I have no clue how this applies to getting survivors recovered. Way too wordy to be of any use to survivors to explain how to use this to their medical professionals. Writing a protocol is what is needed and you totally fucking failed at that!
Multiple-model iterative learning control with application to stroke rehabilitation
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open access
Abstract
Model-based
iterative learning control (ILC) algorithms achieve high accuracy but
often exhibit poor robustness to model uncertainty, causing divergence
and long-term instability as the number of trials increases. To address
this, an estimation-based multiple-model switched ILC (EMMILC) approach
is developed based on novel theorem results which guarantee stability if
the true plant lies within a uncertainty space defined by the designer.
Using gap metric analysis, EMMILC eliminates restrictive assumptions on
the uncertainty structure assumed in existing multiple-model ILC
methods. Our design framework minimises computational load while
maximising tracking accuracy. Applied to a common rehabilitation
scenario, EMMILC outperforms the standard ILC approaches that have been
previously employed in this setting. This is confirmed by experimental
tests with four participants where performance increased by 28%. EMMILC
is the first model-based ILC framework that can guarantee high
performance while not requiring any model identification or tuning, and
paves the way for effective, home-based rehabilitation systems.
1. Introduction
Every year 12.2 million people suffer from their first stroke. Approximately 70% of survivors report impaired upper-limb function, and 40% are left with a permanent arm disability (Party, 2023). Fortunately, this lost movement can be recovered by intensive practice of functional tasks (Geller et al., 2023) which enables the brain to fuse new connections in the motor cortex that replace those lost by stroke. This ‘relearning’ is facilitated by haptic, proprioceptive and visual feedback during goal-orientated functional tasks. However, conventional therapy only promotes limited recovery for less severe impairment levels, and is increasingly unaffordable. There is therefore an urgent need for low-cost technology to provide intensive, goal-oriented task training (Ballester, Ward, Brander, et al., 2022).
Functional electrical stimulation (FES) comprises a sequence of electrical pulses that are applied using electrodes to artificially activate muscles. Recent UK National Clinical Guidelines for stroke (Party, 2023) strongly recommend using FES during daily practice of repeated arm movements. However, they highlight that current FES devices used in clinics and hospitals employ open-loop or triggered control (Kristensen et al., 2022, Popović, 2014, Schearer et al., 2012, Wolf and Schearer, 2017). This is due to the need for simple, reliable and fast set-up, however it has resulted in slow and inaccurate upper-limb movements which are not personalised to users and do not promote recovery (Anderson, 2004).
Meta-analyses confirm that FES systems used in clinical upper-limb studies are still overwhelmingly open-loop or triggered by electromyography (Kristensen et al., 2022). A small number of clinical studies have employed simple closed-loop feedback (leung Chan et al., 2009, Hodkin et al., 2018, Pelton et al., 2012, Resquín, Cuesta Gómez et al., 2016), however their tracking accuracy is still relatively low, particularly due to the slow system response and onset of muscle fatigue. Controllers often require extensive tuning for each subject (Resquín, Gonzalez-Vargas et al., 2016, Wiarta et al., 2020) which is impractical in clinical practice due to time constraints and lack of expertise. Higher accuracy tracking has been achieved using model-based FES upper-limb control strategies, including model predictive (Westerveld et al., 2014, Wolf and Schearer, 2022), optimal (Sa-e, Freeman, & Yang, 2020), active disturbance rejection (Liu, Qin, Huo, & Wu, 2020), and sliding mode (Oliveira et al., 2017, Rouse et al., 2016, Wu et al., 2017) control. To avoid the need for time-consuming identification, Razavian et al., 2018, Tan et al., 2011, Wolf and Schearer, 2019 and Wolf and Schearer (2018) use only partial model information, however this degraded tracking accuracy. Like all the above methods, a further drawback was their inability to adequately compensate for fatigue, spasticity and other physiological effects.
Adaptive FES model-based controllers have attempted to improve performance. A prominent example is multiple-model adaptive control (MMAC) (Brend, Freeman, & French, 2015) which defines a set of ‘candidate’ plant models, and a corresponding set of optimal controllers. A bank of Kalman filters are used to switch in the controller whose model best fits the observed plant data. An experimental evaluation with five subjects performing isometric elbow force tracking showed it improved accuracy by 22% compared with standard optimal control. Together with (Wolf, Hall, & Schearer, 2020), this is the only model-based upper-limb controller tested in experiments with multiple subjects that induce prolonged muscle fatigue. There have been other significant advancements in robust upper-limb FES controllers, including switched designs to address electromechanical delays (Allen, Cousin, Rouse and and Dixon, 2022, Sharma et al., 2011), varying geometry of the upper-limb muscles (Allen, Stubbs, & Dixon, 2022), or co-activation of antagonistic muscles (Sun, Qiu, Iyer, Dicianno, & Sharma, 2023). However, they cannot provide guaranteed high performance tracking in the presence of arbitrarily large, unstructured model uncertainty. These approaches have been tested with unimpaired subjects. With one exception (Alibeji, Kirsch, Dicianno, & Sharma, 2017), they have not progressed to tests with neurologically impaired participants.
