Contributed by: Rachel Wood, Universita' Degli Studi Di Parma

Development can be characterised by concepts of regularity, order and stage-wise increase in complexity. Single cells multiply and differentiate to form structures and tissues; a body is formed and begins to act in order to sustain itself. Young animals and human infants reliably develop the physical behavioural and morphological characteristics of their species despite variation both within and without the developing system. Physical and functional features shaped over generations by evolution are faithfully reconstructed in the ontogeny of individuals. The overwhelming regularity of developmental outcome often obscures the messy variation of developmental input.

Introduction
The orderly unfolding of a species-typical ontogeny looks very much like the execution of a plan, a blueprint for the construction of an individual. At first sight, genes are the most likely source of such order, with genetic material as the medium of transmission for developmental information. The majority of developmental theorists refer to notions of interaction between genes and environment in determining developmental outcomes. Even so, the (albeit tacit) idea of a genetic program driving ontogenetic adaptation is central to many approaches. A closer examination of the genetic program concept reveals an infinite regress at its heart. If the full complexity of adult form and function is stored in the genes, then how is this information encoded? What is the mechanism that reads off the specification of an ontogenetic trajectory and how this is translation from DNA to organism controlled? At each step in this regress another mechanism or set of instructions must be proposed and the really hard questions remain unanswered.

Taking a more basic, bottom-up perspective reveals the appearance of invariant order and statistical regularity in developmental process to be deceptive. Developing individuals display considerable variation in their skill acquisition trajectories and, there is an ad hoc quality to the process which leads each agent to mature form and function. The dynamical account of development is one that seeks to account for the noisy variability of individual ontogenetic trajectories and by extension, the concept of a genetic program controlling the acquisition of mature form and function is rejected in favour of a deeper interactive perspective. By this view, multiple processes operating at multiple time scales coalesce to shape species-typical trajectories.

There are two major aspects to the dynamical approach: concepts of interaction and the role of time. Interaction here, refers to more than the notion of some interplay between internal and external factors (i.e. genes and environment). From a dynamical perspective, the question of inside/outside is ill formed, development is better characterised by a notion of reciprocal interplay between multiple factors acting on and in the system in question. Thus, dynamical theory moves away from the notion of development as the unfolding of a genetic program, rather, development proceeds directly from the interaction of heterogeneous subsystems. By extension, in a dynamic account time operates at multiple scales: evolutionary, ontogenetic and down to the scale of individual learning events. Thus a dynamic perspective emphasises timing over order and invokes the notion of structures in time where by temporal organisations come together and dissipate through the interaction of multiple causes.

The application of dynamical analysis to developmental phenomena is well demonstrated by work on motor learning in human infants. Normally developing infants learn track objects visually and then to reach for them; they learn to crawl and then to walk. The age at which an infant will perform any one of these acts can be predicted with some accuracy. Yet, individuals vary considerably in the way in which they acquire even these most basic, species typical behaviours. For example, the majority of infants begin reaching for objects at around 5 months old and by 8 months can reach reliably and accurately. However, their reaching trajectories at the beginning of this phase cover the range from uncontrolled flailing movements to underpowered motions which fail to bring the hand within range of the target. Over time, these very different actions are progressively refined to produce accurate, energetically efficient reaches (Thelen et al 2001). However, it is clear that these very different behaviour styles cannot be rectified by the action of a unitary mechanism. In one case the energetic component of the arm movement must be damped down, in the other it must be boosted. An explanation that can fully account for the interaction of bio-mechanical, neural and maturational factors in motor development is required.

The dynamical systems approach to developmental process
Thelen and Smith (1994) challenge cognitivist and maturational explanations of motor development with an account based on dynamical analysis of movement parameters. Maturational theories of motor development explain the disappearance of reflexive motor behaviour and the acquisition of purposive voluntary action through myelination and differentiation of cortex. On this view, relatively simple subcortical circuits control the behaviour of very young infants. Increasing cortical maturation brings inhibition of stereotyped subcortical output and increasing cortical control of neuromuscular systems (ibid). In a broadly cognitivist account, Zelazo proposes that infants have a native capacity for generating mental representations and that these constructs direct neuromotor development. The transition from reflexive to purposive action is thus mediated by maturation driven change in information processing capacity.

