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Figure 11: The HKB model for coordination dynamics under three different conditions: situated, where the agent receives a sensory input that changes with its motor activity as this produces displacements in the environment; passively-coupled, where the robot receives the exact same sensory stimulation as that of a freely behaving robot (but not caused by its own actions); and decoupled, with no or constant input. receives constant input or none at all (see Figure 11). We assess the importance of sensorimotor-coupling by comparing the robot’s “brain” dynamics under situated and passively-coupled conditions. We can understand these two conditions in analogy with the kittens in Held and Hein’s experiment (1963): the situated robot behaves freely, receiving sensory input as a result of its own movements according to the stated equations. The passively-coupled agent, in contrast, receives sensory signals previously recorded from a situated agent. For this second agent, sensory variations are no longer the result of its own movements. We also compare these two conditions with the dynamics of an isolated HKB system that receives constant input or none at all (see Figure 11).

Figure 11 The HKB model for coordination dynamics under three different conditions: situated, where the agent receives a sensory input that changes with its motor activity as this produces displacements in the environment; passively-coupled, where the robot receives the exact same sensory stimulation as that of a freely behaving robot (but not caused by its own actions); and decoupled, with no or constant input. receives constant input or none at all (see Figure 11). We assess the importance of sensorimotor-coupling by comparing the robot’s “brain” dynamics under situated and passively-coupled conditions. We can understand these two conditions in analogy with the kittens in Held and Hein’s experiment (1963): the situated robot behaves freely, receiving sensory input as a result of its own movements according to the stated equations. The passively-coupled agent, in contrast, receives sensory signals previously recorded from a situated agent. For this second agent, sensory variations are no longer the result of its own movements. We also compare these two conditions with the dynamics of an isolated HKB system that receives constant input or none at all (see Figure 11).

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Figure 1: A map of different schools within embodied approaches to cognitive science. See text for detailed explanation.
Figure 1: A map of different schools within embodied approaches to cognitive science. See text for detailed explanation.
Figure 2: Map of representationalist and anti-representationalist trends among different AN ENN ATI ABS FA BRB GRIODED SAé-4hx8 fA Eh Ae hw inl AAARAa More-over, the enactivist conception of an organism’s world (the lived and experienced environment) is not something that precedes the organism and is therefore prone to be captured or encapsulated by an agent’s cognitive subsystem. It is the very constitution and activity of the agent as a whole that en-acts a world. If anything, representing is an activity that comes much later (and mostly as a social activity) in the development of cognitive skills and adaptive capacities, a form of social symboliza-tion that requires a complex repertoire of cognitive resources to come about and be properly explained (social coordination, communicative intention, creativity, etc.).
Figure 2: Map of representationalist and anti-representationalist trends among different AN ENN ATI ABS FA BRB GRIODED SAé-4hx8 fA Eh Ae hw inl AAARAa More-over, the enactivist conception of an organism’s world (the lived and experienced environment) is not something that precedes the organism and is therefore prone to be captured or encapsulated by an agent’s cognitive subsystem. It is the very constitution and activity of the agent as a whole that en-acts a world. If anything, representing is an activity that comes much later (and mostly as a social activity) in the development of cognitive skills and adaptive capacities, a form of social symboliza-tion that requires a complex repertoire of cognitive resources to come about and be properly explained (social coordination, communicative intention, creativity, etc.).
Figure 3: Agent-environment coupling. The world is partitioned into components describing the dynamics of the environment, the agent and their interaction. The agent’s body is further subdivided into sensory and motor interfaces as well as its “nervous system’.
Figure 3: Agent-environment coupling. The world is partitioned into components describing the dynamics of the environment, the agent and their interaction. The agent’s body is further subdivided into sensory and motor interfaces as well as its “nervous system’.
Table 1: Categorisation of sensorimotor structures with respect to their dependency or environmental and agential factors. Table 1 presents a summary of our categorisation of sensorimotor structures with respect to their dependency on environmental and agential factors.
Table 1: Categorisation of sensorimotor structures with respect to their dependency or environmental and agential factors. Table 1 presents a summary of our categorisation of sensorimotor structures with respect to their dependency on environmental and agential factors.
Figure 4: Minimal agent and its circular (wrap-around) 1-D environment (horizontal axis). The agent possesses a sensor (S) that measures the distance to objects in front of it (narrow ot wide Gaussian shapes), and feeds into a set of hidden neurons (H) of the agent’s neural network. The hidden neurons in turn are recurrently connected to themselves and drive the motor neuron M controlling the agent’s horizontal velocity. where h is the height of the shape, x the position of its peak and +w corresponds to the maxima of the functions derivative, i.e., to the inflection points where its slope is steepest.
