For each first and second step, we estimated the time delay (i.e., RT1 and RT2) between the step in target position and the subsequent whole-body-movement response (see Figure 3). This was achieved by modeling the closed loop relationship between the target (step sequence) and response (head position) as a low order, zero delay, autoregressive moving average (ARMA) process (for details see: Loram et al., 2012; van de Kamp et al., 2013). Next, the step sequence was reconstructed by sequentially and individually adjusting the instant of each step. This procedure, optimizing the fit of the ARMA model, was done in two consecutive ways; (1) reconstruction of the step sequence using a single equal adjustments of the instant of all steps -in effect determining the time delay of the ARMA model in Figure 3 and (2) reconstruction of the step sequence allowing individual adjustment of the instant of each step (i.e., the optimized ARMA in Figure 3). By optimizing the delay to each step, this “set-point reconstruction” procedure provides a distribution of response delays to first and second steps (see RT1 and RT2 in Figure 3). The statistical analysis of these delays in the second stage enables testing for refractoriness.

To compare the distributions of RT1 and RT2 over ISIs (levels 1 through 7) a two factor (Stimulus Number and ISI) repeated measures ANOVA design is used. To evaluate significant main and interaction effects post-hoc ANOVAs were run. To maximize statistical power, bi-directional, and unidirectional step-pairs were analysed in one group.

The two stages outlined above allow us to test the following null hypotheses:

(i) Distributions of RT1 and RT2 are equal (i.e., a hypothesis of zero refractoriness would predict equal ranges (5–95th percentile) and means in the distributions of RT1 and RT2).

If these hypotheses are rejected, the following tests provide evidence discriminating against continuous control and quantifying the extent of refractoriness in this whole body movement task.

If, in Stage 2, we find evidence of refractoriness which favors the alternative hypothesis that the single channel/IC model does apply to multi segment control of movement, the following tests would reveal its open-loop interval

(v) Repeat the regression method explained in (iv), assuming a least mean squares fit with slope constrained to −1 [i.e., if a response is triggered by the first step a slope of −1 is predicted in the relationship between average RT2 and ISI for ISI < open-loop interval (Pashler et al., 1998; Gawthrop et al., 2011)].

The evidence for refractoriness in this whole body movement task is clear even with a relatively small sample of trials and participants. This evidence of increased delays for RT2 at low ISI is consistent with sustained manual control of an external, second order, single degree of freedom system (van de Kamp et al., 2013). The similarity includes the evidence that the increased delay for RT2 vs. RT1 is reduced at the smallest ISI. The current results demonstrate refractoriness in sustained movement control of the whole body. This result extends the relevance of refractoriness in sustained control beyond manual tracking where it might be argued that control of the hand is more refined and specialized than control of the postural muscles in the legs and trunk. This result also extends the relevance of refractoriness beyond control of a uniaxial joystick the task in our previous work (Loram et al., 2011, 2012; van de Kamp et al., 2013) because this whole body task requires coordinated control of multiple kinematic segments. Our results appear contradictory to the current prevailing hypotheses of optimal feedback control in which feedback proceeds continuously along low level feedback loops in which the goal and strategy are preset. Thus, the interpretation we have made previously (van de Kamp et al., 2013) applies also to this task of moving the whole body to control head position and the reader is referred to that discussion. The key point is that refractoriness is not compatible with a continuous, time invariant and linear process and that because the system is refractory, redundant, time varying with sensory delay and containing many DOFs, a serial process along a single channel is relevant to the control of such a system. The reader will probably not be surprised that human motor control is non-linear. However, the finding of refractoriness, a systematic time variance in which responses show increased delay when they follow a closely preceding response, points to a modular element or process in the human motor control architecture that authors usually neglect.

