Modelling human balance using switched systems with linear feedback control

An improved intermittent control model of postural sway during quiet standing implemented by a data driven approach

This paper proposes a new intermittent control model during human quiet standing, which is consisted of postulated "regular intervention" and "imminent intervention". The regular intervention is within the main control loop, and its trigger condition is equivalent to the switching frequency of center of pressure (COP) data calculated by wavelet transform. The imminent intervention will only be triggered after the postural sway angle exceeds a certain threshold. In order to prove the effectiveness of the new model, the simulation results of the new model and the model proposed by Asai et al. (2009) are compared with the experimental data. The setting parameters of both models are retrieved by Bayesian regression from the experimental data. The results show that the new model not only could exhibit two power law scaling regimes of power spectral density (PSD) of COP, but also show that indices of the probability density function distance, root mean square (RMS), Total Sway Path, displacement Range, 50% power frequency of center of mass (COP) between the simulation results and the experimental data are closer compared to the existing model. Moreover, the limit cycle oscillations (LCOs) obtained from the simulation results of the new model have a higher degree of matching with those retrieved from the experimental data.

Methods for integrating postural control into biomechanical human simulations: a systematic review

Understanding of the human body's internal processes to maintain balance is fundamental to simulate postural control behaviour. The body uses multiple sensory systems' information to obtain a reliable estimate about the current body state. This information is used to control the reactive behaviour to maintain balance. To predict a certain motion behaviour with knowledge of the muscle forces, forward dynamic simulations of biomechanical human models can be utilized. We aim to use predictive postural control simulations to give therapy recommendations to patients suffering from postural disorders in the future. It is important to know which types of modelling approaches already exist to apply such predictive forward dynamic simulations. Current literature provides different models that aim to simulate human postural control. We conducted a systematic literature research to identify the different approaches of postural control models. The different approaches are discussed regarding their applied biomechanical models, sensory representation, sensory integration, and control methods in standing and gait simulations. We searched on Scopus, Web of Science and PubMed using a search string, scanned 1253 records, and found 102 studies to be eligible for inclusion. The included studies use different ways for sensory representation and integration, although underlying neural processes still remain unclear. We found that for postural control optimal control methods like linear quadratic regulators and model predictive control methods are used less, when models' level of details is increasing, and nonlinearities become more important. Considering musculoskeletal models, reflex-based and PD controllers are mainly applied and show promising results, as they aim to create human-like motion behaviour considering physiological processes.

Periodic motions in a class of discontinuous delayed systems with a parabolic boundary

Various periodic motions are investigated for a mass-spring-damper oscillator described by second-order discontinuous delayed systems with a parabolic boundary. The G-function related to a delayed variable is first developed to judge the crossing, sliding, and grazing motions at the boundary points. Then, basic and local mappings, together with their motion equations, are classified by current and delayed states of a local flow. It is shown that periodic motions can be predicted analytically in terms of the return mapping and the initial value function provided posteriorly. Finally, numerical simulations are given to illustrate the existence of slowly oscillating periodic solutions without or with sliding portions as well as a crossing periodic solution not slowly oscillating. These results not only enrich and extend switchability theory of discontinuous delayed systems, but also reveal some complicated periodic behaviors which cannot be found in continuous delayed systems and discontinuous systems without time delay.

Predictor feedback models for stick balancing with delay mismatch and sensory dead zones

Human stick balancing is investigated in terms of reaction time delay and sensory dead zones for position and velocity perception using a special combination of delayed state feedback and mismatched predictor feedback as a control model. The corresponding mathematical model is a delay-differential equation with event-driven switching in the control action. Due to the sensory dead zones, initial conditions of the actual state cannot always be provided for an internal-model-based prediction, which indicates that (1) perfect prediction is not possible and (2) the delay in the switching condition cannot be compensated. The imperfection of the predictor is described by the delay mismatch, which is treated as a lumped parameter that creates a transition between perfect predictor feedback (zero delay mismatch) and delayed state feedback (mismatch equal to switching delay). The maximum admissible switching delay (critical delay) is determined numerically based on a practical stabilizability concept. This critical delay is compared to a realistic reference value of 230 ms in order to assess the possible regions of the threshold values for position and velocity perception. The ratio of the angular position and angular velocity for 44 successful balancing trials by 8 human subjects was used to validate the numerical results. Comparison of actual human stick balancing data and numerical simulations based on the mismatched predictor feedback model provided a plausible range of parameters: position detection threshold 1°, velocity detection threshold between 4.24 and 9.35°/s, and delay mismatch around 100-150 ms.

