Edward Chace Tolman (1886 – 1959) was an American psychologist. He was most famous for his studies on behavioral psychology.
In my research for the write-up for this post, I found that the introduction to Endo and Arkin's 2000 paper on Implementing Tolman's Sowbug the best.
I've reproduced the introduction here, but the full paper is available in pdf form here.
Implementing Tolman's Schematic Sowbug:
Behavior-Based Robotics in the 1930's
by Yoichiro Endo Ronald C. Arkin – 2000
This paper reintroduces and evaluates the schematic sowbug proposed by Edward C. Tolman, psychologist, in 1939. The schematic sowbug is based on Tolman's purposive behaviorism, and it is believed to be the first prototype in history that actually implemented a behavior-based architecture suitable for robotics. It predates both Brooks' subsumption and Braitenberg's vehicles by approximately a half century. The schematic sowbug navigates the environment based on two types of vectors, orientation and progression, that are computed from the values of sensors perceiving stimuli. Our experiments on both simulation and real robot proved the legitimacy of Tolman's assumptions, and the potential of applying the schematic sowbug model and principles within modern robotics is recognized.
Figure 1: Tolman's Purposive Behaviorism
Tolman's Schematics Sowbug Model Based on his purposive behaviorism, Tolman proposed the concept of the schematic sowbug (Figure 2) in 1939.
Figure 2: Tolman's Schematic Sowbug.
The following are brief descriptions of these features, summarized from Tolman's writings:
Receptor Organ: The Receptor Organ is a set of multiple photo-sensors that perceive light (or any given stimuli) in the environment. These sensors are physically mounted on the front end surface of the sowbug, forming an arc. An individual sensor outputs a value based on the intensity of the stimuli.
Orientation Distribution, Orientation Need, and Orientation Tensions: The Orientation Distribution, shown as a line graph drawn inside the front-half of the sowbug, indicates the output values of the photo-sensors. The height of each node in the graph is the value of the corresponding photo-sensor in the Receptor Organ. For example, if there is a light source (or any given stimulus) on the left-hand side of the sowbug (as shown in Figure 2), the nodes on the left-hand side of the graph become higher than the ones on the right-hand side. The height of the nodes is also determined by a specific Orientation Need (a little column rising up from the stippled area). This stippled area is referred to as the Orientation Tensions. The Orientation Need is a product of the Orientation Tension, where the level of Orientation Tension corresponds to the degree of the motivational demand. For example, if the stimulus is a food object, Orientation Tension is determined by the degree of the sowbug's hunger. Moreover, it is assumed that if the sowbug is facing directly toward the stimulus, the Orientation Need decreases.
Orientation Vector: The vectors pointing at the sides of the sowbug are the Orientation Vectors. The length of the right-hand side vector is the total sum of the left-hand side Orientation Distribution, and the length of the left-hand side vector is the total sum of the right-hand side Orientation Distribution. When an Orientation Vector is generated, the sowbug will rotate toward the direction it is pointing. For example, if there is only a right-hand side vector pointing towards the left, the sowbug will try to rotate in a counter-clockwise direction. If there are two vectors pointing toward each other, the net value (after summation) will be the direction the sowbug will try to rotate. The Orientation Vector will not cause translational movement of the sowbug, only rotational.
Progression Distribution, Hypothesis, and Progression Tensions: The Progression Distribution is also shown as a line graph drawn inside the rear-half of the sowbug.
The shape of the Progression Distribution is proportional to the shape of the Orientation Distribution. However, the height of the Progression Distribution is determined by the strength (or certainty) of a specific Hypothesis. For example, if the sowbug is reacting to a food stimulus, the level of Hypothesis is how much the sowbug believes "this stimulus source is really food." The level of a Hypothesis becomes higher the more the sowbug assumes that the stimulus is indeed food. A Hypothesis is a product of the Progression Tensions and the past experience relative to this speci c stimulus.
