Robot Hardware

For our initial model, we selected a simple robot well suited to prototyping and research of an exploratory nature: the Elisa-3⁴ (see Figure 3). This is a small, round, two-wheeled Arduino-based robot, 5 cm in diameter and 3 cm in height. It is equipped with a ring of eight infrared (IR) “distance” sensors with a range of approximately 5 cm and four downward pointing IR “ground” sensors. These sensors provide the robot with a rudimentary (coarse and noisy) capability to detect both the proximity of objects around it and dark and light areas on the ground. It additionally has radio communications to receive and transmit messages with a PC, which we use to log data for quantitative analysis of results. Finally, it has colored LED lights on its top, which we used to visually signal its internal activity.

Since this robot has limited capabilities for manipulation and perception of external objects,⁵ we model grooming by having it “rub” its side sensors against objects in the environment to improve its (simulated) “integument”: the state of its external surface, analogous to the state of an animal’s fur or feathers.

Environment

For the purposes of data collection and analysis, we have placed the robot in a small walled area containing objects appropriate to the sensorimotor capabilities of the robot. Our environment had to support both “healthy” and pathological behaviors. We therefore placed in the environment a number of resources—“energy sources” (light patches on the floor) and “grooming posts” (plastic pipes)—that could provide the means for the robot to satisfy its survival-related needs (energy) and its other needs (grooming for maintenance of integument), but which could also provide the opportunity for pathological behavior.

An internal “integrity” variable keeps track of the (simulated) physical integrity of the robot. It decreases following collisions and other types of contact with objects (detected by the distance sensors): These include the arena walls and the grooming posts placed within the arena. If this damage causes the robot’s integrity to fall to zero or below, the robot will “die” and stop in place. In the absence of collisions, the integrity would slowly increase as the robot “heals.” In the architecture of the robot, the integrity variable is linked with the robot’s motivation to avoid objects, including the grooming posts, providing an internal conflict with the motivation to groom. This gives both a cost to the grooming behavior and a “cue” to stop. This element of the architecture allows us to investigate the extent to which the grooming behavior is compulsive, specifically, the extent to which it continues even though it directly damages the robot (see the “Consensus Stage (Stage 2)” section, compulsive grooming).⁶

In healthy (adaptive) decision-making, the robot will alternate between grooming (or seeking a grooming resource) and feeding (or seeking an energy resource). In the compulsive behavior situation, the robot will groom to the extent that it adversely affects its survival, either because its energy level falls too low or because it damages itself though contact with the grooming post.

Behavior Control Architecture

The specific robot model and action selection architecture that we have implemented draw on our previous work on motivation-based robot behavior controllers (Cañamero, 1997; Cañamero & Avila-García, 2007; Lewis & Cañamero, 2014, 2016), while also being inspired by animal models of OC-spectrum disorders.

In the robot architecture used in this study, four competing motivations guide the behavior of the robot. These motivations are urges to action determined by a combination of the four corresponding internal homeostatically controlled “physiological” variables, which provide the robot with “needs,” and by the robot’s perception of the environmental resources that can be used to manage those variables. The decision-making behavior control software provides the robot with strategies to prioritize and satisfy these needs.

An overview of the behavior control (also known in the literature as action selection) mechanism is shown in Figure 2. We describe the components of the architecture (the high-level design of the software) in the following subsections.

Physiological Variables

Our robot has four homeostatically controlled physiological variables, shown in Table 1: energy, integrity, and two integument variables (one for each side). The physiological variables take values in the range [0, 1,000], with 1,000 being the ideal value in all cases. The variables change both over time and as a function of the robot’s interactions with its environment, reflecting the current state of the robot. Following a model of homeostatic control, the difference between the actual value and the ideal value of each variable generates an error signal indicating the magnitude of the mismatch (in this case, deficit).

Two of the physiological variables (energy and integrity) have a fatal limit of zero (the robot dies if the value falls to zero). The two other variables, related to “integument,” can be thought of as analogous to an animal’s fur or feather condition: something that needs to be maintained for viability (e.g., waterproofing, efficient flight) but that does not directly cause death if it falls too low. In our robot implementation, low values of the integument variables have no physical consequences on the robot (e.g., they do not affect its physical integrity or its travel speed or any other aspects), but they will trigger a motivation to maintain the variable within a good range of values (correct the error between the actual and ideal values of this variable) by grooming.

Sensors, Cues, and Motivations

The robot uses its infrared distance sensors and ground sensors to detect obstacles, grooming posts, and energy resources in the environment. These correspond to environmental cues or incentive stimuli that influence the motivational states of the robot to avoid (obstacles), groom (at grooming posts), or consume (energy resources). The numerical size of the perceived cue is in the range [0, 100] and is determined by the sensed distance of the obstacle or by the color detected by the ground sensors for the energy resources and grooming posts.