Quantitative evaluation of posture control in rats with inferior olive lesions

Impairment of inferior olivary neurons (IONs) affects whole-body movements and results in abnormal gait and posture. Because IONs are activated by unpredicted motion rather than regular body movements, the postural dysfunction caused by ION lesions is expected to involve factors other than simple loss of feedback control. In this study, we measured the postural movements of rats with pharmacological ION lesions (IO rats) trained to stand on their hindlimbs. The coordination of body segments as well as the distribution and frequency characteristics of center of mass (COM) motion were analyzed. We determined that the lesion altered the peak properties of the power spectrum density of the COM, whereas changes in coordination and COM distribution were minor. To investigate how the observed properties reflected changes in the control system, we constructed a mathematical model of the standing rats and quantitatively identified the control system. We found an increase in linear proportional control and a decrease in differential and nonlinear control in IO rats compared with intact rats. The dystonia-like changes in body stiffness explain the nature of the linear proportional and differential control, and a disorder in the internal model is one possible cause of the decrease in nonlinear control.

Response to perturbation during quiet standing resembles delayed state feedback optimized for performance and robustness

Postural sway is a result of a complex action–reaction feedback mechanism generated by the interplay between the environment, the sensory perception, the neural system and the musculation. Postural oscillations are complex, possibly even chaotic. Therefore fitting deterministic models on measured time signals is ambiguous. Here we analyse the response to large enough perturbations during quiet standing such that the resulting responses can clearly be distinguished from the local postural sway. Measurements show that typical responses very closely resemble those of a critically damped oscillator. The recovery dynamics are modelled by an inverted pendulum subject to delayed state feedback and is described in the space of the control parameters. We hypothesize that the control gains are tuned such that (H1) the response is at the border of oscillatory and nonoscillatory motion similarly to the critically damped oscillator; (H2) the response is the fastest possible; (H3) the response is a result of a combined optimization of fast response and robustness to sensory perturbations. Parameter fitting shows that H1 and H3 are accepted while H2 is rejected. Thus, the responses of human postural balance to “large” perturbations matches a delayed feedback mechanism that is optimized for a combination of performance and robustness.

The assessment of center of mass and center of pressure during quiet stance: Current applications and future directions

This perspective article provides a brief review of our understanding of how center of pressure (CoP) and center of mass (CoM) are traditionally utilized to measure quiet standing and how technological advancements are allowing for measurements to be derived outside the confines of a laboratory setting. Furthermore, this viewpoint provides descriptions of what CoP and CoM outcomes may reflect, a discussion of recent developments in selected balance outcomes, the importance of measuring instantaneous balance outcomes, and directions for future questions/research. Considering the enormous number and cost of falls annually, conclusions drawn from this perspective underscore the need for more cohesive efforts to advance our understanding of balance performance. As we refine the technology and algorithms used to portably assess postural stability, the question of which measurement (i.e. CoP or CoM) to utilize seems to be highly dependent on the question being asked. Further, the complexity of the question appears to span multiple disciplines and cultivate exploration of the intrinsic mechanisms of stability. Recently developed multi-dimensional methods for assessing balance performance may provide additional insight into balance, improving our ability to predict balance impairments and falls outside the laboratory and in the clinic. However, additional work will be necessary to understand the clinical significance and predictive capacity of these outcomes in various fall-prone populations.

