This web page summarizes the article which is published in journal of Adaptive Behavior. For details and discussions, please see the article or an early version of the work.

To afford or not to afford:
A new formalization of affordances towards affordance-based robot control
Erol Şahin, Maya Çakmak, Mehmet R. Doğar, Emre Uğur and Göktürk Üçoluk

I.INTRODUCTION

The affordance concept, from its beginnings, has been a misty one. Despite the existence of a large body of literature on the concept, upon reviewing the literature, one encounters different façades of this term, sometimes contradictory, rather like the description of an elephant by the six blind man in the famous Indian tale. We, as roboticists, are interested in how the concept of affordances can change our views about the control of an autonomous robot and so we set forth to develop an affordance-based robot control architecture. In our quest, we reached an understanding of this elusive concept, such that it can be formalized and used as a base for autonomous robot control. The formalization presented in this paper summarizes our work on this quest which was developed within the MACS project, but included additional aspects of the affordance concept that went beyond the core work.

II. AFFORDANCE CONCEPT

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. To this end, he identified optical variables in the perceptual data that are meaningful. Based on the studies of meaningful optical variables and the Gestaltist conception of the immediate perception of meanings of the things, 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 in an environment. Although one may be inclined to talk about affordances as if they were simply properties of the environment, they are not. J.J. Gibson believed that affordances are directly perceivable (a.k.a. direct perception) by the organism, thus the meaning of the objects in the environment are directly apparent to the agent acting in it. This was different from the contemporary view of the time that the meaning of objects were created internally with further “mental calculation” of the otherwise meaningless perceptual data.

To date, there has been much confusion regarding the concept of affordances. We believe that there are a number of reasons for this confusion: 1- J.J. Gibson’s own understanding of affordances evolved over time. 2- J.J. Gibson’s own ideas on the concept were not finalized during his lifetime, as Jones concludes in [Jones, 2003]. 3- J.J. Gibson’s idea of affordance can be fully understood only in contrast to the background of contemporary ideas on perception, rather than in isolation. 4- J.J. Gibson defined affordances as a concept that relates the perception of an organism to its action, whereas his main research interest laid in the perception aspect. 5- J.J. Gibson’s own discussions on affordances were often blended with his work on visual perception.

Affordance-Related Research on Ecological Psychology

Affordance-Related Research on Cognitive Science
E.J. Gibson defined learning as a perceptual process and named her theory of learning “perceptual learning”. She argued that learning is neither the construction of representations from smaller pieces, nor the association of a response to a stimulus. Instead, she claimed, learning is “discovering distinctive features and invariant properties of things and events” [Gibson, 2000] or “discovering the information that specifies an affordance” [Gibson, 2003].

Studies on affordance, reviewed so far, have not provided any ideas regarding its relation to other higher-level cognitive processes. Neisser, in his “Cognition and Reality” book [Neisser, 1976], tried to place affordances and direct perception into a complete cognitive system model and tried to link them with other cognitive processes such as recognition. According to him, J.J. Gibson was right in stating that the meanings of the environment are directly available, and “information is not processed, but it is directly picked up since it is already there (in the light)”. Invariance attuned detectors are used for this purpose. However, he claimed, the Gibsonian view of affordances of perception is inadequate, since “it says so little about perceiver’s contribution to the perception act”. Instead, he suggests a perceptual system where a cycling activity continuous over time and space occurs. Neisser also tried to integrate both constructive and direct theories of perception. As a result, in [Neisser, 1994], he constructed a three-layered perceptual system, whose first and third layers correspond to direct perception and recognition, respectively.

Affordance-Related Research on Neurophysilogy and Neuropsychology

Affordance-Related Research on Autonomous Robotics
The concept of affordances is highly related to autonomous robot control and it has influenced studies in this field. We believe that, for a proper discussion of the relationship of the affordance concept to robot control, the similarity of the arguments of J.J. Gibson’s theory and reactive/behavior-based robotics should first be noted. The concept of affordances and behavior-based robotics emerged in very similar ways as opposing suggestions to the then dominant paradigms in their fields. They are both constructed based on the critisism of the dominant models and methods which favored modeling and inference. They both defend a direct relationship between agent and its environment, and tight coupling between perception and action. They are both on the side of “picking up only relevant information from the environment”, and perceiving the environment economically.