Does the evidence of refractoriness imply a serial process along a single channel? If RT2 were linearly related to ISI with a gradient of −1, then as clearly articulated by Pashler and Johnston (1998) that would be consistent with a serial process along a single channel in which a second process cannot start until a first process has completed. Within a control system, this idea is represented within an intermittent control paradigm in which feedback cannot be applied until a minimum open loop interval has elapsed (Figure 1) (Gawthrop and Wang, 2009, 2011; Gawthrop et al., 2011; Gawthrop and Gollee, 2012; Loram et al., 2012). The minimum open loop interval, or intermittent interval as it is called, is an implementation of the single channel PRP as expressed by Craik (Vince, 1948) and Pashler (Pashler et al., 1998). Within this event driven intermittent control paradigm (Figures 1, 7), elapse of the minimum open loop interval is one of the two necessary conditions for triggering a feedback informed control trajectory. This ensures that control proceeds serially as a sequence of control actions that are constrained to be ballistic for at least the minimum open loop interval. This serial process along a single channel, and the associated refractoriness, is not represented by state related switching in which a state dependent error signal crosses a threshold. State related triggering is advocated by some authors (Asai et al., 2009; Suzuki et al., 2012) and is represented in the second triggering condition of our intermittent control paradigm (Figure 1).

The purpose of the model simulations in Figure 6 is to show that: (1) a continuous model does not show refractoriness, (2) a gradient of RT2 vs. ISI shallower than −1 is compatible with the single channel hypothesis, and (3) a reduced RT2 at the lowest ISI (i.e., departure from the red line in Figure 5) is compatible with the IC model by using a sampling delay. As illustrated in Figure 6, our model simulations show that the largest ISI at which RT2 is significantly larger than RT1 gives the open loop interval and that that the ISI at which the RT2 is largest shows the sampling delay.

Departure from the linear relationship between RT2 and ISI at small ISI or a gradient of −1 does not invalidate the single channel hypothesis (Figure 6). For this explicitly single channel model (Figures 1, 7), when one events is triggered for each target step, following the minimum open loop interval, the gradient is −1 (Figure 6B). If additional events are subsequently triggered, by an error signal crossing a threshold (e.g., due to increased noise) the slope will be less than −1. Setting the event threshold to zero so events trigger internally at the maximal possible rate will result in a gradient of −0.5 and a range of reaction times equal to the intermittent interval (Figure 6C). If applied noise is high enough, the relationship between RT2 and ISI is not defined by the IC model and the slope is zero (Loram et al., 2012). Supplementing the intermittent control model with low pass filtering of the set-point and a sampling delay (i.e., the delay between the event and the sampling instant cf. Figure 1) leads to RT2 decreasing as ISI decreases resulting in a peak in RT2 at a ISI which is equal to the sampling delay (Figure 6D). This feature reproduces the amplitude transition function (ATF) observed by Barrett and Glencross (1988a,b), in which participants combine their responses to first and second steps stimuli for small ISIs. Depending on parameter settings for noise levels, event thresholds, sampling delays, and low pass filtering; varying relationships between RT2 and ISI can be simulated consistent with the single channel hypothesis. The key evidence supporting a serial process along single channel hypothesis is the evidence of refractoriness. The decrease in RT2 with decreasing ISI at the lowest inter-stimulus-intervals may indicate incomplete convergence to a single channel for those lowest-inter-stimulus intervals (Resulaj et al., 2009).

The existence and nature of the modules in the control architecture is far from settled. For instance, regularity and low-dimensionality in the motor output are often taken as an indication of modularity but could they simply be a by-product of optimization and task constraints? Moreover, what are the relationships between modules at different levels, such as muscle synergies and basic action concepts?

Our data for this whole body tracking task and for the visuo-manual tasks that we have studied (cf. van de Kamp et al., 2013) shows refractoriness compatible with a single channel hypothesis as embodied in our intermittent control model (Figure 1). From psychology, refractoriness of this kind has been demonstrated to be associated with response selection according to a single channel hypothesis (Pashler et al., 1998). Biological systems are characterized by redundancy at multiple levels. Many joint configurations can produce the same end effector location, many actuator/muscle activation patterns produce the same joint torque, many control/neural activation patterns and pathways can produce the same actuator/muscle activation. Our data, combined with the evidence from psychology, leads us to propose that a process of selecting one movement alternative from the many possible occurs within the feedback loop that regulates this head tracking task (cf. Figure 7).