Following a classical model in ethology, we use the long-standing concept of motivational states (Colgan, 1989), defined in terms of the drives set by the deficits or errors of the internal variables, combined with external environmental cues (incentive stimuli). Our robot has four different motivations, each linked to the satisfaction of a physiological variable (see Figure 2). The internal drives and the external incentive cues combined provide a level of intensity to each motivation at each point in time, which reflects its relevance to the current situation. The motivational intensity is calculated according to the formula proposed in Avila-García and Cañamero (2004) (modified from a classical formula in ethology; Tyrrell, 1993, p. 139):

where deficit_i (the error signal) is the difference between a variable’s current value and its ideal value as perceived by the robot (see section “Modeling Compulsive Behavior”), cue_i is the size of the corresponding cue, and α is a scaling factor to scale the size of the exteroceptive component. In our experiments, α will equal 0.05. This value was empirically determined in pretrials to allow the robot with a realistic target value (nonpathological or baseline condition 1 in our experiments) to have enough persistence in satisfying its needs to be able to survive in the environment.

As the values indicating the intensity of the motivations change over time, depending on the external and internal perceptions, at certain points, the motivation with the greatest intensity (i.e., the most pressing need) will be overtaken. This will result in a change of motivational state and hence of the behavior executed to satisfy it, and it could be viewed as an analog for a “stop signal” for the current behavior.

Behaviors

The robot has a number of discrete behaviors of different types (rounded boxes in Figure 2). The execution of some of these behaviors allows the robot to directly satisfy its motivations, and hence correct the errors of the physiological variables, while other behaviors allow the robot to “search” (move about the environment avoiding objects) for the resources required to satisfy these needs. Let us note that the robot will only move around the environment or execute a behavior if at least one of its motivations is active.

We have grouped the behaviors into four “higher level” behavioral subsystems, each one linked to a motivation: groom left group, groom right group, eat group, and avoid. These behavioral subsystems (except for avoid) are composed of smaller, simpler behaviors, which can be executed independently, simultaneously, or sequentially depending on the state of the robot and the external stimuli detected. For example, the eat behavioral group is composed of the consummatory (goal-achieving) behavior “eat,” which is executed if the robot is hungry and food is detected and located at the mouth; “orient to food,” which is executed if the robot is hungry and food is detected nearby; and “search (for food),” which is an appetitive (goal-seeking) behavior that will make the robot wander around the environment until food is detected. Searching behaviors (for an energy resource or a grooming post) involve the robot wandering around the environment (i.e., traveling in random directions, while avoiding objects), typically until the incentive stimulus of the motivation that triggered the search is found. Searching does not involve any knowledge of the environment on the part of the robot and does not occur in any particular direction. The only information about energy resources and grooming posts that the robot uses in this search is the ability to recognize them when it encounters them.

Action Selection

The robot controls its behavior as follows: At each time step (100 ms), the robot recalculates its four motivations and sorts them from highest to lowest. This order determines the order in which it prioritizes the satisfaction of its physiological variables in that action selection step. To satisfy the motivations, we use a slightly modified “winner-take-all” action selection policy, as follows. The robot will try to satisfy the highest ranked motivation (the “winner motivation”) first. To do so, the winner motivation triggers the behavioral subsystem linked to it, and one or more of the simpler behaviors that constitute this subsystem (nested rounded boxes in Figure 2) are executed, depending on whether the preconditions for their execution (e.g., in the case of the eat behavior, presence of food detected) are met. If, while satisfying the winner motivation, a behavior that satisfies a lower ranked motivation can also be executed, then it will be executed. This means that two behaviors can sometimes be executed simultaneously. Our robot can execute two behaviors simultaneously only if the two behaviors use distinct sets of actuators. For example, the “orient to food” behavior, which allows the robot to approach and stop at an energy resource, uses the wheels, while the behavior to consume the resource uses the virtual “mouth,” and thus the two behaviors can be executed concurrently. This allows the robot to consume an energy resource as it aligns itself with the resource. In certain cases, two behaviors can execute due to different motivations, for example, the eat behavior can be executed opportunistically as the robot passes over a resource while searching for a grooming post, as the mouth actuator is not otherwise occupied.

Note that, since the grooming posts are obstacles that the robot can collide with, they will also act as a cue for the avoid behavior. Whether the avoid behavior is actually executed depends on the intensity of the motivation to avoid, which depends on the values of the cue and the robot’s integrity.

Modeling Damage and Grooming

Damage to the robot (e.g., through collisions) and the effect of grooming on the robot’s integument are implemented using the IR distance sensors. Damage and grooming use independent mechanisms (summarized in Figure 3) designed with the goal that interaction with environmental objects can be potentially beneficial or damaging to the robot: Grooming involves a small possibility of damage, but not so much that a normal amount of grooming risks serious damage to the robot. The various constants in these calculations were determined empirically to meet these design goals.

To calculate damage, the distance sensors are checked every 50 ms and compared to the previous values. The calculated damage is subtracted from the current integrity. Two types of damage are possible; collisions and sustained rubbing, described as follows:

• •   Collisions. If the closest IR reading crosses a “touch” threshold (a value of 850, corresponding to an object approximately 3 mm from the robot), then a “collision” is deemed to have occurred, and a value for the damage is calculated depending on the size of the change in the sensor readings that have crossed the threshold. A maximum value of 100 is applied to this type of damage, to stop a single unlucky collision killing the robot in one blow.
• •   Sustained rubbing. When the IR sensor values maintained a value over the threshold of 900 (indicating a very close object), then a constant value of 2 damage is applied (hence a maximum of 40 per second).

