisms. Such systems can be modelled by two interacting components (Figure 4.3.1). The first is an applicability predicate (Connell, 1990) which determines if the sign-stimulus is present and the second is a transfer function which transforms the sensory input to an actuator output. When the applicability predicate recognizes the sign-stimulus, it activates (or facilitates) the transfer function that consequently starts to generate an output.

The applicability predicate corresponds to a rudimentary perceptual categorization while the transfer function corresponds to a motor control system. In many animals, the influence of the perceptual system is not to activate a motor system but to inhibit (or supress) it. For example, an earthworm deprived of its Œbrain' will start to crawl unconditionally (Shepherd 1988). In this case, the role of the brain is to inhibit the motor action when it is not needed. Logically, the two cases are identical.

Figure 4.3.1 The internal structure of a behavior module. (a) An applicability predicate, P, determines if it is appropriate for the module to produce an output. If this is the case, the control output is generated from the input by the transfer function f. (b) The applicability predicate determines when it is appropriate to inhibit the transfer function.

Note the relation between a behavior module and structures of the type that are used in classical symbolic AI. The main difference between a behavior module and such a structure is that a behavior module is a fixed, and usually physical, unit that includes a control strategy with the action command. See Nilson (1994) for an example of a symbolic structure that is very similar to a behavior module.

More complex action patterns can be generated if many behavior modules are connected in a sequence within an engagement system (See section 3.2). There are four distinct ways to do this depending on two variables. The first choice is whether the linking between the modules is internal or external, and the second depends on whether the behavior modules use sensory feedback or not (figure 4.3.2).

For a fixed-action pattern, the function f generates a time-dependent actuator output that is independent of any sensory input. As a result, the sign-stimulus sets off a sequence of actions that are executed without any regard for their consequences in the world (figure 4.3.2a). An action sequence of this type is thus internally-linked and does not use feedback. This is the type of behavior that was associated with a response chain in section 2.7.

Internally-linked sequences have the problem that they generate the whole sequence of movements, even if this does not have the expected impact on the external world. This problem can be overcome with the help of externally-linked behavior modules (figure 4.3.2b). In this case, the behavior modules communicated with each other through the world (Brooks 1991a). The first behavior module generates an action that has consequences in the world which are detected by the second behavior module in the sequence, and so on. If the outcome of a behavior is not the expected one, the action chain will be terminated, or a jump will be made to a more appropriate place in the sequence. The movements are still rigid, however, since no sensory feedback is used. In section 2.7, this type of behavior was assumed to be generated by an S-R chain. Brooks (1991a, b) has made a strong case for the use of externally-linked control systems for robots.

To generate better behavior, both internally and externally-linked behaviors can make use of sensory information, both in the form of perception and proprioception. Figures 4.3.2c and d show two architectures of this type. The stimulus-approach sequence that was introduced in section 2.7 is an example of a behavior sequence that uses feedback in each step.

Figure 4.3.2 Four types of action sequences. (a) Fixed-action pattern: a sequence of actions a1, a2 and a3 is generated without any sensory feedback when the sign-stimulus Ss is detected. (b) Hierarchical action pattern communicating through the world. Each behavior module produces an action ai which has certain consequences ci in the world. These in turn trigger the next behavior module. (c) Fixed behavior sequence where each behavior module uses sensory feedback. (d) Hierarchical action sequence with feedback. Species-specific drive actions are typically of this kind.

In real animals, externally-linked behaviors are best known through the work of Tinbergen (Tinbergen 1951/1989), who called them hierarchically arranged instincts or hierarchical motor patterns. A related concept is that of a species-specific drive action (Lorenz 1977, p. 57). An important aspect of such sequences is that each behavior leads to a new and more specific situation where a new sign-stimulus can be found. For example, a bat's search for insects can be divided into a distinct set of phases in this way (Simmons 1989). The first phase consists of search for a prey. When a prey is detected, a second phase starts. At this point, an approach behavior commences and continues until the bat is within approximately one meter of the target. Here the third phase begins, and the bat begins to track the insect. Finally, a terminal behavior is executed which leads to the capture of the prey. In the bat, the various phases of the appetitive behavior can be distinguished both by the behavior of the animal and by the sound signals it emits to locate its prey (Compare section 2.2).

Action Selection

In this section, we will consider a number of different ways in which behaviors can be composed. In behavioral robotics, this selection process is often refered to as arbitration or action selection, and the nodes in the network of behavior modules that are responsible for the combination are called arbitration nodes. The role of these systems is to control the coordination of different actions.