Thelen and Smith argue Zelazo's proposal that changes in cognitive capacity (specifically processing speed) drive motor development, amounts to a form of back door genetic nativism. The invocation of a native capacity for generating cognitive structures which then drive neuromotor development begs the question of how such structures are specified in genetic material. By contrast, the dynamical approach to motor development is primarily a process driven account. Thus, motor learning is not best understood in terms of a series of prescribed, invariant stage transitions (e.g. crawling to standing to walking) but rather should be seen as the net result of a confluence of neural, anatomical and experiential processes. Thus, there is no unitary driver or primary cause for motor development, rather, it is seen to be a self-organising process operating under constraints.

Thelen and Smith's analysis of infant motor learning provide persuasive evidence for the value of this approach. Thelen and colleagues observed that supine infants make alternating kicking movements and that these movements become a stepping pattern when the infant is held upright on a treadmill which is maintained throughout the first year of life. This behaviour is also affected by body size and arousal so that slimmer babies step more than heavier infants and excited infants step more than sleepy ones (Adolphe, 2002). In a further study Thelen et al. manipulated the leg mass of infants aged between two and six weeks. Infants stepped less and with weaker flexion of the knee joint when their legs were weighted and when limb mass was reduced by submerging the legs in water an increase in stepping was observed (1984). Thelen et al. conclude that postnatal growth, which occurs very rapidly in the first three months, is the factor which causes the stepping reflex to disappear. Thus, stepping is limited by muscle strength which fails to keep up with weight gain in this period (ibid) of very rapid growth.

Dynamical systems tools for modelling
Perseverative reaching in infants is still the subject of much debate despite being extensively researched for approximately 50 years. Perseverative reaching refers to an unexpected behaviour of infants faced with a manual search task involving the retrieval of a toy hidden in one of two containers (Piaget’s ‘A not B’ error task [1952, 1980]). In the canonical version of the task, when the toy is swapped from location A to location B infants of approximately 7-12 months persist in reaching to location A to retrieve it. A great many explanations have been advanced to account for this finding, the majority based around the notion that A not B errors represent a failure in the infant’s knowledge about events in the world. However, from a dynamical perspective the error is caused not by what the infant knows but what it does, thus the manual search data can be integrated with other findings in locomotor development (Thelen et al., 2001).

The dynamic field model of the A not B error was constructed to test the formal dynamic systems account of infant perseverative reaching proposed by Thelen et al (ibid). In the model, movement parameters such as amplitude, spatial direction and velocity are represented as activation fields; thus, movement can be represented by the assignment of values to parameters. The specification of a movement corresponds to a particular pattern of activation in the field representing a movement parameter. The decision to reach one way or the other is determined by three inputs to the decision field, these inputs (task parameters, parameters of the cueing event and memory for previous reaches) are, like movement parameters, assumed to be continuous and can thus be specified as locations in the space. Thelen et al found that with this model they were able to simulate results obtained in A not B experiments with infants including context, age and delay effects. The model suggests that competition between the history of the system (i.e. body-coded memory for previous reaches) and current perceptual specification as responsible for the perseverative reaching and the A not B error.

Dynamical approaches in adaptive systems research
The development of form and function is clearly also an area of major interest for researchers working with artificial systems. Natural development comprises mechanisms of on-line adaptation that provide agents with bodies and behaviour, which are closely fitted to an ecological niche. Such on-line adaptation is an important goal for researchers seeking to construct intelligent systems and a central research question for experimenters using artificial developmental systems as test-beds for theories of natural ontogenetic adaptation.

The dynamic neural field approach has been used in cognitive robotics to model action understanding and decision making in collaborative problem solving tasks. Effective joint action requires each agent to interpret the movements of others in terms of a mutual goal and to formulate an apposite response. Erlhagen & Bicho (2006) describe an architecture for robot collaborative action based on the framework of coupled dynamic neural fields. Here, dynamic fields are used to represent the functionality of neural populations in particular brain regions. The dynamics of individual fields evolve under the influence of external visual input and their interaction specifies decision variables for specification for a motor action sequence. Erlhagen and Bicho tested this architecture in experiments with robots performing joint search and action interpretation task. In the search task, the robot was required to select and move an appropriate object based on the activity of its partner. In the action interpretation paradigm a robot was required to selectively reproduce one of two grasping actions demonstrated by a human model. Erlhagen and Bicho obtain effective performance of both types of task with the dynamical neural fields architecture and their findings attest to the value of the approach as a design tool for building neuro-plausible control architectures for autonomous systems.