To implement grooming, the distance sensors are checked every 100 ms and compared to previous values. Two sets of sensors are used: (IR1, IR2, IR3) for the right side and (IR5, IR6, IR7) for the left side, corresponding to the two integuments. If a sensor value indicates a close object (a value above 150) and the value has increased since the previous reading, while the value of the adjacent sensor toward the front of the robot has decreased (indicating the movement of a grooming post from front to back of the robot), then a “stroke” counter is incremented, indicating movement in the “correct” direction (front to back). Conversely, a sensor indication of a movement in the “wrong” direction (back to front) is considered as an “anti-stroke” and decrements the stroke counter. The overall value of the counter indicates whether the overall movement on one side is a stroke (>0) or an anti-stroke (<0). If a stroke has occurred, then the actual value of the corresponding integument (left or right) is increased by 20 times the count value; if an anti-stroke has occurred, then the actual value of the corresponding integument is decreased by −5 times the (negative) count value.

Modeling Compulsive Behavior

Following the signal attenuation model, in this article, we model compulsive behavior by manipulating the robot’s perception of the internal errors linked to its physiological variables. More concretely, we manipulate the robot’s perceived ideal (“target”) value for the integuments. This will affect the decision-making (action selection) process in the calculation of the “error” in Figure 2 or the deficit in Equation 1.

To model “typical” or “healthy” decision-making, we consider the case where the perceived ideal value is equal to the real “perfect” value (i.e., 1,000, which is as far from the fatal limit as possible). This value can be achieved and so is a “realistic” target. However, as we have seen in previous work, a robot will typically stop attending to a need before the related physiological variable reaches its ideal value, due to competition from other needs. The point when the value of the active motivation is overtaken by another motivation (which consequently becomes the active motivation) can be thought of as the robot receiving the stop signal for that behavior (although in our model, it might be more accurately thought of as an “attend to another need and switch behavior” signal).

To model “pathological” conditions, we consider values for the perceived ideal value that are not achievable, even theoretically: in this model, values greater than 1,000, which is the maximum possible value the variable can take. Since these values are not valid values for the integument, having such a target value can be thought of as a “perceptual error” or distorted perception in the robot.

As outlined in the section “Deduction Stage (Stage 4),” if the signal attenuation model of OCD holds, we would hypothesize that this manipulation, analogous to attenuating the signal for successful grooming as we increase the target value, would result in an exaggerated (more intense) motivation to perform the selected behavior. In turn, this increased motivation would out-compete the other needs and thus produce an increase in the performance and perseverance of the grooming behavior. If this effect is sufficiently large, we would expect it to be maladaptive, and this would be measurable by at least some of our metrics.

Methods

The experimental setup is shown in Figure 4. It consists of an 80 cm × 80 cm square surrounded by 45-mm-high wooden walls that can be detected with the robot’s distance sensors. The floor is covered in paper, which is printed gray, except for two light areas and two dark areas, which can be detected by the robot’s ground sensors and which indicate the presence of food and grooming resources, respectively. Two 35-mm-diameter white plastic pipes are fixed in place in the centers of the dark areas to be used as grooming posts.

We conducted 20 runs in each of the following conditions:

• 1.   Realistic target values. Perceived ideal values for integuments = 1,000
• 2.   Mildly unrealistic target values. Perceived ideal values for integuments = 1,100
• 3.   Highly unrealistic target values. Perceived ideal values for integuments = 1,200

Note that Conditions 2 and 3 correspond to target values (perceived ideal values) that are not achievable, even in theory, because they lie outside the range of the variables (see section “Modeling Compulsive Behavior”). In these conditions, an error is always perceived, even in the absence of a “real error” (a mismatch between the actual value and a realistic ideal value within the range of the variable, which is 1,000). This “distorted perception” of the target value gives rise to “perceptual errors” that cannot be corrected through behavior or by interaction with the environment because the target values lie outside the range of the variable and therefore the urge to correct it is always present. These conditions fall under the category of “comparator defect” in Pitman’s possible sources of a persistent error signal.

The numerical values for Conditions 2 and 3 were empirically determined following some informal pretrial runs. In these, we observed that the value of 1,200 resulted in highly persistent grooming—the robot would frequently groom until it died, so it was selected as the most extreme value to test—while the value of 1,100, halfway between the baseline condition and our extreme value, showed very different behavior, with the robot stopping grooming before it died.

On each run, the robot’s physiological variables were initialized to the middle value of the range (500 out of 1,000) for energy and both integuments, so that the robot would need to work to maintain all these variables, which decrease over time if not actively maintained. For the integrity variable, an initial value of 900 (out of 1,000) was chosen to allow the robot the approach grooming posts and maintain its integument, rather than starting in a “half-damaged” state and being overmotivated to avoid objects. The robot was started at the center of the arena, equidistant from all four resources (see Figure 4) facing directly toward one side of the arena in one of four alternating directions (labeled “north,” “south,” “west,” and “east”). The alternating direction was done to reduce any bias that the initial direction might impose, since this may influence which resource a robot would encounter first. Runs lasted for 6 min each, or until the robot died. The values of its physiological variables, motivations, sensor values, and the currently executing behaviors were recorded every 250 ms and transmitted to a PC via its radio link.

