Making embodiment measurable

Tom Quick1 and Kerstin Dautenhahn2

1Department of Computer Science, University College London
Gower Street, London, WC1E 6BT

2Department of Cybernetics, University of Reading
Whiteknights, Reading, UK




  Abstract. Recognising the embodiment of physical systems in their environment impacts hugely on the design of robots, in terms of both challenges and opportunities for the designer. Despite this significance, use of the term 'embodiment' is governed largely by tacit assumptions with regard to its meaning. We present a new and explicit definition of what it means for a system to be embodied. This definition provides a solid and intuitive basis for the quantification of embodiment, offering significant practical benefits for practitioners.  




1   Introduction

What is it that is so special about bodies? Many would agree that there is something special about bodies - that having one bestows particular qualities on the relationship between an agent (or more generally, a 'system'), and its environment [1, 2]. We offer an answer to this question, getting at the heart of what it means to be 'embodied.' We do this by defining a particular relationship that holds between all embodied systems and the environments within which they are embodied. As this relationship is measurable, this provides a basis for quantifying embodiment - for, potentially, establishing the extent of embodiment in any given system, and understanding how to manipulate and maximise embodiment.



2   Interpreting 'embodiment'

Despite the fact that exploiting embodiment offers real opportunities to those who would design and build robots, the term is typically used without being directly defined. A significant initial assumption in almost all cases is that to be 'embodied' is 'to have a physical body.' Explicit consideration of the nature of embodiment tends to be neglected in favour of reflection on the consequences of this assumption - 'from recognising embodiment these consequences follow: _____' (cf. [3],) or 'with this approach we can exploit embodiment: _____' (cf. [4, 5].) It is perhaps not entirely surprising that those whose work deals primarily with robots should be favourably disposed to such a tacit interpretation of 'embodiment.' Conversely, it is interesting to note that considerably greater attention is paid to the term where the embodiment perspective is brought to bear in the context of software, where material considerations are far less applicable [6-8].



3   A matter of degree

'All bodies are embodied - but some bodies are more embodied than others.' The lack of any clear definition of what it is to be embodied makes it hard to deal with such a proposition. It is true that different sorts of robot have different relationships with the world - a Koala, for example, has greater sensory capability than does a Khepera. The nature and extent of embodiment has an impact on the capabilities of a system in its environment [9]. Without a basic definition of embodiment it is very difficult to engage with these issues at a quantitative level. Research that explicitly addresses embodiment by applying high-level interpretive constructs over the consequences of having a physical body can be of little direct use here, and often come with significant theoretical assumptions built in (cf. [6, 7].)



4   Minimal embodiment defined

The significance of 'having a body' is often articulated through appeal to both the dynamics inherent in a physical system's structure, and the way in which those dynamics reflexively relate to the operational environment in which they are observed. Striking examples can be found in [1, 5, 10, 11].

Beer in particular places great emphasis on the role of sensorimotor dynamics and structural coupling in the generation of autonomous behaviour in robotic systems [12]. Structural coupling, in the sense used by Maturana and Varela [13], describes a process that occurs through repeated non-destructive perturbations between a system and its environment, each having an effect on the dynamical trajectory of the other, and this in turn effecting the generation of and responses to subsequent perturbations.

The following definition draws on this perspective, defining embodiment as that which establishes a basis for structural coupling by creating the potential for mutual perturbation between system and environment. Embodiment is, in this sense, not solely a feature of a system in an environment, but is grounded in the relationship between the two.

  A system X is embodied in an environment E if perturbatory channels exist between the two. That is, X is embodied in E if for every time t at which both X and E exist, some subset of E's possible states with respect to X have the capacity to perturb X's state, and some subset of X's possible states with respect to E have the capacity to perturb E's state.  

This definition is minimal - expressing what it is about all physical things that makes them embodied, not ruling anything out on the basis of higher level theoretical considerations (insisting on a necessary role for 'beliefs' or 'intentions,' for example.)

Simply fulfilling this description is not sufficient to generate interesting forms of behaviour. However, the definition also contains variables such as the number of possible states and the scope for their perturbation. These provide a basis for addressing how, through quantitatively different coupling relationships, different forms of behaviour might arise. In the chemotactic bacterium Escherichia coli for example, a successful 'run and tumble' strategy arises through the coupling of the dynamics peculiar to that system, with its environment, across the bacterium's sensory and effector surfaces (see [14] for a more extensive description of the nature of E. coli's embodiment, and a fuller discussion of this definition of embodiment.)



5   Measuring embodiment

The definition of embodiment presented offers the opportunity to explicitly quantify embodiment. It does not specify or impose any particular metric, but by grounding embodiment in a relationship that does in principle permit quantification, the quantification of embodiment is made possible. For example, one might measure embodiment in terms of the total complexity (as defined in [15]) of the dynamical relationship between system and environment over all possible interactions.

Various qualities of both system and environment might contribute to this, all of which may vary over time. In the following sub-sections, we look at two candidates, 'perturbatory bandwidth,' and 'structural variability.'

5.1   Perturbatory bandwidth

We define perturbatory bandwidth in terms of the range of events that the system and its environment can produce that the other is sensitive to (or equally, perturbable by,) and where appropriate, the force with which those events can be produced.

