Iterative Learning Control of FES-Assisted Gait

Functional electrical stimulation (FES) is used in the rehabilitation and treatment of stroke patients to support weak motor functions. Since FES dynamics are highly individual and time-varying, the use of closed-loop control methods is required whenever precise motions shall be generated.
A challenging example is the drop foot syndrome which is characterized by insufficient dorsiflexion of the foot and can be treated by FES of the peroneal nerve or the tibialis anterior and peroneus longus muscle. For this particular application, we are developing control schemes inspired by Iterative Learning Control (ILC): In each step, a time varying stimulation intensity profile is applied, which is adjusted at the end of each swing phase. These profile updates are based on the difference between the desired and the recorded foot angle profile during the previous step. Various learning strategies and angle measurement techniques are investigated, as well as different approaches for synchronization of the stimulation with the gait.
Furthermore, we are extending the classic ILC theory to variable pass length systems in order to cope with the variability of the human gait. These new methods are evaluated in experiments with healthy subjects and with stroke patients. Some of the major results are presented in the following.

Iterative learning control adapts the stimulation intensity profile from step to step and thereby achieves persistently good foot angle profiles during swing phase despite time-varying effects like muscular fatigue.

Closed-Loop Control of Drop Foot Stimulators

Many people have walking deficits after suffering a stroke. Foot drop, i.e. insufficient dorsiflexion of the foot during the swing phase of gait, is a frequent phenomenon, which is conventionally treated by passive ankle-foot orthoses. Functional electrical stimulation (FES) represents an advantageous alternative. However, most commercially available stimulators are of the on/off type. A simple heel switch inside the shoe triggers the stimulation, which is then applied with constant intensity during the swing phase. For such systems, the stimulation intensity either needs frequent manual adjustment, or must be set to an unnecessarily high value, which causes rapid fatigue of the stimulated muscles. These problems can be overcome if the dorsiflexion angle is measured and used to adjust the stimulation intensity automatically. Due to the repetitive nature of gait, it is particularly promising to employ iterative learning control (ILC) techniques for these adjustments.

Apparently, the success of such control schemes depends critically on the measurement of either the dorsiflexion ankle joint angle or the foot-to-ground angle. We have investigated two different sensor technologies: one approach uses bioimpedance measurements via skin electrodes [1] [2]. An alternative approach is to equip the shoe or foot with an inertial sensor [3], which allows for determination of the foot-to-ground angle. By attaching a second inertial sensor to the shank, it is also possible to calculate the dorsiflexion ankle joint angle. See IMU-Based Gait Analysis for details.

Iterative Learning Control with Variable Pass Length

Another challenge is the irregular gait of stroke patients and the resulting significant variation of the duration of the swing phase, i.e. the pass length in this ILC system. Even if we consider humans walking at constant speed, e.g. on a treadmill, then the duration of swing phase varies and steps are often cut short by putting the foot down, e.g. when balance or strength is lost. Assuming that up to this point the movement was hardly different from the movement in a full-length step, we should use the data gathered in these aborted steps for learning. Even more important, if the stimulation profile is insufficient, then the toes touch ground early. In that case we must use the unfinished trial's data for learning since otherwise the stimulation profile of the next step will be just as insufficient. Typically, these issues are either ignored completely, or a heuristic approach is used hoping for convergence to be maintained. To overcome this situation, we are developing an extension of the ILC theory, including stability and monotonicity criteria, for the case of variable pass length. First results have been published in [4]. We believe that these results will also be useful for other ILC applications where variable iteration duration is a phenomenon that cannot be neglected.

Coupled Error and Pass Length Dynamics

In order to isolate the effect that insufficient stimulation has on early ground contact, and thus on the pass length, we performed experiments in which the subjects were sitting. Gait phase changes and ground contacts were simulated. More precisely, we used foot motion data from a walking experiment to calculate, for each moment during swing phase, which foot angle would make the foot touch the ground. In the experiments with sitting subjects, each trial was aborted whenever the actual angle fell below the theoretical ground contact angle of the current time instant. Only the foot angle data that had been gathered before ground contact was used for learning. Despite this limited information, the ILC algorithm achieved full pass length and learned to produce the entire desired angle profile in just a few steps.

Experimental evaluation of ILC for FES-induced foot dorsiflexion. By simulating gait phases and ground contact, the effect of insufficient stimulation on early ground contact, and thus on the variance of pass length, is assessed.

A video of one of the experiments is available by clicking on the figure above. For technical details please see [5] and [6].