The concept of action selection will be the basis for the theory of motivation that will be developed in chapter 6. Here, we will only consider the most basic forms of action selection and behavior composition which are needed by a reactive agent. The different types of arbitration methods are summarized in figure 4.3.3 below.

Let us start with the additive composition. Two behavior modules generate control signals that are simply added together. As we have already seen, this is the mechanism that is mostly used to combine potential fields (Arkin 1990). A nice property of this method is that it does not matter whether we sum the potentials or the gradients to get the composed behavior. This follows from the fact that - is a linear operator. Thus, if Gi(z) is a set of potential reward functions,

(Equation 4.3.1)

The left hand expression corresponds to the situation where the individual potential reward functions are first added together before the direction of movement is calculated. The right hand expression corresponds to the case where each behavior module generates its own actuator output which is subsequently added together with the other. Since the individual behavior modules may include an applicability predicate that controls whether the module generates an output or not, no additional arbitration is necessary in many cases.

Figure 4.3.3 Summary of the different arbitration methods. The vector-valued actuator commands from behavior modules A and B are called a and b, respectively. The output from the arbitration node is called c. Strength outputs are called sa and sb and gating signals are called ga and gb. In central selection, the gating signals are functions of a central motivational state M. This state, in turn, depends on the strength output from A and B.

One drawback with additive composition is that it generates unsuitable behavior in some cases. If there are a number of goals close to the creature in the environment, it will appoach the average position of the goals instead of one distinct goal. This is obviously not a very good strategy although it does manifest in real animals.

An animal can overcome the problem of multiple goals by using maximum composition. In this arbitration scheme, only the control signal with the largest magnitude is allowed to control the creature. This is similar to response competition which has been an important part of many theories of behavior (Hull 1934, Grelle 1981). Note that, in general, the control signals are vectors and not scalars. As a consequence, it is necessary to look at the magnitude of the whole vector and not only at the individual components when a control signal is selected.

The subsumption architecture invented by Brooks (1986) is yet another variation on this theme. In this architecture, arbitration depends on a fixed hierarchy of the control signals. The arbitration nodes are called suppressor nodes. When the behavior module at the top generates an output, it supresses the control signals from the lower behavior module. This situation is shown in figure 4.3.3. The behavior-based robots built by Brooks (1990) and coworkers) show that it is possible to construct quite complex systems using an arbitration scheme of this type.

Supression can alternatively be seen as a form of inhibition. Inhibitory signals can either decrease the intensity of the output of the other module or can be used to inhibit it completely. This second situation can be interpreted as if the applicability predicate of the behavior module at the bottom depends on the output of the top module.

It is also possible for the behavior modules to mutually inhibit each other. When mutual inhibition is used, it is possible for the behavior modules to compete in such a way that only one of them will be able to generate an output signal. In the neural network literature, this is usually refered to as a "winner take all" architecture (Compare section 2.3). In many respects, this arbitration scheme is similar to maximum composition, but with one important difference. When maximum composition is used, it is the magnitute of the output signals that determine which behavior will win. With mutual inhibition, this need not be the case. It is quite possible for the inhibitory output to be very strong and the control signal to be very weak at the same time. This makes it possible to have a very strong tendency to do very little. The signal that represents the strength of the behavior module will be called the strength output in order to distinguish it from the control output (See figure 4.3.3).

An even more complex behavior selection scheme can be called central selection. It is similar to mutual inhibition in that the different behavior modules compete for activation. Another similarity is that the signal that determines the strength of each behavior tendency is independent of the control signal. A central motivational module is used to collect the strength outputs from each behavior module and select which control signals should be let through the arbitration node. In chapter 6, we will study how the strength outputs can be used to represent the estimated potential reward that will be received if the behavior module from which they emanate are activated. We will argue that the motivational system is based on this type of arbitration. In this case, the strength output from the behavior modules are used as incentive signals (See chapter 6).

Finally, it is possible to select action according to a stochastic function. In random selection, the probability for a certain action is proportional to its strength. If a0Šan are a set of behaviors generated by the behavior modules A0ŠAn, the probability that Ai will be performed is calculated from, for example, a Bolzmann-distribution as,

(Equation 4.3.2).

The parameter T is called temperature and controls the randomness of selection (Ackley, Hinton and Sejnowski 1985). The probability of selecting the largest signal increases with decreased temperature. When T approaches infinity, the arbitration becomes entirely random. When it is close to 0, the behavior with the largest strength is always selected. As in the case of central selection, it is possible to let strength outputs control the choice instead of the actual behavior signals. Random selection is, thus, a form of central selection since the choice of behavior must be based on strength inputs from all behavior modules.