Select Data to Be Collected

During our experiments, we need to collect data to evaluate the adaptive or maladaptive value of the robot’s decision-making process. In terms of OC-spectrum conditions, to compare the balance between the satisfaction of different needs, we need to record the values of the physiological variables, the values of the motivations, and the behaviors that the robot is currently executing. To allow post hoc examination of the robot’s behavior, we additionally record its sensor readings and wheel speeds.

Metrics

We evaluated the performance of the robot in each condition and run using four types of metrics:

• 1.   Survival-related metrics, specifically, death rates (the number of robots that died during the run) and duration of life for each run (up to 6 min).
• 2.   Metrics relating to the regulation of physiology (well-being, physiological balance, maintenance of physiological variables away from dangerously low values, maintenance of integument). These give a measure of the success of a living robot in managing its physiological variables as a result of its decision-making, either at a specific time or over its lifetime. These help to compare the performance of robots that do not die. They are calculated from the recorded values of the physiological variables.
• 3.   Behavior of the robot. The behaviors that the robot executed are included in our logged data, so we can use this record to compare different robots’ behaviors without needing to resort to external observation.
• 4.   Motivational balance. Since our robot controller is based on the four motivations defined in the “Sensors, Cues, and Motivations” section, we can use this internal information to analyze the robots’ motivational balance, which reflects how much time they spend attending to each of their physiological needs.

We provide the mathematical definitions of these measures and use them to evaluate the results of our experiments in the following section.

Death Rates, Duration of Life

Death rates for each condition are shown in Table 2 (first column). Let us first consider Condition 1 (realistic target values). The two Condition 1 robots to die both survived 49 s, and the runs were very similar. Both of them found a grooming post in this time, spent some time grooming, and then left due to motivation to find an energy resource. After this, they both encountered a second grooming post, and although they both groomed, they did this for only about 1 s before leaving again in search of an energy resource.

In Condition 2 (mildly unrealistic target values), three robots died. Since we recorded internal data for the robots, including their motivations, we can examine what happened, including why they made their decisions. Let us look at what happened during the lives of the three robots that died:

• •   The first Condition 2 robot to die survived 52 s. It had found a grooming resource soon after starting and spent 15 s grooming before leaving. It soon found another grooming post and remained grooming for approximately 9 s. It left the post with only 6 s worth of energy and failed to find an energy resource in this short time. We remark that the integument that the robot attended to was low (only 24 greater than the energy) when the robot prioritized it over the similarly low energy, meaning that the robot had two pressing competing needs.
• •   The second Condition 2 robot to die survived 297 s. After 200 s, both of its integuments had fallen to zero, and when it found a grooming post, it stayed there grooming for approximately 1 min, increasing its integuments while its energy level fell. By the time it left the post, it had approximately 15 s worth of energy left, and it did not find an energy resource before dying. As in the first case, the low integuments meant that the robot had multiple pressing needs.
• •   The third Condition 2 robot to die survived 124 s. After finding its first grooming post and grooming, it left with approximately 30 s worth of energy and was wandering the arena to find an energy resource. However, during this time, it found another grooming post and opportunistically groomed for 10 s. When it left the second grooming post, it had less than 10 s worth of energy with which to find an energy resource.

Of the 19 deaths in Condition 3 (with the highly unrealistic target values), 17 occurred due to the energy falling to zero while the robot was grooming. In all of these cases, the integument in question had already reached its ideal value (i.e., its maximum value of 1,000), so further grooming was not achieving anything. In the remaining two cases where the robot died, these were also caused by the energy reaching zero. In both cases, the robot had stopped grooming within the last 5 s, and was now wandering—in one case motivated to find an energy resource, in the other case motivated again to find a grooming post. The mean survival time for Condition 3 was 134 s (including the robot that survived).

Well-being

To evaluate the robot’s current state, in terms of its physiological variables, we used metrics that we call well-being (Lewis & Cañamero, 2016), which provide the average level of all four of the physiological variables at each point in time. Intuitively, well-being gives an indication of the robot’s internal “health” at a point in time, with high values indicating good health (the physiological variables are high, close to the ideal value) and low values indicating poor health (the physiological variables are low, close to the fatal limit).

We calculated two different well-being metrics by taking the arithmetic and the geometric means of the physiological variables at each sample time, giving, respectively, the arithmetic well-being and geometric well-being. Both means are unweighted, that is, in both means, the four components contribute equally to the final value. However, the value of the geometric well-being is more strongly affected by those physiological variables that have values close to the critical value of zero—which is also the fatal limit for energy and integrity—and that, for this reason, can be considered the most pressing. We also calculate the more broadly used arithmetic well-being because it gives a more familiar and intuitive way of calculating the average, since it gives the “middle” value.

Applying these metrics to our experimental data, the mean values of each well-being metric over all the runs in each condition are shown in Table 2 (second and third columns). In both the arithmetic and geometric cases, these values were calculated in three steps. First, in each run, in each of the conditions, we calculated the well-being of the robot at each “time step” (each point in time for which data were collected). Second, we calculated the mean well-being over the lifetime of the robot in each run (20 runs per condition, 60 in total). Finally, we calculated the overall mean for each condition as the mean of the 20 “lifetime means” (1 per run) from the previous step. The mean values of the geometric well–being for each run are shown in Figure 5.