Selection of task in the space of performance variables and translation to elemental variables seems common to many schemes. To aid discussion of this question, we show in Figure 7 two main schemes. In the first scheme (see Figures 7A,B), the redundancy problem is solved outside the main feedback loop within a planner. The planner provides hierarchically and temporally prior settings to the main feedback loop, which is continuous and parallel in nature. We regard this scheme as broadly representing the prevailing idea of biological control discussed by many authors within the continuous optimal feedback paradigm (e.g., Li et al., 2004; Todorov, 2004; Todorov et al., 2005; Lockhart and Ting, 2007; Karniel, 2011, 2013; Pruszynski and Scott, 2012; Safavynia and Ting, 2012). It has been argued that this scheme is, however, un-biological (Cisek, 2005). In the second, alternative, scheme (see Figures 1, 7C,D) we propose a new hypothesis that the redundancy problem is solved within the feedback loop in a refractory response selector. The refractory response planner continuously observes multiple sensory input and multiple possible task-goal choices. The refractory response selector converges the redundant possibilities into a single output which is communicated intermittently to the response execution process. The response execution process translates the single output synergistically to the multiple muscles according to its current parameter settings. Once these are selected, the underlying control actions in the space of the elemental variables can be achieved by lower order mechanisms such as pattern generators, muscle modes, synergies, or optimal feedback systems. This second scheme generalizes the intermittent control hypothesis presented in Figure 1.

Exploitation of redundancy is biologically important. Biological systems generally exploit redundancy to improve robustness and flexibility of control (Karniel, 2011). The exploitation of all available DOFs to maximize performance and flexibility is generally a sign of skill and learning (Bernstein, 1967, page 107–108), whereas the elimination of available DOFs is usually a symptom of declining ability through age (Hsu et al., 2012), disease (Oude Nijhuis et al., 2008; Pasman et al., 2011), or fear (Adkin et al., 2002).

Utilization of redundant possibilities requires selecting one possibility from many at any instant. Fundamentally, the process is one of convergence and as stated by Cisek (2005), “the processes of motor planning appear to be inextricably entwined in the processes of decision-making.” Important questions are whether convergence should narrow to a single channel and whether convergence should lie within or outside the main feedback loop. For example choice might be exercised once in selecting one strategy which is employed continuously via low level feedback mechanisms or choice might be exercised online during execution of the task in mechanisms which allow or require choice to be exercised iteratively within the feedback loop between sensory input and motor output. We see two relevant issues, namely compatibility and optimization of coordination, and rate of implementation of selection.

Compatibility and optimization of coordination: Some human tasks are incompatible. We cannot point and make a fist; we cannot flex our knees while at the same time extending them; we cannot walk and stand still simultaneously. Some tasks are partially compatible, for example walking and pointing. To avoid simultaneous engagement in mutually incompatible tasks is obviously essential. More subtly, the selection of compatible routines and the suppression of routines which are partially incompatible or merely inappropriate must underlie skilled and economical task performance. When we perform compatible tasks simultaneously such tasks need to be fully integrated to prevent mutual interference. One way to do this is to select sequentially a compatible family of lower level modules such as pattern generators, muscle modes, and synergies which translate the command to control actions. By using a single channel, only one such compatible family is selected at one time and all others are held off. For this experiment staying upright and tracking a dot might be two independent compatible tasks, two independent incompatible tasks, or one coordinated task. Our reasoning is that optimization of coordination of two tasks (dot tracking and staying upright) by eliminating mutual interference—in effect—becomes the same thing as controlling a single task in the task-space. Hence we offer the rationale that optimization of coordination leads to unification of control into a single synergy requiring a single channel for its selection.

Rate of implementation. We suggest that maintaining the response selection process within the feedback loop, maximizes the rate at which response selection can be translated to motor output as an open loop process. The alternative of placing the response selection process temporally or hierarchically outside the feedback loop reduces the rate of translating response selection to motor output because it imposes the closed loop dynamics of the feedback control loop onto the translation between response selection and motor output (cf. Figure 7).

To summarize, until the point of selection, competitive commands could be prepared in parallel as envisaged in models of decision making (Cisek, 2005; Sinha et al., 2006; Carpenter et al., 2009; Noorani et al., 2011). After selection, competitors should be suppressed (Neumann, 1996). The duration of the suppression should be sufficient for the command to be executed without interference. Convergence of parallel input to a sequential, serial process along a single channel seems the ideal solution to maximize optimal, coordinated function. The serial process involves planning, selection and temporary inhibition of competing responses prior to low dimensional motor output. The serial, ballistic nature of the process removes the obligation of closed loop dynamics from response generation. The consequences are intermittent control and refractoriness. Because all input is squeezed through a single channel this is often referred to as a “bottleneck.”