Behavior in Relation to Multiple Objects

In any realistic situation, the environment consists of a large number of objects, some of which are appetitive and some which are aversive. Those objects which are appetitive and those which are aversive may change over time as the needs of the animal change. At a single moment, however, the potential rewards corresponding to each object in the environment can be considered constant. In Lewin's theory, this is called the valence of an object (Lewin 1935). The valence is responsible for the strength and direction of the forces around an object. An object with a positive valence will attract the individual, while an object with negative valence will push the individual away from it. The forces from all the objects in the environment are combined to describe the behavior of the animal. This clearly corresponds to the addition of potential fields which was discussed above. In this section, we will consider the dynamics of situations with more than one object. The presentation will start with some classical examples of conflicts.

The Approach-Approach Conflict Consider a runway with food placed at each end (figure 4.3.4). A hungry rat that is placed in the middle of this runway has the same distance to both pieces of food and is, thus, in a state of conflict. The potential reward function for the situation does not tell the animal in which direction to move. This is called an approach-approach conflict (Lewin 1935). Two approach tendencies compete with each other in such a way that they neutralize each other. The resulting behavior of the animal, if it were to follow the potential reward function, would be to remain at its current location. However, any movement toward one of the goals would make the force toward that goal stronger and toward the opposite goal weaker, and the animal would start to approach it.

Figure 4.3.4 The approach-approach conflict in a runway with a goal object at each end.

As pointed out by Miller (1944), the point in the runway exactly in the middle between the two goals corresponds to an unstable equilibrium point. This equilibrium holds for all points along the line that divides the runway in the middle. This line is called the Voronoi border between the two basins of attraction for the two goal objects. Figure 4.3.5 shows the Voronoi borders of an environment which consists of 3 objects with equal positive valences. In general, the different object may have different valences, and the borders between the basins of attraction will not be at equal physical distance from the goal objects.

Figure 4.3.5 The general approach-approach conflict occurs at the Voronoi borders between the basins of attraction around different goal objects.

Figure 4.3.5 illustrated the basins of attraction as they are generated by the potential reward functions of the environment. When the animal tries to follow this function based on its momentary sensory input, the situation looks a little different. Figure 4.3.6, shows how a creature that uses a combined approach behavior will behave in an environment with four goal objects. The simulated creature is placed at each location in space and is allowed to move until it reaches a goal. If it reaches the goal at the top left, the starting position is marked by a black dot; if it reaches any other goal first, the starting position is marked in white. The creature is initially oriented toward the center of the environment. This means that the figure only shows one projection of all the possible initial locations and postures.

As can be seen, the creature fails to follow the potential reward function for many initial locations. It appears that the initial orientation of the creature plays a larger role in determining its goal than the distance to the closest goal. As can be expected, a creature that first orients toward the closest goal will behave more in agreement with the potential reward function.

Figure 4.3.6 (a) The environment. (b) The basins of attraction in a simulation of combined approach. (c) Unsafe points.

The simulation shows that there exist locations very close to each other which result in different goals. For a given uncertainty s, let us define a location as unsafe when there is another location at a distance less than s that results in a different goal object (See Peitgen, Jürgens and Saupe 1992). Figure 4.3.6c shows the set of unsafe locations for the situation in figure 4.3.6a. The area of these points can be considered as a measure of the width of the boundaries between the basins of attraction for the two goals.

In Hull's analysis of the approach-approach conflict, he thought it necessary to include an oscillation function that would generate the required deviations from the unstable equilibrium seen in animal experiments. In the simulation shown here, deviations from the equilibrium points are the result of deterministic chaos. This has some important consequences.

First, since the choice of goal is sensitive to the initial location of the creature, it is not, in general, possible to predict which goal the creature will approach with any certainty. Note that this is not a result of any randomness in the behavior but is an inherent property of many environments with multiple competing goals.

Second, the boundary between different basins of attractions can not be considered as a line, but must be seen as a region. Usually, such a region is of fractal dimension. A further discussion of these properties would, however, lead us too far away from the topic of this book. The interested reader is instead referred to the clear-cut presentation of the relation between dynamical systems, chaos and fractals that can be found in Peitgen, Jürgens and Saupe (1992).