Postural instability via a loss of intermittent control in elderly and patients with Parkinson's disease: A model-based and data-driven approach

Postural instability is one of the major symptoms of Parkinson's disease. Here, we assimilated a model of intermittent delay feedback control during quiet standing into postural sway data from healthy young and elderly individuals as well as patients with Parkinson's disease to elucidate the possible mechanisms of instability. Specifically, we estimated the joint probability distribution of a set of parameters in the model using the Bayesian parameter inference such that the model with the inferred parameters can best-fit sway data for each individual. It was expected that the parameter values for three populations would distribute differently in the parameter space depending on their balance capability. Because the intermittent control model is parameterized by a parameter associated with the degree of intermittency in the control, it can represent not only the intermittent model but also the traditional continuous control model with no intermittency. We showed that the inferred parameter values for the three groups of individuals are classified into two major groups in the parameter space: one represents the intermittent control mostly for healthy people and patients with mild postural symptoms and the other the continuous control mostly for some elderly and patients with severe postural symptoms. The results of this study may be interpreted by postulating that increased postural instability in most Parkinson's patients and some elderly persons might be characterized as a dynamical disease.

Acting together, destabilizing influences can stabilize human balance

The causes of falling in the elderly are multi-factorial. Three factors that influence balance stability are the time delay, a sensory dead zone and the maximum ankle torque that can be generated by muscular contraction. Here, the effects of these contributions are evaluated in the context of a model of an inverted pendulum stabilized by time-delayed proportional-derivative (PD) feedback. The effect of the sensory dead zone is to produce a hybrid type of control in which the PD feedback is switched ON or OFF depending on whether or not the controlled variable is larger or smaller than the detection threshold, Π. It is shown that, as Π increases, the region in the plane of control parameters where the balance time (BT) is greater than 60 s is increased slightly. However, when maximum ankle torque is also limited, there is a dramatic increase in the parameter region associated with BTs greater than 60 s. This increase is due to the effects of a torque limitation on over-control associated with bang-bang type switching controllers. These observations show that acting together influences, which are typically thought to destabilize balance, can actually stabilize balance. This article is part of the theme issue 'Nonlinear dynamics of delay systems'.

Saturation limits the contribution of acceleration feedback to balancing against reaction delay

A nonlinear model for human balancing subjected to a saturated delayed proportional-derivative-acceleration (PDA) feedback is analysed. Compared to the proportional-derivative (PD) controller, it is confirmed that the PDA controller improves local stability even for large feedback delays. However, it is shown that the saturated PDA controller typically introduces subcritical Hopf bifurcation into the system, which can also lead to falling for large enough perturbations. The subcriticality becomes stronger as the acceleration feedback gain increases or the saturation torque limit decreases. These explain some features of human balancing failure related to the increased reaction delay of inactive elderly people.

Postural Stability Variables for Dynamic Equilibrium

Experiments on the maintenance of postural stability on flat stationary support surfaces (quiet standing) that show only limited modes of the potential configurations of balance stability have dominated investigations of balance in quiet upright standing. Recent studies have revealed coordination properties of the whole body in maintaining dynamic postural stability with the application of moving platform paradigms. This paper examines properties of candidate collective variables for postural control within the dynamic systems framework. Evidence is discussed in this paper for: (i) self-organization properties of dynamic postural balance; (ii) enhanced variability and entropy prior to a phase transition between center of mass and center of pressure coupling; (iii) co-existence of intermittent postural control strategies that oscillate between periodic to chaotic transitions to maintain upright postural balance. These collective findings indicate postural attractor dynamic states progressively emerge to the changing task constraints of a moving platform revealing insights into the deterministic and stochastic properties of the multiple time scales of human postural behavior.

Scaling oscillatory platform frequency reveals recurrence of intermittent postural attractor states

The study of postural control has been dominated by experiments on the maintenance of quiet upright standing balance on flat stationary support surfaces that reveal only limited modes of potential configurations of balance stability/instability. Here we examine the self-organization properties of postural coordination as revealed in a dynamic balance task with a moving platform. We scaled a control parameter (platform frequency) to investigate the evolving nature of the coupled oscillator dynamics between center of mass (CoM) and platform. Recurrent map measures were used to reveal whether episodic postural control strategies exist that can be scaled by systematically changing the magnitude of platform motion. The findings showed that at higher platform frequencies (1.2 Hz), the CoM-Platform coupling was less deterministic than lower platform frequencies and evolved to intermittent postural control strategies that oscillated between periodic-chaotic transitions to maintain upright postural balance. Collectively, the recurrence map measures indicated that quasi-static postural attractor states were progressively emerging to the changing task constraints of platform frequency in the maintenance of postural stability. It appears that several dynamic modes of intermittent coupling in postural control can interchangeably co-exist and are expressed as a function of the control parameter of platform frequency.