There was a statistically significant difference for the arithmetic well-being between conditions (ANOVA, p = 0.020), with Tukey HSD post hoc analysis showing that Condition 3 (highly unrealistic target values) differed from Condition 2 (mildly unrealistic target) (p < 0.03), but no statistically significant differences between other pairs of conditions. Turning now to the geometric well-being, there was again a statistically significant difference between the different categories (ANOVA, p = 2.5 × 10⁻⁴). In this case, Tukey HSD post hoc analysis showed that Condition 3 (highly unrealistic target values) differed from both Condition 1 (p < 0.005) and Condition 2 (p < 0.001), while Conditions 1 and 2 did not differ significantly from each other.

The fact that the difference in the geometric well-beings was statistically more significant than the difference between the arithmetic well-beings (both in terms of the p-value for the ANOVA and there being a significant difference between Conditions 1 and 3) illustrates a desirable property of the geometric well-being metric: the larger effect of small (“critical”) physiological variables on the overall value. This means that the geometric well-being is strongly affected by those variables with large errors, reflecting more accurately the significance of poorly maintained variables. Conversely, for the arithmetic well-being, one well-maintained variable can cancel out the effect of a poorly maintained variable, so in an extreme case, a robot could maintain one variable well but die quickly due to neglecting a survival-related variable and still have a high arithmetic well-being over its lifetime.

In summary, as expected, a highly unrealistic target value (Condition 3) is disadvantageous in that it results in a lower geometric well-being than either the realistic target value (Condition 1) or the mildly unrealistic target value (Condition 2). However, contrary to what we would expect, a mildly unrealistic target value (Condition 2) is not disadvantageous compared to the realistic target value (Condition 1): The trend, although not statistically significant, is that our chosen mildly unrealistic target value results in a higher mean well-being than a realistic target value and so may be advantageous, as measured by these metrics. This can be viewed as an advantage of a more cautious decision-making strategy for the management of the integument variables: For the same value of integument, the motivation to groom is higher. Even if the advantage of Condition 2 does not hold true in further experiments, our results indicate a nonlinear response of the well-being metrics to the changing perception of the target value.

Physiological Balance/Variance of the Physiological Variables

We calculated the “physiological balance” as the variance of the four physiological variables at each “point in time” (i.e., the variance of the four values at each sampling time rather than for the entire series of values for each individual variable). Intuitively, this gives a measure of whether, at that point in time, the robot has managed the physiological variables evenly (the four variables have similar values, so the balance [their variance] is low) or whether the robot has kept some variables high while allowing others to fall (the four variables have a wide range of values, so the balance [their variance] is high). A high value can be thought of as a “poorly balanced” management of the four physiological variables, although in some scenarios, it may be advantageous, for example, it might be a good strategy for the robot to increase the value of one variable when resources are abundant if it is likely that the relevant resource will be scarce in the future.

Applying this metric to our experimental data, we calculated the physiological balance in a three-step process. First, in each run in each condition, we calculated the physiological balance at each “time step” (each point in time at which data were collected). Second, we calculated the mean physiological balance over the lifetime of the robot in each run (20 runs per condition, 60 in total; these values are shown in Figure 6). Finally, we calculated the overall mean for each condition as the mean of the 20 “lifetime means” (1 per run) from the previous step. These values are shown in Table 2 (fourth column).

There was a statistically significant difference between conditions (ANOVA, p < 1 × 10⁻⁶), with Tukey HSD post hoc analysis showing that Condition 3 (highly unrealistic target values) differed from the other two conditions (p < 0.001), although there was no statistically significant difference between Conditions 1 and 2.

In summary, as with the well-being metric, a highly unrealistic target value is disadvantageous in terms of physiological balance. However, the chosen mildly unrealistic target value (Condition 2) is not statistically different from the realistic target value (Condition 1) for this metric.

Maintenance of Variables Away From Dangerous Values

To evaluate how well our robots kept their physiological variables from falling to dangerous values (near to zero, the critical limit of the variables), we calculated the percentage of the robots’ lifetime during which any variable was = 0, ≤ 100, ≤ 200, ≤ 300. These percentages are shown in Figure 7, and the specific values for a variable = 0 in Table 2 (last column). Here lower values (smaller percentages of time) are better, since they indicate less time spent with a variable in the “danger zone” close to the critical limit.⁷

In summary, as with the well-being metrics, a highly unrealistic target value is disadvantageous in terms of maintaining the physiological variables above the dangerous values. However, contrary to what we would expect, the mildly unrealistic target value is not disadvantageous compared to the realistic target value condition: Given our results, it may be advantageous compared to the realistic target value, in that the physiological variables were better maintained away from the low values.

Maintenance of Integument

Focusing more closely on the maintenance of the integument variables, we calculated the percentage of the robots’ lifetime during which either of the two integument variables were higher than the other two physiological variables (“best maintained”) or lower than the other two physiological variables (“worst maintained”). These are shown in Figures 8 and 9. Note that since we have two integuments, one side may be the best maintained, while at the same time the other side is the worst maintained.