Some roboticists have already been explicitly using ideas on affordances in designing behavior-based robots. For example, Murphy [Murphy, 1999] suggested that robotic design can benefit from ideas in the theory of affordances such that complex perceptual modeling can be eliminated without loss in capabilities. She studied three case studies and drew attention to the importance of the ecological niche in the design of behaviors. Likewise, Duchon et al. [Duchon et al., 1998] benefited from J.J. Gibson’s ideas on direct perception and optic flow in the design of behaviors and coined the term Ecological Robotics for the practice of applying ecological principles to the design of mobile robots.

The use of affordances within Autonomous Robotics is mostly confined to behavior-based control of the robots, and its use in deliberation remains a rather unexplored area. In Cognitive Science, some cognitive models related affordances only with low-level processes [Norman, 2002], others viewed affordances as a part of a complete cognitive model [Gibson, 2000, Neisser, 1994, MacDorman, 2000]. Similarly, in robotics, some hybrid architectures inherit properties related to affordances only at their reactive layer [Arkin and Balch, 1997, Connell, 1992]. Recently a number of robotic studies focused on the learning of affordances in robots. These studies mainly tackled two major aspects. In one aspect, affordance learning is referred to as the learning of the consequences of a certain action in a given situation [Fitzpatrick et al., 2003, Stoytchev, 2005b, Stoytchev, 2005a]. In the other, studies focus on the learning of the invariant properties of environments that afford a certain behavior [MacDorman, 2000, Cos-Aguilera et al., 2003, Cos-Aguilera et al., 2004]. Studies in this latter group also relate these properties to the consequences of applying a behavior, but these consequences are in terms of the internal values of the agent, rather than changes in the physical environment.

III. PRIOR FORMALIZATION OF AFFORDANCES
One of the earliest attempts to formalize affordances came from Turvey [Turvey, 1992]. In his formalism, Turvey defined an affordance as a disposition. Here, a disposition is a property of a thing that is a potential, a possibility. These potentials become actualized if they combine with their complements. In this formalism, although the actualization of affordances requires an interaction of an agent on the environment to produce a new dynamics, Turvey explicitly attached affordances to the environment that the organism is acting in. A criticism of Turvey’s formalism came from Stoffregen [Stoffregen, 2003]. His view places affordances in the organism-environment system as a whole instead of defining it as a property of the environment: “Affordances are properties of the animal-environment system, that is, that they are emergent properties that do not inhere in either the environment or the animal.” Chemero [Chemero, 2003] also criticized Turvey’s view which placed affordances in the environment regarding them as environmental properties. Partially in agreement with Stoffregen’s proposal, Chemero suggested that: “Affordances are relations between the abilities of organisms and features of the environment.” One of the main differences between the two similar formalisms of Stoffregen and Chemero, which both define affordances at the organism-environment scale, is that while Stoffregen’s definition of affordance does not include the behavior exploiting the affordance, Chemero’s definition does include it.

Steedman’s formalization [Steedman, 2002b] skips the perceptual aspect of affordances (e.g. the invariants of the environment that help the agent perceive the affordances, and the nature of these invariants and the relation of them to the bodily properties of the agent etc.), but instead it focuses on developing a representation where object schemas are defined in relation to the events and actions that they are involved in. For instance, Steedman suggests that a door is linked with the actions of ‘pushing’ and ‘going-through’, and the pre-conditions and consequences of applying these actions to the door. The different actions that are associated with a particular kind of object constitute the Affordance-set of that object schema, and this set can be populated via learning. This makes the formalization also suitable for planning, for which Steedman argues that reactive/forward-chaining planning is the best candidate. Steedman’s formalization is, as far as we know, the first attempt to develop a formalization of affordances that allows logical/computational manipulation and planning.