Microchaos in human postural balance: Sensory dead zones and sampled time-delayed feedback

Models for the stabilization of an inverted pendulum figure prominently in studies of human balance control. Surprisingly, fluctuations in measures related to the vertical displacement angle for quietly standing adults with eyes closed exhibit chaos. Here we show that small-amplitude chaotic fluctuations ("microchaos") can be generated by the interplay between three essential components of human neural balance control, namely time-delayed feedback, a sensory dead zone, and frequency-dependent encoding of force. When the sampling frequency of the force encoding is decreased, the sensitivity of the balance control to changes in the initial conditions increases. The sampled, time-delayed nature of the balance control may provide insights into why falls are more common in the very young and the elderly.

Postural control during quiet bipedal standing in rats

The control of bipedal posture in humans is subject to non-ideal conditions such as delayed sensation and heartbeat noise. However, the controller achieves a high level of functionality by utilizing body dynamics dexterously. In order to elucidate the neural mechanism responsible for postural control, the present study made use of an experimental setup involving rats because they have more accessible neural structures. The experimental design requires rats to stand bipedally in order to obtain a water reward placed in a water supplier above them. Their motions can be measured in detail using a motion capture system and a force plate. Rats have the ability to stand bipedally for long durations (over 200 s), allowing for the construction of an experimental environment in which the steady standing motion of rats could be measured. The characteristics of the measured motion were evaluated based on aspects of the rats’ intersegmental coordination and power spectrum density (PSD). These characteristics were compared with those of the human bipedal posture. The intersegmental coordination of the standing rats included two components that were similar to that of standing humans: center of mass and trunk motion. The rats’ PSD showed a peak at approximately 1.8 Hz and the pattern of the PSD under the peak frequency was similar to that of the human PSD. However, the frequencies were five times higher in rats than in humans. Based on the analysis of the rats’ bipedal standing motion, there were some common characteristics between rat and human standing motions. Thus, using standing rats is expected to be a powerful tool to reveal the neural basis of postural control.

Control at stability's edge minimizes energetic costs: expert stick balancing

Stick balancing on the fingertip is a complex voluntary motor task that requires the stabilization of an unstable system. For seated expert stick balancers, the time delay is 0.23 s, the shortest stick that can be balanced for 240 s is 0.32 m and there is a [Formula: see text]° dead zone for the estimation of the vertical displacement angle in the saggital plane. These observations motivate a switching-type, pendulum-cart model for balance control which uses an internal model to compensate for the time delay by predicting the sensory consequences of the stick's movements. Numerical simulations using the semi-discretization method suggest that the feedback gains are tuned near the edge of stability. For these choices of the feedback gains, the cost function which takes into account the position of the fingertip and the corrective forces is minimized. Thus, expert stick balancers optimize control with a combination of quick manoeuvrability and minimum energy expenditures.

Intermittent muscle activity in the feedback loop of postural control system during natural quiet standing

The origin of continual body oscillation during quiet standing is a neural-muscular-skeletal closed feedback loop system that includes insufficient joint stiffness and a time delay. Thus, muscle activity and joint oscillations are nonlinear during quiet standing, making it difficult to demonstrate the muscular-skeletal relationship experimentally. Here we experimentally revealed this relationship using intermittent control theory, in which non-actuation works to stabilize the skeletal system towards equilibrium. We found that leg muscles were activated/inactivated when the state point was located in the opposite/same direction as the direction of anatomical action, which was associated with joint torque actuating the body towards equilibrium. The derivative values of stability index defined in the phase space approximately 200 ms before muscle inactivation were also larger than those before activation for some muscles. These results indicate that bipedal standing might be achieved by monitoring the rate of change of stability/instability components and generating joint torque to stabilize the body. In conclusion, muscles are likely to activate in an event-driven manner during quiet standing and a possible metric for on/off switching is SI dot, and our methodology of EMG processing could allows us to extract such event-driven intermittent muscle activities.