Figure 8, showing the percentage time as the largest physiological variable, shows a trend toward better management of at least one integument. However, this should be considered in the context of Figure 9, where there is not a clear trend as to the worst managed variable. Looking at the evolution of the physiological variables in Condition 3, the robot would often concentrate on grooming one side, at the expense of the other, and the maintenance of integument metrics reflects this fact.

In our robot model, this concentration on grooming one side is connected with the perception of the salience of the grooming post. In our implementation, when grooming is happening, due to the position of the grooming post on one side of the robot, the post cannot be perceived by the IR sensors on the other side of the robot, and therefore the post does not provide an incentive stimulus for the motivation to maintain the integument on the other side of the robot. When the robot has a more realistic (lower) target integument, the action of grooming one side is more likely to be interrupted, providing more opportunities to switch to the other side.

Balance of Behaviors

To evaluate how the robot divided its time among behaviors, we used the internally logged data to calculate the amount of its lifetime spent in grooming and eating, combined over all robots in each condition, shown in Table 2 (fifth and sixth columns). For its remaining lifetime, the robot was searching for a resource (this does not account for all the time spent searching, since occasionally the robot would pass over an energy resource and would eat opportunistically without stopping its search).

As we can see from Table 2, the percentage of time spent grooming increases with the increased perceived ideal value of the integument in Conditions 1–3. The percentage of time eating decreases as the target integument increases, but not as much as the grooming increases, and there is only a small decrease between Conditions 1 and 2. This indicates that the robots with mildly unrealistic target values are spending less time searching and more time executing consummatory behaviors. This may be an indication that there is some adaptive value in a mildly unrealistic target.

Balance of Motivations

Since we are considering OC-spectrum disorders, we wanted to check if our robot had anything analogous to obsessions. To evaluate the robots’ “concerns,” we calculated the percentage of the robots’ lifetime during which the motivation with the highest intensity was either to feed, avoid, or groom. We additionally calculated the corresponding percentages of time during which the robot was wandering around in search of either an energy resource or a grooming post. The results are shown in Table 3.

These figures indicate that all robots spent the majority of their lifetime motivated to groom (i.e., attending to either of the two integuments, either by active grooming or by searching for a grooming post) and the smallest part of their lifetime motivated to avoid objects (since in general the robots did not experience much damage from collisions). As expected, as the perceived integument target value became more unrealistic through the three conditions, the amount of time when the highest motivation was to groom increased, and the amount of time when the other motivations were highest decreased. However, the change was not smooth across the conditions, with a larger change in motivations to feed and to groom occurring from Condition 2 to Condition 3. Although this result is preliminary, it suggests a nonlinear response of the internal motivations (“concerns”) to the different perceived ideal values in the different conditions.

Possible Advantages of an Unattainable Target

While the highly unrealistic target values (Condition 3) led to almost inevitable death, examining Condition 2 indicates that a mildly unrealistic target value may confer an advantage to our robot. We can see this in several of our results, listed below. With this positive perspective on the unachievable targets, we could characterize them as “idealistic” rather than “unrealistic.”

First, an advantage of mildly unrealistic target values can be seen in the increased arithmetic and geometric well-beings for Condition 2 compared to Condition 1 (Table 2, second and third columns), indicating better overall “health.”

Second, if we look at the percentage of lifetime during which our robots had zero (worse maintained) integument (Table 2, last column), we see that in Condition 2, the percentage is smaller than for Condition 1. In a situation where maintaining integument aids survival (as is typically the case in animals), this smaller amount of time where the value of an integument was zero represents an advantage. We see the same advantage (reduced times for Condition 2) in considering the percentage of time that any of the physiological variables were below particular values (Figure 7). The high values for Condition 3 reflect that the robot would typically neglect one integument while focusing on the other. However, we are cautious about drawing conclusions from this difference in Condition 3, since it may be the shorter lifetimes in Condition 3 that make the percentage of lifetime larger.

Third, we can look at the balance between the time spent grooming and the time spent feeding (Table 2, fifth and sixth columns). Comparing Condition 2 to Condition 1, the percentage of time spent grooming increases by a moderate amount (from 34.5 to 39.4) as expected, but while the time spent feeding does decrease, it does so by only a small amount (from 21.3 to 20.6). This can be viewed as due to increased persistence of the consummatory grooming behavior making more use of the resource when it is available. Rather than the time eating, it is principally the time spent searching that is reduced by the increased grooming.

Fourth, the relatively small penalty that we have observed for increasing the target value in Condition 2 is also apparent in the small increase in variance of the essential variables (Table 2, fourth column, and Figure 6), indicating that the physiological balance is minimally affected.

It should be noted that none of these differences between Conditions 1 and 2 was found to be statistically significant, which is not unexpected, since the value of 1,100 was not chosen for the purposes of testing an improved performance in the robot compared to Condition 1 (there might be some target value either above or below 1,100 where the improved performance is more marked). However, these different lines of evidence all point to advantages of a target value greater than 1,000. This question of advantages of a mildly unrealistic value is, therefore, a hypothesis for future research. It may be the case that the optimal value is somewhere between 1,000 and 1,100, the exact value depending on the metric chosen and the environment, as well as other variables. Such potential advantages of mildly unrealistic target values also contribute to the debate about possible evolutionary origins of OCD (Glass, 2012).