ILC with Random Pass Length in Treadmill Experiments

While the subject walks on a treadmill at constant speed, the stimulation is synchronized with the gait by a detailed gait phase detection via the intertial sensor on the foot, which also provides the foot angle. The observed difference between the actual angle profile and the reference profile is used to update the stimulation intensity profile before the next heel-rise. The deviation between both profiles is reduced to a small value and the desired foot motion is achieved within a few steps. But even after convergence, this update is performed in each foot-flat phase. Thereby, the stimulation profile is always adapted to yield the desired motion, even when muscular fatigue or similar slow variances in the system dynamics occur. A video of one of the experiments is available by clicking on the figure below. Technical details can be found in [7].

Experimental evaluation of ILC for FES-induced foot dorsiflexion. Starting with a very low initial stimulation intensity profile, the ILC achieves the desired foot motion within two learning steps. Vertical lines indicate toe-off and heel-strike as detected via the inertial sensor.

These experimental results prove the effectiveness of ILC for use in closed-loop drop foot stimulators. By measuring the foot-to-ground angle and using this information to adapt the stimulation profile via ILC, muscular fatigue and similar variances in the stimulation dynamics are compensated automatically. Thus, it is possible to achieve a constantly physiological and symmetric gait.

Publications

  1. ↑
    Nahrstaedt, H., Schauer, T., Shalaby, R., Hesse, S., Raisch, J.. Automatic Control of a Drop-Foot Stimulator Based on Angle Measurement Using Bioimpedance. Artificial Organs, 32 pages 649–654, 2008.
    Bibtex
    Author : Nahrstaedt, H., Schauer, T., Shalaby, R., Hesse, S., Raisch, J.
    Title : Automatic Control of a Drop-Foot Stimulator Based on Angle Measurement Using Bioimpedance
    In : Artificial Organs,
          32 pages 649–654, 2008.
    Date : 2008
     | PDF | DOI 
  2. ↑
    Nahrstaedt, H., Schauer, T., Hesse, S., Raisch, J.. Iterative Learning Control of a Gait Neuroprosthesis (Article in German). at - Automatisierungstechnik, 56 (9):494–501, 2008.
    Bibtex
    Author : Nahrstaedt, H., Schauer, T., Hesse, S., Raisch, J.
    Title : Iterative Learning Control of a Gait Neuroprosthesis (Article in German)
    In : at - Automatisierungstechnik,
          56 (9):494–501, 2008.
    Date : 2008
     | PDF | DOI 
  3. ↑
    Negard, N.-O.. Controlled FES-assisted gait training for hemiplegic stroke patients based on inertial sensors. Doctoral Thesis, TU Berlin, 2009.
    Bibtex
    Author : Negard, N.-O.
    Title : Controlled FES-assisted gait training for hemiplegic stroke patients based on inertial sensors
    In :
          Doctoral Thesis, TU Berlin, 2009.
    Date : 2009
     | PDF | Link 
  4. ↑
    Seel, T., Schauer, T., Raisch, J.. Iterative Learning Control for Variable Pass Length Systems. In Preprints of the 18th IFAC World Congress, pages 4880–4885, Milan, Italy, 2011.
    Bibtex
    Author : Seel, T., Schauer, T., Raisch, J.
    Title : Iterative Learning Control for Variable Pass Length Systems
    In : In Preprints of the 18th IFAC World Congress,
          pages 4880–4885, Milan, Italy, 2011.
    Date : 2011
     | PDF | DOI | Link 
  5. ↑
    Seel, T., Schauer, T., Raisch, J.. Variable Pass Length ILC in FES-based Drop Foot Rehabilitation. In Workshop AUTOMED, Aachen, Germany, 2012.
    Bibtex
    Author : Seel, T., Schauer, T., Raisch, J.
    Title : Variable Pass Length ILC in FES-based Drop Foot Rehabilitation
    In : In Workshop AUTOMED,
          Aachen, Germany, 2012.
    Date : 2012
     
  6. ↑
    T. Seel, T. Schauer, J. Raisch. Iterative Learning Control with Variable Pass Length applied to FES-based Drop Foot Treatment (in German). at - Automatisierungstechnik, 61 (9) 2013.
    Bibtex
    Author : T. Seel, T. Schauer, J. Raisch
    Title : Iterative Learning Control with Variable Pass Length applied to FES-based Drop Foot Treatment (in German)
    In : at - Automatisierungstechnik,
          61 (9) 2013.
    Date : 2013
     | PDF | DOI | Link 
  7. ↑
    T. Seel, S. Schäperkötter, M. Valtin, C. Werner, T. Schauer. Design and Control of an Adaptive Peroneal Stimulator with Inertial Sensor-based Gait Phase Detection. In 18th Annual International FES Society Conference, San Sebastian, Spain, 2013.
    Bibtex
    Author : T. Seel, S. Schäperkötter, M. Valtin, C. Werner, T. Schauer
    Title : Design and Control of an Adaptive Peroneal Stimulator with Inertial Sensor-based Gait Phase Detection
    In : In 18th Annual International FES Society Conference,
          San Sebastian, Spain, 2013.
    Date : 2013
     | PDF 
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