The Avoidance-Avoidance Conflict Another type of conflict situation occurs when the objects at each end of the runway are aversive. Given that the creature uses active avoidance behavior away from each of the two aversive objects, it will eventually end up in the middle of the runway. In the ideal situation, this location constitutes a stable equilibrium (figure 4.3.7). In a real situation however, the heading of the creature will influence the two potentials and it will oscillate around the middle of the runway.

Figure 4.3.7 The Avoidance-Avoidance Conflict

The Approach-Avoidance Conflict The final conflict situation is the approach-avoidance conflict that results when a location is both appetitive and aversive at the same time (figure 4.3.8). We have already seen that this conflict is present when an animal encounters an unknown object. However, situations of this type can also be artificially produced, for example by placing both an appetitive and an aversive object at the same place (Lewin 1935, Miller 1944; see also figure 4.2.17).

Figure 4.3.8 The Approach-Avoidance Conflict

4.4 An Elementary Reactive Repertoire

In this section, we will develop a basic set of reactive behaviors, most of which will not be goal-directed. To behave appropriately, a creature will need a large set of such behaviors. The repertoir we will consider here is only meant as a rudimentary example. It shows the diversity of the innate behavior modules that must be present before an animal can do anything at all. Most of all, the innate behavioral repertoir makes it possible for the animal to stay alive long enough to make use of its learning abilities. These behaviors can be seen as reactions to problems that are certain to be present in the environment, that is, problems that do not generally gain any advantage from learning.

Grooming

Grooming behavior will be generated by a set of nodes that activate each other in sequence. Each node moves the whiskers to a certain position, and the sequence of activation will, thus, generate a stereotypic motion of the whiskers. A network architecture of this type has been called an avalanche since it cannot be stopped once it has started (Grossberg 1986). The network in figure 4.4.1 shows an avalanche of this type. When the integrating node to the left receives an input signal, it start to oscillate as described in section 2.3. Every time its output signal is high, it will start the avalanche which in turn produces a stereotypical action pattern. This is, thus, a simple case of an internally-linked behavior.

Figure 4.4.1 An avalanche triggered by an oscillator produces a stereotypical action pattern.

Such behaviors are very common in real animals. "Typically, rats lick their fur, then scratch themselves, and then fiddle with their feet. The different components usually appear in this order." (Bolles 1984, p. 436) Grooming is obviously much more complex than the behavior generated by the network here, but the notion of an avalanche does, nevertheless, capture an essential feature of such behavior.

The Orienting Reaction

The orienting behavior of our creatures will consist of three phases. The first is the inhibition of any ongoing behavior by activation of the behavioral inhibition system (See figure 4.2.10). This is usually called external inhibition (Pavlov 1927) in order to distinguish it from internal inhibition which will be discussed in chapter 5. In the second step, an orientation movement will be performed toward the stimulus using the method described in figure 4.2.11. Finally, an exploratory behavior will be executed. Such a behavior will typically be a combination of an approach and an avoidance behavior. The stimulus will be approached from a distance, but avoided when the creature comes closer to it, as shown in figure 4.2.17. The activation of these three phases can be controlled by an avalanche in a manner similar to the grooming behavior above.

There is one problem with this orienting behavior which we have already mentioned. When many stimuli are present in the environment, the creature may sometimes orient toward the average position of them and not to one of them. One solution to this problem is to let the creature use a spatiotopic representation of the environment. In such a representation, a specific node is allocated to the representation of every location in the environment around the creature. Since each stimulus is mapped onto its own node, or set of nodes, the locations will not blend into each other. This is the type of representation that is used within the orienting system of many real animals (Stein and Meredith 1993). Such a system resides in the superior colliculus in mammals and the homologous optic tectum of birds and reptiles.

This more complex type of orienting system will not be used here for two reasons. The first is that it requires a very large network which would make our creatures unnecessarily complex. The second is that a spatiotopic representation is more suitable for a creature that uses other modalities such as vision and hearing. A neural network model of this type of orienting system is presented in (Balkenius 1995; see also chapter 9).

Reactive Defense Mechanisms

Aversively motivated behavior will play a rather small role in this book, but it will, nevertheless, be useful to consider some basic behaviors of this kind. It has already been suggested that it is possible to model some defense mechanisms by a behavioral gradient that makes the creature freeze when the aversive stimulus, such as a predator, is far away and flee when it is closer. While this type of system is a very crude analogy to the defensive behaviors of real animals, it shows how the intensity of the stimulus gradient around an object can be used to select different behaviors. This is, thus, a kind of arbitration mechanism.

Figure 4.4.2 A network that selects an output s1Šs4, depending on the level of the input signal s0.