Dynamical approaches have also been used to model interactive learning in humanoid robots Tani et al (in press). Here, a continuous time, recurrent neural network control architecture (CTRNN) is used to implement the acquisition of object manipulation skills with the aid of a human tutor. Time plays an explicit role in the internal dynamics of CTRNN controllers as each node in the network uses an individual time constant to determine the temporal scale at which it integrates of inputs. This mechanism gives CTRNNs the capacity to respond to event ocurring at heterogeneous temporal scales. In the experiments described by Tani et al. The robot learns through repeated modification of its motor behaviour which is physically guided by a human tutor until the right action is performed. Tani et al. describe a co-developmental mechanism operating between tutor and robot in which the tutor learns the affordances and customary movement patterns of the robot and patterns are in turn, progressively shaped through interaction until the task is mastered (ibid). Tani et al discuss the necessity for tutors to adapt their approach to the intrinsic movement preferences of the robot learner. On this view, movement patterns which share structure with patterns already acquired are more easily learned than completely novel actions. Thus, robot and tutor co-develop a mutual pattern of respectively acting and shaping so that as the robots repertoire of movement patterns is increased so is the range of shaping actions available to the tutor.

The dynamical approach to human motor learning has demonstrated the interaction between morphology and behaviour in ontogenetic adaptation. Infant motor activity is fundamentally constrained by attributes such as the length and weigh of limbs. Experiments with robots have further explored these issues and demonstrated the effects of freezing and freeing morphological degrees of freedom (DOF) on motor learning. Lungarella and Berthouze (2003) explore the interaction of multiple plastic mechanisms operating at multiple time scales using a physical robot tasked with learning to pendulate. The robot is suspended from frame by a passive joint, two of the five joints in each of its legs are progressively frozen and the freed and the effects on swinging behaviour observed. In the 2-DOF condition (where both hip and knee joints are free), the observed behaviour is highly variable . Performance is improved and becomes more stable when the knee joint is frozen but the best results are obtained with subsequent release of the frozen DOF (ibid.) Lungarella and Berthouze account for this result in terms of a boot-strapping effect whereby the freezing of DOF allows physical entrainment to intrinsic body dynamics to occur. Thereafter with the freeing of the second DOF a process of neural entrainment takes place (in conjunction with joint synergy) which the control frequency of the lower limb coordinates with the control frequency of the upper limb section. Thus, hip and ankle move in phase and the amplitude of ankle oscillation and the efficacy of the pendulation behaviour as a whole is increased (ibid).

After nearly two decades of research into the dynamics of ontogenetic adaptation there are now many rich possibilities for interaction between researchers working with natural and artificial developmental systems. One of the most promising of these lies in the opportunity for generative modelling approaches in which artificial systems are sued as test-beds for the construction of new dynamical hypotheses to guide future experimentation with natural developmental process. One promising research direction concerns the use of 'minimal' evolutionary robotics modelling techniques to design relatively simple, analytically tractable developmental systems and explore the interaction of adaptive processes operating at geological and ontogenetic temporal scales (Wood and Di Paolo, 2007).

References
Adolph, K. (2002). ‘Babies’ steps make giant strides toward a science of development. Infant Behaviour and Development, 25:86–90.

Erlhagen, W. & Bicho, E. (2006) The dynamic neural field approach to cognitive robotics. Journal of Neural Engineering, 3, R36-R54.

Lungarella, M. and Berthouze, L.(2003) On the interplay between morphological, neural and environmental dynamics: a robotic case study. Adaptive Behaviour, 10 (3-4): 1-18.

Tani, J., Nishimoto, R., Namikawa, J., and Ito, M. (in press) Co-developmental learning between human and humanoid robot using a dynamic neural network model, IEEE Trans. on Systems, Man, and Cybernetics Part B: Cybernetics, Vol. 38, No.1.

Thelen, E., Fisher, D. and Ridley-Johnson, R. (1984) The relationship between physical growth and a newborn reflex. Infant Behavior and Development, 7:479-493.

Thelen, E. and Smith L. (1994) A Dynamical Systems Approach to the Development of Cognition and Action. Bradford Books/ MIT Press

Thelen, E., Schoner, G., Scheier, C. and Smith, L. (2001) The dynamics of embodiment: a field theory of infant perseverative reaching. Behavioural and Brain Sciences, 24:1-86.

Wood, R. and Di Paolo, E. (2007) New models for old questions: Evolutionary robotics and the 'A not B' error. In proc. ECAL 2007.

Zelazo, P. (1998) McGraw and the development of unaided walking. Developmental Review 18: 449-471