Figure 4: Minimal agent and its circular (wrap-around) 1-D environment (horizontal axis). The agent possesses a sensor (S) that measures the distance to objects in front of it (narrow ot wide Gaussian shapes), and feeds into a set of hidden neurons (H) of the agent’s neural network. The hidden neurons in turn are recurrently connected to themselves and drive the motor neuron M controlling the agent’s horizontal velocity. where h is the height of the shape, x the position of its peak and +w corresponds to the maxima of the functions derivative, i.e., to the inflection points where its slope is steepest.
Figure 5: SM environment for approach of narrow and avoidance of wide shapes. Plotted is the sensory activation that results from issuing a motor command that determines agent velocity at a given position. Top row: In the shape of the surfaces one can easily identify the derivative of the Gaussian gradients present in the environment. The amplitude of this derivative varies with agent velocity, reflecting the working of the agent’s sensor, which is proportional to the time-derivative of the sensed distance and therefore dependent on the agent’s speed of movement. Bottom row: actual trajectories (varying from white to black as time progresses) overlaid on a 2d representation of the SM environment.
Figure 5: SM environment for approach of narrow and avoidance of wide shapes. Plotted is the sensory activation that results from issuing a motor command that determines agent velocity at a given position. Top row: In the shape of the surfaces one can easily identify the derivative of the Gaussian gradients present in the environment. The amplitude of this derivative varies with agent velocity, reflecting the working of the agent’s sensor, which is proportional to the time-derivative of the sensed distance and therefore dependent on the agent’s speed of movement. Bottom row: actual trajectories (varying from white to black as time progresses) overlaid on a 2d representation of the SM environment.
Figure 6: Attractor landscape of evolved agent in approach and avoidance conditions. Plotted here is the steady-state motor output as a function of fixed sensory input resulting from a given motor command (velocity) at a given position. Black attractor regions correspond to negative and white regions to positive steady-state velocities (0.6 and -0.2 respectively). Gray areas indicate bi-stable regimes. Actual trajectories are overlaid and colour-coded according to the attractor the agent moves toward at any given time. Arrows indicate approximate tendencies of state change for the different attractor regions. Compare to previous figure of SM environment, which is plotted on the same axes. Figure 6: Attractor landscape of evolved agent in approach and avoidance conditions. the agent’s behaviour. In figure 6 we show the result of carrying out such analysis for our model agent, ie. the qualitative behaviour of the agent for different values of its sensory input. Here, we have determined for each fixed sensor value (which is given by the surface of the SM environment as a function of position and motor command), the steady-state of all the agent’s variables, i.e. the state to which the agent would ultimately converge if given enough time (the attractors). Of these states, we have plotted only the coordinate of the motor command here, as this ultimately drives the agent’s behaviour.
Figure 6: Attractor landscape of evolved agent in approach and avoidance conditions. Plotted here is the steady-state motor output as a function of fixed sensory input resulting from a given motor command (velocity) at a given position. Black attractor regions correspond to negative and white regions to positive steady-state velocities (0.6 and -0.2 respectively). Gray areas indicate bi-stable regimes. Actual trajectories are overlaid and colour-coded according to the attractor the agent moves toward at any given time. Arrows indicate approximate tendencies of state change for the different attractor regions. Compare to previous figure of SM environment, which is plotted on the same axes. Figure 6: Attractor landscape of evolved agent in approach and avoidance conditions. the agent’s behaviour. In figure 6 we show the result of carrying out such analysis for our model agent, ie. the qualitative behaviour of the agent for different values of its sensory input. Here, we have determined for each fixed sensor value (which is given by the surface of the SM environment as a function of position and motor command), the steady-state of all the agent’s variables, i.e. the state to which the agent would ultimately converge if given enough time (the attractors). Of these states, we have plotted only the coordinate of the motor command here, as this ultimately drives the agent’s behaviour.
For a pattern to count as SM coordination the convergence to a (meta-)stable lower dimensional dynamics or its reliability in general is necessary but not sufficient. As illustrated in this case, it is also necessary for this pattern to be functional to the task. In our simple model, the functionality is achieved by establishing a pattern of small oscillations on a particular zone of the object (the right hand side of the narrow peak) using stable oscillations and not establishing any stable pattern when the gradient indicates the presence of the wider peak, using a reliable transient.