Inanimate objects. Such considerations apply even to inanimate material objects. Climatic and geological forces (environment 'E') impact on the location and morphology of geographical features (system 'X'). The effect that any such force has over time depends on the qualities of E and X. A granite outcrop on the Antarctic tundra will be persistently perturbed by wind. The presence of the material in turn impacts greatly on the flow of those perturbatory air-currents. The rich interplay between between the two can give rise to fantastic, convoluted, sometimes Gigeresque, structures. In a harsher environment, perhaps with a great deal of precipitation and water flow, or where softer materials are involved (clay, or coral, for example) the perturbatory balance is shifted, and our geological feature may be worn down to sand, itself very easily perturbed by wind and often relocated over vast distances by air-currents over relatively short periods of time.

Biological systems. Structural coupling through perturbation plays a significant role in both phylogenesis and ontogenesis. There are a number of examples where phylogenic drift is affected by the perturbatory interplay between different species (each constituting a signficant feature of the other's environment,) producing interdependent selective pressures. This is manifest in sensory and effector development in co-evolutionary species. A rabbit's eyes are located at the sides of it head, maximising its field of view, while a fox's reflect the predatory requirements of the relationship - they are located at the front of the head, and provide good binocular vision. Similarly, the heavily interdependent relationship between the cheetah and the antelope feeds into an effector arms race, with ever-increasing selective pressure to maximise speed.

On an ontogenic time scale, one might compare and contrast a motile bacterium with a multi-cellular organism. In the case of E. coli, limited and minimal sensory and effector surfaces provide a low-bandwidth coupling between organism and environment. E. coli 'notices' only a small range of events, defined by the ligands that bind to its receptor complexes. It has no directional sensitivity, and can produce only relatively minor changes in its environment - altering its location in the environment, and consuming chemoattractants. Consider, by way of contrast, the beaver. This organism has a highly developed sensory system, and through behaviours such as dam-building significantly perturbs its environment, and its own ongoing relationship with that environment.

Robots. Significant features affecting perturbatory bandwidth of robots are based on properties that concern the capacity to perturb and be perturbed, such as degrees of freedom (DoF) in effectors, and the frequency bandwidth of electro-magnetic sensors for example.

5.2   Structural variability

How much scope for structural variation triggered through perturbation is there inherent in system and environment? In a simple homeostatic system like a thermostat, there is little scope for variation in behaviour, even given an appropriate operational environment. Consider, in contrast, the vast and highly plastic state space of the human nervous and immune systems [16, 17].

Inanimate objects. Structural variability is by definition a minimal resource in inanimate objects. Their structure is defined largely by environmental contraints and forces - weathering in the case of geographical features, or the laws of physics, which describe constraints that apply to all physical systems. Even despite these limitations, complex interplay between system and environment can still occur, for example during the growth of snowflakes, or where collections of objects are treated as a unit of analysis, affording a great deal of structural variability with regard to the relationships, spatial or otherwise, which hold between component parts.

Biological systems. The dynamical structure of biological systems affords great scope for variation. A biological system must 'do' enough to maintain its own structure over time (cf. [13]) - providing both the potential for change, and defining a unity, or an identity, within which change can occur. In many cases this potential variability is restrained by the action of homeostatic processes, which in turn engenders a capacity and a disposition to respond to perturbatory forces.

From the perspective taken here, the nervous system is significant as a highly flexible intermediary between sensory and effector surfaces. This quality is apparent even in very simplistic nervous systems. Simple insects with a small number of neurons that trigger limb movement can produce a range of gaits by varying the order in which those neurons fire (cf. [12].) This sort of structural plasticity in effect allows animals to use a single body, or collection of body parts in a range of ways.

If we regard behaviour as observed sensori-motor coordinations, then the greater capacity there is for different relationships between sensory and effector surfaces, then the greater the repertoire of potential behaviours, be they innate, habituated or learnt. A nervous system affords a great deal of such variation, in contrast to, for example, the signal transduction pathways of a chemotactic prokaryotic cell.

Robots. If we are to maximise embodiment, flexible and variable internal structures need to be used. Whilst this is not in itself a major insight, one might use this perspective to rate various possibilites (neural networks compared to a subsumption architectures, for example) in terms of quantifiable features such as the extent to which sensory surfaces can impact on structural dynamics, and the possibility of complex internal dynamics, mediating between sensory and effector surfaces, to arise through ongoing mutual perturbation between robot and environment.

Finally, it is interesting to consider the way in which perturbatory bandwidth and structural variability relate to one another. The significance of each depends on the other to some extent. For example, vast arrays of sensitive sensors and powerful effectors would be pointless in the context of a system with only two possible states. Equally wasteful would be a system with the complexity of the human nervous system equipped only with the sensory and effector surfaces of E. coli.



6   Conclusion

Bodies are special because they create the possibility of a coupling relationship between a system and an operational environment. By focusing on this as the heart of embodiment a number of benefits follow. First, embodiment is made measurable, because the relationship is a quantifiable one. Furthermore, the definition is reasonably neutral with respect to higher-level reasoning about embodiment - there is lots of scope for discussion of exactly how coupling occurs, and what observable phenomena are made possible as a result of coupling, for example, although the definition does promote an underlying dynamical systems model. Second, the notion of embodiment is freed from material constraints - a system can be embodied on the terms of the definition with being blessed under a physical ontology. This formally opens the notion of embodiment to domains such as software, whilst still leaving room for discussion of what, if anything, is special about material embodiment.



The authors would like to thank Chrystopher Nehaniv for his ideas and suggestions. This research was funded by an EPSRC studentship.



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