Computed Threshold for Unstoppable Grooming

Finally, mathematical analysis of the algorithm used to compute the intensity of the robot’s motivations allows us to calculate a theoretical threshold for the perceived target integument value, above which grooming would become unstoppable: a perceived target integument value that results in a grooming behavior that will not be stopped by the motivation to feed. The calculation of this limit will be useful in future work when choosing the values of internal parameters. The value is calculated as follows.

First, we need to deduce what the intensity of the motivation to groom is when the grooming behavior continues indefinitely. To do this, let us consider a situation with perfect integument (1,000). In this situation, taking Equation 1, in Condition 1 the motivation to groom is zero, in Condition 2 it ranges from 100 to 600 (depending on the size of the cue), and in Condition 3 it can range from 200 to 1,200. In this calculation, in which we are considering the general case of an arbitrary target value, our experimental data justify the use of the maximum value for the cue to groom. Examining our data, we see that, on the occasions when integument reaches its maximum value, the maximum values for motivational intensity are common; hence the cue in Equation 1 must also be at its maximum value.

In considering the competition between the motivations to groom and to feed while grooming is ongoing, we will assume that there is no energy resource detected (this assumption is realistic in our environment due to the separation of the resources and the short range of the robot’s sensors). Therefore, by Equation 1, the intensity of the motivation to feed is equal to the energy deficit and thus reaches a maximum value of 1,000. Hence we seek the target value T for integument that would give a motivational intensity greater than 1,000 for a maximum cue (100) and perfect integument (1,000). Substituting from Equation 1,

Solving for T with our choice of α = 0.05, we get a minimum value of T = 1,166.7, and for target integument values above this, our robot will be very unlikely to stop grooming once started. This is in agreement with our experimental results, where in Condition 3 our perceived target value (1,200) is greater than T and the robot was highly likely to die from lack of energy while grooming.

Larger values of α would result in values of T closer to 1,000; therefore, from this calculation, we can predict that smaller errors in the perceived target value would result in pathological behavior.

Face Validity

Face validity refers to the descriptive similarity (van der Staay et al., 2009) or “phenomenological” similarity (Willner, 1986) between the robot model and specific features of the phenomenon that is being modeled, in this case, OC-spectrum disorders. This similarity would concern, for example, a specific symptom or a behavioral dysfunction observed in both the patient and the robot model and is not related to the experiential quality that the term phenomenological has in philosophy (in the phenomenological tradition). Therefore the robot behavior should resemble the OC-spectrum disorders being modeled by showing features of the disorders and not showing features that are not seen in the disorders.

Our results show that we achieved high face validity within the scope of our model, focused on compulsions and obsessions: The self-grooming behavior was executed for long periods in Conditions 2 and 3 and the behavior itself is related to OC-spectrum conditions TTM and PSP. The continuation of the grooming behavior beyond the point where the Condition 1 robot would have stopped can be viewed as perfectionism—a characteristic of several OC-spectrum and related disorders (OCD, TTD, body dysmorphic disorder, OCPD) (Fineberg et al., 2015; Fineberg, Sharma, Sivakumaran, Sahakian, & Chamberlain, 2007; Pélissier & O’Connor, 2004). Hence, our work provides experimental support for the theoretical claims about Pitman’s model being able to generate persistent repetitive behavior—that is, that Pitman’s model can generate behavior with face validity.

Our model also shows face validity with respect to the sense of “incompleteness”—an inner sense of imperfection or the perception that actions or motivations have been incompletely achieved (Hellriegel, Barber, Wikramanayake, Fineberg, & Mandy, 2016; Pitman, 1987; Summerfeldt, 2004; Wahl, Salkovskis, & Cotter, 2008)—which is widely viewed as a key aspect of OCD and can be linked with our persistent internally sensed error. In our motivation-based architecture, the motivational systems are goal-oriented embodied sensorimotor loops, and in the pathological case, the perceived need is never satiated, even if an outside observer would say that the goal—grooming to improve integument—has been achieved. In other words, in the pathological case, goal-oriented behavior is never complete because the perceived need is never satiated, and therefore the corrective behavior continues even if the error of the physiological variable has actually been corrected.

In addition, considering the results from our experiments regarding maintenance of integument, the concentration of the robot on grooming one side, even to the neglect of the other side, bears a potential phenomenological similarity with PSP, in which, in some cases, a person may concentrate his or her skin picking in one place, causing skin lesions.

Our model does not yet include other characteristics of OCD, such as additional nonfunctional ritual behaviors (Amitai et al., 2017; Eilam, Zor, Fineberg, & Hermesh, 2012) or indecision aspects (Sachdev & Malhi, 2005) that can occur in OCD and TTM. At its present level of development, our model lacks some key mechanisms hypothesized to be behind such nonfunctional ritual behaviors. For example, our robot has no learning capability, and therefore if the development of nonfunctional rituals is, as some theorize (Eilam, 2017), due to a disrupted behavior learning process, there is no opportunity for the robot to develop such learned rituals. Similarly, indecision is theorized as resulting from an inability to choose between strong competing goals (Pitman, 1987). However, our current model has limited capacity for such conflict, because in the experimental setup presented here, only one resource (and hence only one cue for action) would be detectable by the robot’s short-range sensors, so such competition would be unlikely.