For a pattern to count as SM coordination the convergence to a (meta-)stable lower dimensional dynamics or its reliability in general is necessary but not sufficient. As illustrated in this case, it is also necessary for this pattern to be functional to the task. In our simple model, the functionality is achieved by establishing a pattern of small oscillations on a particular zone of the object (the right hand side of the narrow peak) using stable oscillations and not establishing any stable pattern when the gradient indicates the presence of the wider peak, using a reliable transient.
Figure 8 a) Predicting future sensorimotor events by remembering previous sequences. Suppose the agent has experienced the sequence of events ao7ao1.'This sequence has a match at level / = 1. ao? and ao2 are potential successors. b) Prediction by rearranging eSMCs in new combinations. For continuing the prediction of the branch ao/ao1ao2, no match is found in the tree. The oldest events ate successively discarded until a match is found again (ao2). The resulting sequences are ao1ao1ao2a01ao3 and aotaolao2a03ao1. (Source: Maye and Engel 2012b] (Hoffman et al., 2012). It should be noted that in all cases, the parameter of interest (e.g., what the supporting surface was; whether the robot was near or far from a wall) could not (even in principle) be read off directly from any sensor, but rather was implicit in the patterns of sensorimotor interaction. Using this probabilistic model, with appropriate hardwired evaluative functions (e.g. avoid tumbling; avoid bumper contact) the real and simulated robots were easily able to learn these probabilistic environmental and proprioceptive sensorimotor contingencies, and to achieve real-world tasks. and to achieve real-world tasks.
Figure 8 a) Predicting future sensorimotor events by remembering previous sequences. Suppose the agent has experienced the sequence of events ao7ao1.'This sequence has a match at level / = 1. ao? and ao2 are potential successors. b) Prediction by rearranging eSMCs in new combinations. For continuing the prediction of the branch ao/ao1ao2, no match is found in the tree. The oldest events ate successively discarded until a match is found again (ao2). The resulting sequences are ao1ao1ao2a01ao3 and aotaolao2a03ao1. (Source: Maye and Engel 2012b] (Hoffman et al., 2012). It should be noted that in all cases, the parameter of interest (e.g., what the supporting surface was; whether the robot was near or far from a wall) could not (even in principle) be read off directly from any sensor, but rather was implicit in the patterns of sensorimotor interaction. Using this probabilistic model, with appropriate hardwired evaluative functions (e.g. avoid tumbling; avoid bumper contact) the real and simulated robots were easily able to learn these probabilistic environmental and proprioceptive sensorimotor contingencies, and to achieve real-world tasks. and to achieve real-world tasks.
Figure 9: Transfer entropy for two types of controllers. Cells of the matrix correspond to the information transferred from signals in the columns to signals in the rows. Left: for the random controller little information is being transferred overall. Most salient is the dependency between hip angle sensors and corresponding motors. Right: the regularity induced by the bound-right controller, i.e. the “behaving” agent, leads to a more complex pattern of information transfer, now also between different legs. Figure adapted from (Schmidt et al. 2012).
Figure 9: Transfer entropy for two types of controllers. Cells of the matrix correspond to the information transferred from signals in the columns to signals in the rows. Left: for the random controller little information is being transferred overall. Most salient is the dependency between hip angle sensors and corresponding motors. Right: the regularity induced by the bound-right controller, i.e. the “behaving” agent, leads to a more complex pattern of information transfer, now also between different legs. Figure adapted from (Schmidt et al. 2012).
Figure 10: Model of two-degree of freedom arm controlled by two antagonistic muscle pairs shown with their local spinal circuitry. Ia pathways are shown in red, Ib pathways in orange, and Renshaw cells in gray. Agonist related circuitry is drawn with solid lines and antagonists dashed. Por clarity the shoulder circuitry is shown in less detail. Distribution of Ib afferents across joints is hypothesized to be responsible for their coordination, implicitly accounting for internal loads. coordinates (muscle length). An extension of threshold control proposes that the same holds true on higher levels of the motor control hierarchy (Feldman, 2011). If motor commands were (always) expressed in the same coordinates as sensory consequences, then a forward model would not be needed to translate efference copy into sensory coordinates. Movement generation could then be seen equally as motor- or sensory control. What is specified in goal-directed action is the desired sensory consequence of the goal rather than the muscle forces, that is, both actions and perceptions are encoded in the same sensorimotor frame of reference (Feldman, 2008, 2009). This bears some resemblances with Perceptual Control Theory (Powers, 1973) and Common Coding Theory (Prinz, 1997).
