It is important for a cognitively developing robot to be able to discover its own capabilities and then use them in a goal directed way. Starting from a set of primitive behaviors (or actions) a robot may have no initial knowledge about when to apply these behaviors, and what kind of effects they create once they are applied. The robot first has to learn the possible effects it can create in the environment using these behaviors.
It should also learn when to apply which behavior to create a specific change in the environment. Discovering the uses of its primitive behaviors, the robot can then utilize them in a goal-directed way, and it can use multiple of these behaviors sequentially or simultaneously to achieve more complex effects. The kind of development proposed needs to link between the perception of the environment before the execution of a primitive behavior and the consequences of applying it.
The concept of "affordances" provide us with a tool to establish this link. Affordances, as offered by J.J.Gibson [1] in his ecological approach to psychology, refer to action possibilities that an environment offers to an animal/agent acting in it. J.J.Gibson argued that what animals perceive are these opportunities in the environment to achieve certain behavioral results. In this study, we implemented an affordance learning scheme on a mobile robot, so that, starting from a set of primitive behaviors, it learns to use them goal-directedly.

In his early studies on visual perception, J.J.Gibson tried to understand how the "meanings" of the environment were specified in perception for certain behaviors. For his purpose, he identified meaningful optical variables in the perceptual data. For example, he conjectured that in the case of a pilot landing a plane, the meaningful variable is the optical center of expansion of the pilot's visual field. This variable is meaningful since it indicates the direction of the glide and helps the pilot adjust the landing behavior.
Based on these studies of meaningful optical variables J.J.Gibson built his own theory of perception and coined the term affordance to refer to the action possibilities that objects offer to an organism, situated in an environment. For instance, a horizontal and rigid surface affords walk-ability, a small object below a certain weight affords throw-ability, etc.. The environment is full of things that have different affordances for the organism acting in it.

E.J.Gibson studied the mechanisms of learning of affordances in child development. She considered learning as a perceptual process and named her theory as "perceptual learning". She claimed that learning is "discovering distinctive features and invariant properties of things and events" [2], "discovering the information that specifies an affordance" [3]. She defined this method as "narrowing down from a vast manifold of (perceptual) information to the minimal, optimal information that specifies the affordance of an event, object, or layout" [3]. E.J.Gibson suggested that babies use exploratory activities, such as mouthing, reaching, shaking to gain this perceptual data, and these activities bring about "information about changes in the world that the action produces" [2]. As development proceeds, exploratory activities become performatory and controlled, executed with a goal.
This role of affordances in human development and learning makes it a useful concept to be also used in robot development and learning.

The concept of affordances is highly related to robotics and influenced studies in this field. The parallelism between the theory of affordances and reactive/behavior-based robotics has already been pointed out [4]. Recently, the relation between the concept of affordances and robotics has started to be explicitly discussed.

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IV. FORMALIZING AFFORDANCES
After J.J.Gibson, there has been a number of studies attempting to clarify the meaning of the term affordances and to formalize it. Turvey [14] proposed a formalization, where he defined affordances as "dispositional properties" in the environment, which combine with properties of the animal interacting with it. Stoffregen criticized Turvey's formalism because it attached affordances to the environment [15]. He defined affordances as properties of the animal-environment system that can be attached neither to the environment nor to the animal. Chemero [16] proposed that "affordances are relations between the abilities of organisms and features of the environment" and can be represented as "Affords-phi(feature, ability)", where phi is the afforded behavior. More...



V. REALIZATION OF THE FORMALISM ON A ROBOT
Similar to E.J.Gibson's account of the role of affordances in human development, the proposed formalism provides a framework where a robot starts its development from unintentional primitive behaviors. The robot can first execute these primitive behaviors randomly, but as the development proceeds, it can discover the changes it can consistently create in the environment, and associate these changes with the behaviors it executed and the situations the behaviors are executed in. This will lead to a stage where the robot can execute these primitive behaviors purposefully, to achieve a goal. The stage of discovering the changes it can create corresponds to forming effect equivalence classes in the formalization. Associating these changes with behaviors, and the necessary situations, corresponds to linking effect equivalence classes with behavior equivalence classes and entity equivalence classes. We present an implementation of this development scheme in the rest of this study. More...





VI. CONCLUSIONS AND FUTURE WORKS
The concept of affordances can be utilized in creating robots that learn and develop through interaction with the environment. In this paper, we presented a formalization of the concept to be used in robot control and learning. We laid out the implications of this formalization, both for the psychological/philosophical discussions around the concept, and for its robotics implementations. We proposed that there are three perspectives to view affordances, and much of the confusion around the concept rises from the interchanging use of these. Building on and extending the previous formalizations of the concept, we proposed that affordances can be represented as a relation between, effect, entity, and behavior equivalence classes. Formalizing affordances not as specific relation instances, but as generic relations between equivalence classes gives them their real power of generalizing to novel situations.


BIBLIOGRAHY
List of references


ACKNOWLEDGMENTS
This work was partially funded by the European Commission under the MACS project (FP6-004381).

M.Cakmak, May 2007