IV. THREE PERSPECTIVES OF AFFORDANCES

One major axis of discussions on affordances is on where to place them. In some discussions, affordances are placed in the environment as extended properties that are perceivable by the agent, whereas in others, affordances are said to be a properties of the organism-environment system. We believe that the source of the confusion is due to the existence of three – not one! – perspectives to view affordances. We argue that in most discussions, authors, including J.J. Gibson himself, often pose their arguments from different perspectives, neglecting to explicitly mention the perspective that they are using. This has been one of major sources that have made the arguments confusing, and seemingly contradictory at times.

V. AN EXTENDED AFFORDANCE FORMALIZATION

In this section, we develop a formalism to describe our understanding of affordances. Different from the prior formalizations studies that we have reviewed, our motivation in attempting this task stems from our interest in incorporating the affordance concept into autonomous robot control.

First, we use the term, entity, to denote the environmental relata of the affordance instead of features (as used by Chemero) or object (as generally used). Second, the agent’s relata should represent the part of the agent that is generating the interaction with the environment that produced the affordance, we chose the term behavior to denote this. Third, the interaction between the agent and the environment should produce a certain effect. More specifically, a certain behavior applied on a certain entity should produce a certain effect, e.g. a certain perceivable change in the environment, or in the state of the agent. Based on the previous discussions:

The proposed formalization, with its explicit inclusion of effect, can be seen as a deviation from J.J. Gibson’s view at its outset. It is not. In J.J. Gibson’s writings, the issue of effect had always remained implicit. For instance in the definition of the lift-ability affordance, the expected effect of lifted is implicitly present. One question that may be posed is whether this formalism has equated affordance with effect. This is not the case. The formalism uses effect as the index to (entity, behavior) tuples. In this sense, given a desired effect to be achieved, the agent can directly access which (entity, behavior) can be used to that purpose.

An important aspect of affordances, which is also explicitly stated in our definition, is that they are acquired through the interaction of the agent with the entity. Therefore it is essential to consider the acquisition aspect in order to understand the nature of the three components of our formalism. Note that, whether this acquisition is done through learning, evolution or trial-and-error based design is irrelevant for our discussion.

Affordance Equivance Classes

A relation instance contains knowledge obtained from a single experiment and does not have any predictive ability over future experiments, hence not a relation. As the robot explores its environment, it will populate its knowledge database using such relation instances. Such a database can hardly be called affordances. Affordances should be relations with predictive abilities, rather than a set of unconnected relation instances.

VI. DISCUSSIONS ON THE FORMALISM AND ITS IMPLICATIONS TOWARDS ROBOT CONTROL

We believe that the proposed formalism has laid out a good framework over which the concept of affordance can be utilized for autonomous robot control. Below, we will discuss the major aspects of affordances as proposed within the formalism, and the corresponding implications towards robot control:

• Affordances can be viewed from three perspectives, not one; namely, agent, observer and environment. In our formalism, we defined affordance from these perspectives with the hope that these different but related definitions will be of help in clarifying the discussions around the concept. We consider only the agent and observer perspectives to be relevant and provide the environment perspective only as a means to tie the proposed formalism to some philosophical discussions on the concept.

• Affordances (agent and observer perspective) are relations that reside inside the agent. At a first glance, this claim can be seen to go against the common view of affordances in Ecological Psychology which places affordances in the agent-environment system, rather than in the agent or in the environment alone. However, we argue that representing these relationships explicitly inside the agent does not contradict the existence of these relations within the agent-environment system. As discussed in the previous bullet, we are interested in how the relations within the agentenvironment system are viewed from the robot’s perspective. We argue that these agent-environment relations can be internalized by the robot as explicit (though not necessarily symbolic) relations and can enable robots to perceive, learn, and act within their environment using affordances.

• Affordances are acquired relations. The acquisition aspect is an essential property of the formalization, yet the method of acquisition is irrelevant. Here, acquisition is used as an umbrella term to denote different processes that lead to the development of affordances in agents including, but not limited to, evolution, learning and trial-and-error based design.

• The formalism implies that in order to have robots acquire affordances within their environment, first, relation instances that pertain to the interaction of the robot with its environment need to be populated, and then these relation instances should be merged into relations through the formation of equivalence classes. The issues of how relation instances can be generated, and how relation instances can be merged into affordance relations are open problems that beg to be studied.