Figure 10: Model of two-degree of freedom arm controlled by two antagonistic muscle pairs shown with their local spinal circuitry. Ia pathways are shown in red, Ib pathways in orange, and Renshaw cells in gray. Agonist related circuitry is drawn with solid lines and antagonists dashed. Por clarity the shoulder circuitry is shown in less detail. Distribution of Ib afferents across joints is hypothesized to be responsible for their coordination, implicitly accounting for internal loads. coordinates (muscle length). An extension of threshold control proposes that the same holds true on higher levels of the motor control hierarchy (Feldman, 2011). If motor commands were (always) expressed in the same coordinates as sensory consequences, then a forward model would not be needed to translate efference copy into sensory coordinates. Movement generation could then be seen equally as motor- or sensory control. What is specified in goal-directed action is the desired sensory consequence of the goal rather than the muscle forces, that is, both actions and perceptions are encoded in the same sensorimotor frame of reference (Feldman, 2008, 2009). This bears some resemblances with Perceptual Control Theory (Powers, 1973) and Common Coding Theory (Prinz, 1997).
Figure 12: Signature of the situated HKB model with sensitivity parameter s = 2.5 and the corresponding passively-coupled model. It is represented here as the density distribution The dynamic signature is meant to capture the neurodynamic correlate of gradient-climbing behaviour: i.e. a picture of the patterns of neural change that produce gradient climbing. Note that the neural correlate is not a single state (a specific value of @), this is congruent with the fact that functionally identifiable neural correlates of awareness ate not infinitesimal states but neural! patterns that last around 100ms (Varela 1995). We define the signature as the density distribution over the effective phase space of the neural coordination variable. Figure 12 shows a compatison between the neurodynamic signature of a situated and a corresponding passively decoupled system. It is apparent that the signatures differ significantly, despite the fact that the passively coupled system is receiving the exact same sensory stimulation.
Figure 12: Signature of the situated HKB model with sensitivity parameter s = 2.5 and the corresponding passively-coupled model. It is represented here as the density distribution The dynamic signature is meant to capture the neurodynamic correlate of gradient-climbing behaviour: i.e. a picture of the patterns of neural change that produce gradient climbing. Note that the neural correlate is not a single state (a specific value of @), this is congruent with the fact that functionally identifiable neural correlates of awareness ate not infinitesimal states but neural! patterns that last around 100ms (Varela 1995). We define the signature as the density distribution over the effective phase space of the neural coordination variable. Figure 12 shows a compatison between the neurodynamic signature of a situated and a corresponding passively decoupled system. It is apparent that the signatures differ significantly, despite the fact that the passively coupled system is receiving the exact same sensory stimulation.
Figure 13: A genealogy of the concept of habit. For further details see text.
Figure 13: A genealogy of the concept of habit. For further details see text.
Figure 14. Representation of the dynamical definition of habit. According to this definition (see Figure 14), once a habit is formed, its recurrence is a conditior for its own contin-uation — the habit “calls” for its exercise and its exercise reinforces it: permanence. One way of understanding this circularity is to say that the stability or recurrence o: the behaviour that the habit involves (smoking, reading, jogging) both depends on and reinforce: the mechanisms that give rise to it. Habits therefore imply plasticity. The notion of plasticity involves the capacity of a habit to be shaped or deformed under sensorimotor or neurodynamic “pressure” (meaning perturbations or variations on its stability conditions) and to maintain thi: deformation as its new form. In addition, plasticity is subject to different degrees and tempora scales as we have seen above and may involve different kinds of changes in the different SM ote reitaeaana
Figure 14. Representation of the dynamical definition of habit. According to this definition (see Figure 14), once a habit is formed, its recurrence is a conditior for its own contin-uation — the habit “calls” for its exercise and its exercise reinforces it: permanence. One way of understanding this circularity is to say that the stability or recurrence o: the behaviour that the habit involves (smoking, reading, jogging) both depends on and reinforce: the mechanisms that give rise to it. Habits therefore imply plasticity. The notion of plasticity involves the capacity of a habit to be shaped or deformed under sensorimotor or neurodynamic “pressure” (meaning perturbations or variations on its stability conditions) and to maintain thi: deformation as its new form. In addition, plasticity is subject to different degrees and tempora scales as we have seen above and may involve different kinds of changes in the different SM ote reitaeaana
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