Figure 4.4.2 shows a network that is able to divide a signal into intervals in this way. Each node has a threshold output function, and the threshold increases with increased index on the node. Since each node supresses the output of the nodes with smaller index, the level of the input signal s0 is used to select the output. This network could be used to select the different behaviors depending on the level of fear. A network of this type could form the basis for a fight, flight, or freeze system (Cannon 1932). A similar network could be used to select between offense, defense, or submission depending on the estimated strength of an opponent (Adams 1979). A related function is the choice between an orienting reaction or a defensive reaction depending on the intensity of a stimulus (Raskin 1972, Stein and Meredith 1993). For example, a sound with low amplitude will activate an orienting reaction toward it while a sound with high amplitude will generate a defensive reaction away from it.

Wandering

To navigate succesfully in a more complicated environment, potential fields are not sufficient on their own. There are many behaviors that are useful but cannot be generated from a potential field. In this section, we present a number of behaviors that are useful in the spatial domain, but must be generated in a way that differs from those we have seen so far. These behaviors are not goal-directed and we will refer to them as wandering. Wandering behaviors include, for example, wall-following, corridor-following, obstacle avoidance, and door entrance. Usually, behaviors of this type increase the chances of achieving consummatory behavior, and they can, thus, be considered as appetence behaviors. Wandering can also be considered as undirected exploration (Thrun 1992).

Random Walk In the final example of the previous chapter, we have already seen how to construct a behavior that will move the creature around more or less at random on an empty surface. Such a behavior is often called a random walk. Since such a random walk is not directed at all, it is obvious that it cannot be generated by a potential field and this is, thus, our first example of a behavior of this kind. When the environment is structured, it is often advantagous to use more complex behaviors.

Wall-Following When an animal senses a wall, it is very often useful to be able to follow this wall instead of turning away from it. This is a common behavior of many insects, and for the maze-like environment of our artificial creature, it will obviously be of great utility. We may connect wall-following to the concept of affordance and say that walls afford following (Gibson 1979). Whether the creature will follow the wall or not may depend on its current needs and if wall-following has been rewarded or not.

To accomplish wall-following, all our creature has to do is move in a direction parallel to the wall. To do this, it must use its whiskers to feel the distance to the wall and try to keep this distance constant.

Figure 4.4.3 A network that produces wall following of a wall which is to the right of the creature. When the creature receives no external stimulation, it will turn toward the right since the left motor neuron has a larger resting activity than the left. When the right whisker comes into contact with the right wall, the right motor will receive a larger input signal that will cause the creature to move away from the wall. As a result, the creature will follow the wall.

Figure 4.4.3 shows a nervous system that will sucessfully follow a wall to the right of the creature. When the sensory signals are above a set-point, the creature will turn away from the wall. When the whisker signal is below this value, the creature will, instead, turn toward the wall. As a result of these two opposing forces, the creature will move approximately parallel to the wall (figure 4.4.4a). This is, thus, an example of a servo-mechanism (Gallistel 1980). An identical network can be constructed which lets the creature follow a wall on its left.

An important aspect of the wall-following behavior generated by the nervous systen in figure 4.4.3 is that it is relatively stable. Even if noise is added to the sensory signals, the creature will continue to follow the wall, albeit in a somewhat more random fashion. This is shown in figure 4.4.4b, where 20% noise has been added to the sensors. Figure 4.4.4b shows what happens when the whiskers point straight to the side of the body of the creature. In this case, the wall-following behavior is unstable even though no noise has been added.

Corridor-Following In the artificial world of our creature, and in the classical mazes, corridors are very common. The ability to follow a corridor smoothly does, thus, seems useful. Such a behavior can be generated in a way similar to wall-following, but both whiskers must be used. When the creature is in the middle of a narrow corridor, the signals from each of the whiskers are equally strong. As a consequence, the creature can follow the corridor if it tries to keep the signals from the two whiskers equal. Figure 4.4.5 shows a nervous system that can generate this behavior. A simulation is shown in figure 4.4.6. As can be seen, the creature quickly aligns itself with the two walls and starts to follow the corridor. Again, it is possible to show that the behavior is stable if the whiskers point forwards but unstable if the whiskers point straight out from the sides.

Figure 4.4.4 Wall following. (a) The behavior of the network in figure 4.4.3. (b) Stable behavior with 20% noise. (c) Stable behavior with 60% noise. (d) Unstable wall-following results even without noise if the whiskers point directly to the sides.