• Affordances encode “general relations” pertaining to the agent, environment interaction, such as: balls are rollable. Naturally, exceptions to these general relations, such as “the-red-ball-on-my-table is not rollable (since it is glued to the table)” do exist. However, unlike affordance relations, these “specific relations” possess little, if any, predictive help over other cases, such as whether the-blue-ball-on-my-table is rollable or not. The implication for autonomous robot control is the existence of two control systems; an affordance-based one that acquires and uses general relations, and a complementary add-on system that complements the affordance-based system by learning its exceptions.

• Affordances provide a framework for symbol formation. In the proposed formalism, the categorization of raw sensory-motor perceptions into equivalence classes can be considered as a symbol formation process. As also argued in [Sun, 2000], these symbols would be “formed in relation to the experience of agents, through their perceptual/motor apparatuses, in their world and linked to their goals and actions”.

• Affordances provide support for planning. We argue that the proposed formalism creates relations that can also be used as operators for planning. An affordance relation is indexed by its effect and include tuples which store how that particular effect can be achieved. For instance, the <entity> and <behavior> components in the proposed formalism, can be considered to correspond to the pre-condition and action components in the STRIPS representation. A major difference between the STRIPS representation and the affordance representation is the way the operators are indexed.

VII. TOWARDS AFFORDANCE-BASED ROBOT CONTROL

We have conducted a number of experiments with robots to implement and evaluate certain aspects of the proposed formalism. Specifically, we studied on generation of entity, effect and affordance equivalcen classes. Affordance relations are learned from relation-instances as proposed in this document.

VIII. CONCLUSION

The concept of affordances has been both inspirational and misty (which may have contributed positively to its influence over a wide-range of fields). In this paper, we have reviewed the discussions around the concept and explored how the concept can be formalized to be utilized in autonomous robot control. Towards this end, we have taken the view that our thinking should be led towards the point J.J. Gibson indicated, rather than backwards to the end where he left. As a consequence, the proposed formalism extended the Gibsonian notion of affordances in two major aspects. First, although the proposed formalism agrees with the Gibsonian view that affordances are relations within the agentenvironment system, it differs by arguing that these relationships can also be projected onto the agent. Hence, unlike the prior formalizations, the proposed formalism stops short of providing any “perspective-free” definitions for affordances, since it is not considered to be relevant for using the concept in robot control. The philosophical issue of whether an affordance can be defined without reference to any perspectives is possible or not, and how much would such a definition would contribute to the development of a “theory of information pickup” in agents, which constituted J.J. Gibson’s main motivation, will remain as topics towards further discussion.

Second, different from the Gibsonian view, the proposed formalism argues that affordances (for instance, as viewed from the agent perspective) can be internalized and explicitly represented within the agent. The Gibsonian view may reject this extension by arguing that J.J. Gibson had developed the concepts of affordance and direct perception to object the existence of “representations” in the organism. We do not agree with such an argument. In our understanding, J.J. Gibson objected to the view that perception has to create a generic world model, which has been often referred as “representation”, over which the organism infers whether an affordance exists or not. He argued that affordances are directly perceivable, that is, without using a world representation and without making inferences. The proposed formalism represents relations, not world models, within the robot and therefore, we claim that it does not conflict with the J.J. Gibson’s line of thinking.

Extending an already controversial term such as affordance is bound to be subject to criticism. One of the previous commentators of our project warned us of the dangers of being drawn into an already existing hot debate over the term, and suggested that whether a related-sounding but different term, such as “affoodance”, might relieve us from such debates12. This difficult dilemma is expressed in our title which begins with “to afford or not to afford”. We believe that conceiving new terms without properly relating themto already existing terms does more harm than good. Instead, in this paper, we tried to propose properly our formalization and definition of our understanding of the concept and leave the final judgement to the readers.

Finally, we would like to note that the implications of the proposed formalism on the development and implementation of an affordance-based robot control architecture is our current and on-going work in the MACS project. Although we believe that there are many challenges ahead towards this goal, the ideas proposed in this paper will be of help to guide us on this quest.

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