An active balance board system with real-time control of stiffness and time-delay to assess mechanisms of postural stability

Increased time-delay in the neuromuscular system caused by neurological disorders, concussions, or advancing age is an important factor contributing to balance loss (Chagdes et al., 2013, 2016a,b). We present the design and fabrication of an active balance board system that allows for a systematic study of stiffness and time-delay induced instabilities in standing posture. Although current commercial balance boards allow for variable stiffness, they do not allow for manipulation of time-delay. Having two controllable parameters can more accurately determine the cause of balance deficiencies, and allows us to induce instabilities even in healthy populations. An inverted pendulum model of human posture on such an active balance board predicts that reduced board rotational stiffness destabilizes upright posture through board tipping, and limit cycle oscillations about the upright position emerge as feedback time-delay is increased. We validate these two mechanisms of instability on the designed balance board, showing that rotational stiffness and board time-delay induced the predicted postural instabilities in healthy, young adults. Although current commercial balance boards utilize control of rotational stiffness, real-time control of both stiffness and time-delay on an active balance board is a novel and innovative manipulation to reveal balance deficiencies and potentially improve individualized balance training by targeting multiple dimensions contributing to standing balance.

Generation of the Human Biped Stance by a Neural Controller Able to Compensate Neurological Time Delay

The development of a physiologically plausible computational model of a neural controller that can realize a human-like biped stance is important for a large number of potential applications, such as assisting device development and designing robotic control systems. In this paper, we develop a computational model of a neural controller that can maintain a musculoskeletal model in a standing position, while incorporating a 120-ms neurological time delay. Unlike previous studies that have used an inverted pendulum model, a musculoskeletal model with seven joints and 70 muscular-tendon actuators is adopted to represent the human anatomy. Our proposed neural controller is composed of both feed-forward and feedback controls. The feed-forward control corresponds to the constant activation input necessary for the musculoskeletal model to maintain a standing posture. This compensates for gravity and regulates stiffness. The developed neural controller model can replicate two salient features of the human biped stance: (1) physiologically plausible muscle activations for quiet standing; and (2) selection of a low active stiffness for low energy consumption.

The relationship between intermittent limit cycles and postural instability associated with Parkinson's disease

BACKGROUND

Many disease-specific factors such as muscular weakness, increased muscle stiffness, varying postural strategies, and changes in postural reflexes have been shown to lead to postural instability and fall risk in people with Parkinson's disease (PD). Recently, analytical techniques, inspired by the dynamical systems perspective on movement control and coordination, have been used to examine the mechanisms underlying the dynamics of postural declines and the emergence of postural instabilities in people with PD.

METHODS

A wavelet-based technique was used to identify limit cycle oscillations (LCOs) in the anterior-posterior (AP) postural sway of people with mild PD (n = 10) compared to age-matched controls (n = 10). Participants stood on a foam and on a rigid surface while completing a dual task (speaking).

RESULTS

There was no significant difference in the root mean square of center of pressure between groups. Three out of 10 participants with PD demonstrated LCOs on the foam surface, while none in the control group demonstrated LCOs. An inverted pendulum model of bipedal stance was used to demonstrate that LCOs occur due to disease-specific changes associated with PD: time-delay and neuromuscular feedback gain.

CONCLUSION

Overall, the LCO analysis and mathematical model appear to capture the subtle postural instabilities associated with mild PD. In addition, these findings provide insights into the mechanisms that lead to the emergence of unstable posture in patients with PD.