Some authors support a theory of central IC, with a short planning interval (100 ms), neurologically based in a cerebello-thalamo-cortical loop, and related to a form of physiological tremor (“movement discontinuities” or “bumps”) during slow movement (Vallbo and Wessberg, 1993; Neilson and Neilson, 2005; Bye and Neilson, 2008, 2010). However, these high frequency oscillations may simply be an effect of limb resonance (Lakie et al., 2012). Our recent evidence associates IC with longer open loop intervals (250–500 ms) related to the low bandwidth of voluntary control (Craik, 1947; Vince, 1948; Navas and Stark, 1968; Hanneton et al., 1997; Slifkin et al., 2000; Loram and Lakie, 2002; Loram et al., 2005, 2011, 2012; van de Kamp et al., 2013). The “bottleneck” associated with these longer periods of refractoriness does not occur at perceptual or motor stages of information processing, but at some central stage (Pashler and Johnston, 1998; Sigman and Dehaene, 2005). Where is it located? Some brain imaging evidence using dual tasks links have suggested frontal or pre-frontal cortical structures (Jiang and Kanwisher, 2003; Dux et al., 2006). However, Szameitat et al. (2006) have suggested that the increased activity of the prefrontal structures may represent an active task scheduling mechanism (response planning—temporal ordering of the dual tasks) rather than suggesting that this is the site of the bottleneck. It may be that the bottleneck analogy—which suggests a restriction continuously throttling the flow—leads to a search for the wrong type of mechanism. A better metaphor might be that of a conductor, who intermittently engages and suppresses sections of his orchestra. The central limitation is then the rate at which the intermittent adjustments can be made. Where in the brain is an appropriate switching mechanism which involves selective inhibition and facilitation of global motor activity (the central conductor) to be sought?

The basal ganglia are a clear possibility. They are now believed (e.g., Redgrave et al., 1999) to operate as a generic action selection system, receiving input from a broad range of other brain areas, and producing output that selects particular actions to perform. The opposing roles of the two cortical re-entrant loops (direct loop—thalamic facilitation of cortical output via ansa lenticularis) and the indirect loop (thalamic inhibition of cortical output via globus pallidus pars externa) might provide a plausible mechanism to engage and inhibit cortical outputs. Gurney et al. (2001) have suggested a basal ganglia mechanism whereby salient actions are selected and promiscuous actions are suppressed, rather like center—surround antagonism in visual processing. There is evidence that the basal ganglia are important to response selection, are associated with refractoriness and are part of the IC loop (Houk et al., 2007). These findings have been used to link the basal ganglia with computational models of IC and with neurological and behavioral deficits in decision making and action selection associated with Parkinson's disease, schizophrenia and Attention Deficit Disorder (ADD) (Houk et al., 2007). This justifies the possibility that functional deficits in Parkinson's disease including the initiation and selection of new responses, freezing, and postural rigidity might be related to deficits in the IC loop. Clearly, it would be interesting to find physiological and anatomical evidence positively linking IC to the basal ganglia. Do they work as an intermittently adjusted selector switch, and what happens when this switch is damaged by disease?

Robots, like humans contain redundant possibilities within a multi-segmental structure. The rationale for a serial, single channel process as necessary to optimize task selection and coordination from redundant possibilities applies equally in this case as it does for humans. Intermittent control implements a serial, single channel process as the appropriate engineering solution to control problems in which there is a time consuming online computational process (Ronco et al., 1999). When the actuators, the system being controlled and the external constraints are time invariant, then the control signal can be computed rapidly from measured quantities, the reference signal, and pre-computed parameters such as the gains of a continuous optimal controller. However, when the actuators, system and constraints are time varying then online optimization and computation of the control signal is desirable. Intermittent open loop predictive control uses an intermittently moving time horizon which allows slow optimization to occur concurrently with a fast control action. This approach allows handling of time varying systems and constraints at the expense of increased online computational requirement. Thus, intermittent control provides for a time consuming online optimization process which lies at the heart of flexible predictive control. A serial, single channel process, and its implementation through intermittent control, appears to be a valuable element missing from current schemes.