Figure 4.4.5 Network that produces corridor-following behavior in a narrow corridor. Without sensory stimulation, the creature moves straight ahead. When it comes into contact with a wall, it will make a compensatory movement away from it. If the creature can sense both walls at the same time, it will align itself with the corridor.

Figure 4.4.6 Corridor-Following. (a) The behavior produced by the network in figure 4.4.5. (b) Stable behavior with 20% noise added. (c) Stable behavior with 40% noise. (d) Unstable behavior results if the whiskers point directly to the sides. Although the creature begins aligned with the corridor, its behavior starts to oscillate after a while.

Obstacle Avoidance Another useful ability is to move around obstacles. In the simplest case, this means that the creature should simply turn when it senses something with one of its whiskers. A more sophisticated strategy would enable the creature to continue in its original direction when the obstacle has been negotiated. To do this, the creature must keep track of its deviation from the original path.

Figure 4.4.6 shows a simple network that accumulates deviations from the original direction of movement. When the obstacle avoidance starts, the whiskers control the movement away from the obstacle. During this operation, the node, R, is supressed by the whiskers and the the nervous system accumulates the deviation from the original direction of movement in an integrating node called D.

When the obstacle has been avoided, the node R is disinhibited, which lets the accumulated deviation in D direct the creature back toward its original path through the connection a. The connection weight a determines how fast the creature will return to its original path. A computer simulation of the behavior produced by this circuit can be found in figure 4.4.7.

Figure 4.4.7 A simple network for obstacle avoidance. When the creature turns away from an obstacle, the node D will accumulate the deviation from the original direction. When the obstacle has been negotiated, node D will turn the creature back on its original path through node R.

Figure 4.4.8 Computer simulation of the network in figure 4.4.6. When the creature senses an obstacle, it turns away until its whiskers stops reacting. When this happens, the creature tries to return to its original heading.

The signals of the type accumulated in D are somtimes called efference copies (Gallistel 1980). They are copies of the signals sent to the motor system. The accumulation of turning signals is, thus, a form of dead-reckoning (Gallistel 1990). A similar mechanism can be used for path-integration to update the location of the creature as it moves around in the environment (Gallistel 1990, Touretsky and Redish 1995).

When the creature is performing an approach behavior, obstacle avoidance is much simpler. The perception of the goal will automatically turn the creature in its original direction again when the obstacle has been avoided.

Choice Each of the networks presented above in this section should be considered as a behavior module. It is clear that many behavior modules of these types must be combined before some interesting wandering behavior can occur. The first requirement is to add an applicability predicate described in section 4.3 which determines when it is appropriate to perform each behavior. For example, the wall-following behavior should only be induced when a wall is present. More generally, it is possible to use the various arbitration mechanisms described in section 4.3 to choose between the different behaviors.

4.5 Conclusion

We have seen how an animal can react to four classes of stimuli: appetitive, aversive, neutral and unknown. Each of these stimuli are encountered during either appetitive, aversive or orienting behavior. In an appetitive situation, the behavior of the animal makes it likely that it will find some desired object such as food. Figure 4.5.1 summarizes the main components of the appetitive behavior of our creature. Note that neutral avoidance is only encountered during appetitive behavior as a special case. It is goal-directed in the sense that the location of the goal controls the behavior, but it is also similar to wandering since the avoidance is not goal-directed.

Figure 4.5.1 Summary of the behaviors used in an appetitive situation.

The different types of aversively-motivated behaviors are shown in figure 4.5.2. Note that passive avoidance can only be used in combination with some appetitive behavior since its only function is to inhibit such a behavior.

Figure 4.5.2 Summary of aversively motivated behaviors.

In the final class situation that we have considered, the animal is required to investigate a novel stimulus. The behavior produced is called an orientation reaction and consists of the three components shown in figure 4.5.3.

Figure 4.5.3 The components of the orientation reaction

The orientation reaction is different from appetitive and aversive behavior in that it must exist together with some learning ability. Without learning, the creature will never retain anything about a stimulus, and, thus, every experience will be novel. As a consequence, the creature will never stop its orientation reaction. In the next chapter, we will see how learning can influence this reaction and extinguish it when the stimulus is no longer novel. We will also see how learning can be used in both the appetitive and the aversive situation.



This text is an excerpt from:
Natural Intelligence in Artificial Creatures
© 1995 by Christian Balkenius
Lund University Cognitive Studies 37
ISBN 91-628-1599-7
ISSN 1101-8453
ISRN LUHFDA/HFKO--1004--SE
The printed version of the book can be ordered from:
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