Smooth enlargement of human standing sway by instability due to weak reaction floor and noise

Human quiet standing is accompanied by body sway. The amplitude of this body sway is known to be larger than would be predicted from simple noise effects, and sway characteristics are changed by neurological disorders. This large sway is thought to arise from nonlinear control with prolonged periods of no control (intermittent control), and a nonlinear control system of this kind has been predicted to exhibit bifurcation. The presence of stability-dependent transition enables dynamic reaction that depends on the stability of the environment, and can explain the change in sway characteristics that accompanies some neurological disorders. This research analyses the characteristics of a system model that induces transition, and discusses whether human standing reflects such a mechanism. In mathematical analysis of system models, (intermittent control-like) nonlinear control with integral control is shown to exhibit Hopf bifurcation. Moreover, from the analytical solution of the system model with noise, noise is shown to work to smooth the enlargement of sway around the bifurcation point. This solution is compared with measured human standing sway on floors with different stabilities. By quantitatively comparing the control parameters between human observation and model prediction, enlargement of sway is shown to appear as predicted by the model analysis.

Complexity and dynamics of switched human balance control during quiet standing

In this paper, we use a combination of numerical simulations, time series analysis, and complexity measures to investigate the dynamics of switched systems with noise, which are often used as models of human balance control during quiet standing. We link the results with complexity measures found in experimental data of human sway motion during quiet standing. The control model ensuring balance, which we use, is based on an act-and-wait control concept, that is, a human controller is switched on when a certain sway angle is reached. Otherwise, there is no active control present. Given a time series data, we determine how does it look a typical pattern of control strategy in our model system. We detect the switched nonlinearity in the system using a frequency analysis method in the absence of noise. We also analyse the effect of time delay on the existence of limit cycles in the system in the absence of noise. We perform the entropy and detrended fluctuation analyses in view of linking the switchings (and the dead zone) with the occurrences of complexity in the model system in the presence of noise. Finally, we perform the entropy and detrended fluctuation analyses on experimental data and link the results with numerical findings in our model example.

Auto-regressive moving average analysis of linear and discontinuous models of human balance during quiet standing

Linear Time Invariant (LTI) processes can be modelled by means of Auto-Regressive Moving Average (ARMA) model systems. In this paper, we examine whether an ARMA model can be fitted to a process characterised by switched nonlinearities. In particular, we conduct the following test: we generate data from known LTI and nonlinear (threshold/dead-zone) models of human balance and analyse the output using ARMA. We show that both these known systems can be fitted, according to standard criteria, with low order ARMA models. To check if there are some obvious effects of the dead-zone, we compare the power spectra of both systems with the power spectra of their ARMA models. We then examine spectral properties of three posturographic data sets and their ARMA models and compare them with the power spectra of our model systems. Finally, we examine the dynamics of our model systems in the absence of noise to determine what is the effect of the switching threshold (dead-zone) on the asymptotic dynamics.

Intermittent control models of human standing: similarities and differences

Two architectures of intermittent control are compared and contrasted in the context of the single inverted pendulum model often used for describing standing in humans. The architectures are similar insofar as they use periods of open-loop control punctuated by switching events when crossing a switching surface to keep the system state trajectories close to trajectories leading to equilibrium. The architectures differ in two significant ways. Firstly, in one case, the open-loop control trajectory is generated by a system-matched hold, and in the other case, the open-loop control signal is zero. Secondly, prediction is used in one case but not the other. The former difference is examined in this paper. The zero control alternative leads to periodic oscillations associated with limit cycles; whereas the system-matched control alternative gives trajectories (including homoclinic orbits) which contain the equilibrium point and do not have oscillatory behaviour. Despite this difference in behaviour, it is further shown that behaviour can appear similar when either the system is perturbed by additive noise or the system-matched trajectory generation is perturbed. The purpose of the research is to come to a common approach for understanding the theoretical properties of the two alternatives with the twin aims of choosing which provides the best explanation of current experimental data (which may not, by itself, distinguish between the two alternatives) and suggesting future experiments to distinguish between the two alternatives.