Progression Vector: Progression Vectors are located at the rear-end corners, left and right, of the sowbug, pointing toward the front. These vectors represent the velocities of the left-hand side and right-hand side motors of the sowbug, respectively. As for Orientation Vector, the length of the left-hand side Progression
Vector is determined by the right-hand side of Progression Distribution, and the length of the right-hand side Progression Vector is determined by the left-hand side of Progression Distribution. In other words, if there is a stimulus on the left-hand side of the sowbug, it will generate a larger right-hand side vector, and try to move forward while turning to the left, similar to the notion described decades later by Braitenberg. However, if the sowbug sustains negative experiences regarding the stimulus, the hypothesis then becomes weaker, and it will not move towards the stimulus.
The main behavioral characteristic of the schematic sowbug is its positive phototactic behavior. With the combination of the Orientation Vector and Progression Vector, the sowbug is expected to respond to the stimulus in the environment by orienting and moving towards it based on its Orientation Need and Hypothesis. Since both the Orientation Need and Hypothesis are determined by the internal state of the sowbug, which changes as the sowbug increases its experiences with the stimulus,
the trajectory of the sowbug is not consistent for different trials even if the external conditions are setup same.
The word "tropism" in Loeb's "tropism theory" describes how plants and low-level organisms try to turn towards a light source. According to Fleming who translated
Loeb's work, the origin of the word "tropism" comes from a Greek word "trope" for turning. Loeb, a biologist, studied animals' phototactic behavior by trying to figure out how photosensitive substances in animals' bodies undergo chemical alternations by light, and how they would effect the animals' motor behavior [10]. This study let Blum create a model of a phototactic animal by connecting its left-hand side photo-sensors to the right-hand side motor, and right-hand side photo-sensors to the left-hand side motor, and compared it to the statistical results taken from the experiments with cucumber beetles. This again is very similar in spirit to Braitenberg's later descriptions of vehicles exhibiting similar phototactic behaviors. Even though Tolman proposed his system a half-century before Braitenberg did, they were both inspired by Loeb's "tropism theory", and their systems should exhibit similar behaviors. However, Braitenberg's model was implemented with Progression
Vectors only, while Tolman's model has both Orientation and Progression Vectors as Blum's model does.
From a roboticist's point of view, Tolman's schematic sowbug is remarkable because it was the first prototype that actually described a behavior-based robotics
architecture in history, to the best of our knowledge. It was a half-century before Brooks developed the subsumption architecture in the mid-1980's. However, it should be noted that Tolman's schematic sowbug is not a purely reactive architecture. Past training and internal motivational state will also affect the behavior.
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Conclusion:
Tolman's schematic model is the first instance in history, to our knowledge, of a behavior-based model suitable for implementation on a robot. While useful conceptually as a model, it was the goal of this research to test indeed whether or not the model could be implemented on real robots.
The primary features of Tolman's schematic sowbug were successfully implemented in both simulation and on a real robot. The results of the simulation experiment were consistent with Tolman's assumption for the sowbug in which he expected to observe its phototactic behavior; when the stimulus was in the field, the sowbug rotated itself to face the stimulus; and if there was enough belief in the hypothesis, the sowbug moved towards the stimulus. It was also observed that, when the internal state (Hypothesis) of the sowbug is different, the sowbug produces different trajectories even though the external conditions are set up identically. The results from the real robot experiment proved that it is indeed possible to apply Tolman's schematic sowbug in robotics. Future research could expand the model as currently implemented more completely to draw together more closely psychological models of animal behavior and robotic systems.
References:
Tolman, E.C. "Prediction of Vicarious Trial and Error by Means of the Schematic Sowbug." Psychological Review. ed. Langfeld, H.S. Vol. 46, 1939, pp. 318-336.
Tolman, E.C. "Discrimination vs. learning and the schematic sowbug", Psychological Review, Vol. 48, 1941, pp. 367-382.