Adding further complexity would allow us to produce such nonfunctional ritual behaviors using different mechanisms, such as those mentioned, and to compare experimentally these different hypotheses.

In summary, although our robot’s behavior does not exactly match an OC-spectrum condition, it exhibits those aspects that we would expect, given the scope and complexity of our model. A simple model like ours also allows for an incremental investigation of the behavior, in which different aspects of the condition are the result of specific additions to the model.

Construct Validity

Construct validity indicates the degree of similarity between the underlying mechanisms of the model and of the condition (Epstein, Preston, Stewart, & Shaham, 2006). In the context of animal models, Joel (2006) specified that the underlying mechanisms for construct validity may be either physiological or psychological. According to van der Staay et al. (2009), construct validity reflects the “soundness of the theoretical rationale.” In our robot model, we do not directly model psychological constructs, and we see them as being more related to face validity (e.g., the sense of incompleteness discussed in the previous section).

When talking about underlying mechanisms, animal models have tended to focus on specific elements, such as the involvement of specific brain areas, receptors, chemicals, or genes (Camilla d’Angelo et al., 2014, Table 1). Construct validity in this case is then based on finding specific mechanisms underlying a phenomenon (e.g., symptoms) in the animal model and the human condition. Such a view of construct validity might be critically questioned by approaches that emphasize species-specific features and differences, such as models grounded in ethology.

Such a view of construct validity also implies that the idea of robot models having construct validity might be problematic and questioned on various grounds, for example, the fact that robots and biological systems are made of different matter or that the models and algorithms implemented in robots are simplifications of biological constructs. However, what critics consider as weaknesses of these models can also be considered as strengths. The fact that robot models are simplifications allows us to capture key selected structural, functional, or dynamic elements for a focused, rigorous investigation. The adoption of a cybernetics perspective that focuses on interaction dynamics, processes, and general principles also means that we can model aspects of underlying physiological mechanisms relevant to OCD that are more general than the specific types of underlying mechanisms that animal models have focused on; for example, we can implement processes that model effects on perception that may be hypothesized to involve specific chemicals, without having to model the specific chemicals themselves. In addition, in robot models, mechanisms underlying a phenomenon can be modeled at different levels of granularity from different theoretical perspectives. These complementary constructs, models, and levels could be experimentally tested and compared, bridging gaps across levels and conceptual perspectives, which is a crucial issue in cross-disciplinary and translational research.

From a conceptual perspective, construct validity for our robot model would be linked to the construct validity of the cybernetic and signal attenuation models of OCD, since the underlying mechanisms that we use to model OCD are closely related to the mechanism they postulate. In all of the three models (the robot model and the two conceptual models), the emphasis is on the dynamics of interaction among the elements of a regulatory system rather than attempting to locate the problem in and modeling specific brain areas or specific genes. All these models share the use of cybernetics notions and conceive of OCD as a disorder in the decision-making process, in particular, the presence of a high error signal that cannot be eliminated by behavioral output. One of the causes that Pitman proposes for this persistent high error signal is an intrinsic comparator defect, and our pathological case is generated by a fault in the robot’s comparator system that gives rise to an error signal that cannot be eliminated through the robot’s behavior. In terms of the signal attenuation model, the robot’s behavior does not result in feedback as to the success of the behavior since the error signal remains high, so the behavior continues.

Whereas the signal attenuation model has received more attention and has provided more examples of construct validity, we have found little direct investigation of Pitman’s model as it applies to humans with OC-spectrum disorders; it thus remains largely theoretical. At this early stage of our research, we can therefore only claim limited and indirect construct validity for our robot model.

Robot models that we have used in previous work, based on similar motivational architectures, have included elements that could allow us to link to anxiety, perception of harm, or an excessive reliance on habits (as opposed to instrumental acts), all of which have been the basis of conceptual models of OCD. This could potentially allow us to expand the construct validity of our model in relation to other theoretical models.

Reliability

An animal or robot model is said to be reliable if the experimental outputs are reproducible (in the sense that the exact experiments can be reproduced, possibly by different experimenters, producing the same results) and extended replications can be run (e.g., conceptual replications, in which the same underlying concepts can be tested in different ways).

As a robot model with an explicitly programmed controller and a highly controlled environment, we would expect the reliability of our model to be high (highly reproducible) compared to animal models. Indeed, with relatively few runs, we obtained statistically significant results.

Predictive Validity

Predictive validity indicates that the behavior of the robot model can be used to make reliable predictions about the condition being modeled. A particularly important aspect of this is that the model can be used to make predictions about outcomes in the human condition and which interventions will, or will not, work with some degree of accuracy.

This aspect of predictive validity, highly important for clinical research purposes, is currently lacking in our model. In our experiments, we did not investigate any “treatments,” and at this early stage in the development of the model, we could expect only limited predictive validity. However, this is an important point to be developed in future work, so that our experiments can inform future clinical research.