Human stick balancing: an intermittent control explanation

There are two issues in balancing a stick pivoting on a finger tip (or mechanically on a moving cart): maintaining the stick angle near to vertical and maintaining the horizontal position within the bounds of reach or cart track. The (linearised) dynamics of the angle are second order (although driven by pivot acceleration), and so, as in human standing, control of the angle is not, by itself very difficult. However, once the angle is under control, the position dynamics are, in general, fourth order. This makes control quite difficult for humans (and even an engineering control system requires careful design). Recently, three of the authors have experimentally demonstrated that humans control the stick angle in a special way: the closed-loop inverted pendulum behaves as a non-inverted pendulum with a virtual pivot somewhere between the stick centre and tip and with increased gravity. Moreover, they suggest that the virtual pivot lies at the radius of gyration (about the mass centre) above the mass centre. This paper gives a continuous-time control-theoretical interpretation of the virtual-pendulum approach. In particular, by using a novel cascade control structure, it is shown that the horizontal control of the virtual pivot becomes a second-order problem which is much easier to solve than the generic fourth-order problem. Hence, the use of the virtual pivot approach allows the control problem to be perceived by the subject as two separate second-order problems rather than a single fourth-order problem, and the control problem is therefore simplified. The theoretical predictions are verified using the data previously presented by three of the authors and analysed using a standard parameter estimation method. The experimental data indicate that although all subjects adopt the virtual pivot approach, the less expert subjects exhibit larger amplitude angular motion and poorly controlled translational motion. It is known that human control systems are delayed and intermittent, and therefore, the continuous-time strategy cannot be correct. However, the model of intermittent control used in this paper is based on the virtual pivot continuous-time control scheme, handles time delays and moreover masquerades as the underlying continuous-time controller. In addition, the event-driven properties of intermittent control can explain experimentally observed variability.

Learning an intermittent control strategy for postural balancing using an EMG-based human-computer interface

It has been considered that the brain stabilizes unstable body dynamics by regulating co-activation levels of antagonist muscles. Here we critically reexamined this established theory of impedance control in a postural balancing task using a novel EMG-based human-computer interface, in which subjects were asked to balance a virtual inverted pendulum using visual feedback information on the pendulum's position. The pendulum was actuated by a pair of antagonist joint torques determined in real-time by activations of the corresponding pair of antagonist ankle muscles of subjects standing upright. This motor-task raises a frustrated environment; a large feedback time delay in the sensorimotor loop, as a source of instability, might favor adopting the non-reactive, preprogrammed impedance control, but the ankle muscles are relatively hard to co-activate, which hinders subjects from adopting the impedance control. This study aimed at discovering how experimental subjects resolved this frustrated environment through motor learning. One third of subjects adapted to the balancing task in a way of the impedance-like control. It was remarkable, however, that the majority of subjects did not adopt the impedance control. Instead, they acquired a smart and energetically efficient strategy, in which two muscles were inactivated simultaneously at a sequence of optimal timings, leading to intermittent appearance of periods of time during which the pendulum was not actively actuated. Characterizations of muscle inactivations and the pendulum¡Çs sway showed that the strategy adopted by those subjects was a type of intermittent control that utilizes a stable manifold of saddle-type unstable upright equilibrium that appeared in the state space of the pendulum when the active actuation was turned off.

Acceleration feedback improves balancing against reflex delay

A model for human postural balance is considered in which the time-delayed feedback depends on position, velocity and acceleration (proportional-derivative-acceleration (PDA) feedback). It is shown that a PDA controller is equivalent to a predictive controller, in which the prediction is based on the most recent information of the state, but the control input is not involved into the prediction. A PDA controller is superior to the corresponding proportional-derivative controller in the sense that the PDA controller can stabilize systems with approximately 40 per cent larger feedback delays. The addition of a sensory dead zone to account for the finite thresholds for detection by sensory receptors results in highly intermittent, complex oscillations that are a typical feature of human postural sway.

Balancing on tightropes and slacklines

Balancing on a tightrope or a slackline is an example of a neuromechanical task where the whole body both drives and responds to the dynamics of the external environment, often on multiple timescales. Motivated by a range of neurophysiological observations, here we formulate a minimal model for this system and use optimal control theory to design a strategy for maintaining an upright position. Our analysis of the open and closed-loop dynamics shows the existence of an optimal rope sag where balancing requires minimal effort, consistent with qualitative observations and suggestive of strategies for optimizing balancing performance while standing and walking. Our consideration of the effects of nonlinearities, potential parameter coupling and delays on the overall performance shows that although these factors change the results quantitatively, the existence of an optimal strategy persists.