Iterative learning control (ILC) is one of the few model-based control schemes that have been applied to FES-based upper-limb control with impaired patients. It has shown its success in five clinical trials (Freeman, 2016) with more than
patients with stroke (Kutlu, Freeman, Hallewell, et al., 2016) or multiple sclerosis (Sampson et al., 2016). ILC is formulated for systems that repeat the same finite duration tracking task, and aims to capture the idiom that ‘practice makes perfect’. It updates the control input using information from previous attempts, which exactly matches the rehabilitation scenario. Early ILC algorithms did not use model information (Arimoto et al., 1984, Freeman et al., 2005, Nahrstaedt et al., 2008), however the field rapidly expanded to leverage model-based updates in order to provide greater accuracy and convergence properties for wider system classes. Examples of the broad range of model-based ILC approaches are contained in Bristow et al., 2006, Owens, 2016 and Rogers, Chu, Freeman, and Lewin (2023) and the references therein. An essential aspect of ILC that has been widely studied is long-term robust stability (Bradley, 2010, Freeman et al., 2005, Meng and Moore, 2017), which refers to the system’s ability to maintain stability after initial convergence, even in the presence of modelling errors. For example, Ratcliffe et al. (2005) showed that a common ILC update will diverge if a multiplicative model uncertainty has a phase angle greater that in magnitude. Addressing long term stability is especially crucial in a rehabilitation setting to ensure that the intensive FES training remains effective, comfortable and safe over extended periods of use.
Several ILC schemes have been applied to FES based upper limb rehabilitation, with standard model-based updates proving most accurate. Tests with stroke participants showed they outperforming conventional model-based strategies by an order of magnitude (Freeman, 2016). Over the course of fifteen years, ILC has progressed from purely elbow extension to full arm reaching tasks (Kutlu et al., 2016) including hand and wrist motion via a 24 channel FES electrode array (Excell, Freeman, Meadmore, et al., 2013). Although accuracy has been high, the time needed for identification has become prohibitively long, and recent trials which avoided re-identification by reusing previous models yielded significantly degraded tracking accuracy (Kutlu et al., 2016).
To solve the above deficiencies, a new control approaches is needed that requires little or no model identification tests, but is capable of accurate tracking in the presence of substantial model uncertainty (e.g. fatigue, spasticity and electrode movement). ILC is an obvious starting point given its pedigree in rehabilitation, and there already exist a range of robust ILC algorithms that may be suitable for application in rehabilitation. However, closer inspection reveals these have focused on highly structured parametric (Ahn et al., 2005, Xu and Xu, 2013) or multiplicative/additive (Donkers et al., 2008, Freeman, Lewin et al., 2009, Owens et al., 2014) forms. Model predictive and simple adaptive strategies have also been embedded into the ILC framework to address time-iteration-dependent uncertainties. Unfortunately, their accuracy is subject to modelling error (Ma, Liu, Kong, & Lee, 2021) and relies on restrictive assumptions on the form of uncertainties (Zhang, Meng, & Cai, 2023). Methods that can be applied to more general uncertainties typically require substantial identification/training time, excessive tuning, or place additional structural assumptions (Lee et al., 2000, Meng, 2019, Meng and Moore, 2017). A promising avenue are ILC approaches that update the model in order to better capture the plant dynamics. Li, Wang, and Liu (2014) and Li and Zhang (2010) used fuzzy neural networks to approximate multiple underlying nonlinear models and select the best one for ILC at every time sample. Longman, Peng, Kwon, et al. (2011) updated the model in between ILC trials using a standard model identification approach. This focused on linear systems, and only considered inverse ILC. It also did not provide any stability or robust performance guarantees. Instead of switching between different ILC updates, Zhu, Xu, Huang, et al. (2015) specified multiple linear models to capture unknown iteration-varying parameters, and designed a single ILC update using
tools which can stabilise all specified models. Similarly, Padmanabhan, Bhushan, Hebbar, et al. (2021) captured parametric uncertainty by producing multiple linear models, and designed ILC using a convex combination of all plants. Unfortunately, there is currently no switched multiple model framework that derives robust performance bounds for the most common ILC update structure when the plant model is subject to a general class of modelling uncertainty specified by the designer. Additionally, there is no principled multiple-model guidelines allowing the designer to systematically and efficiently generate the required plant models and associated ILC updates. In terms of application, none of the above approaches has been used in FES upper limb rehabilitation.
This paper develops a multiple-model ILC framework that addresses the above limitations. It is motivated by the previous multiple-model approach of Brend et al. (2015), which applied optimal control to stabilise the isometric elbow using FES. This was a direct application of theory developed in Buchstaller and French (2016a) and Buchstaller and French (2016b) which considered only regulation (i.e. maintaining the system states at zero). Despite this narrow remit, the MMAC theory is less conservative than competing multiple-model approaches since it derives bounds on the output that do not scale with the number of plant models. In addition, it permits a broader class of uncertainties through use of the gap metric, a powerful measure of plant mismatch. Our results in Freeman and French (2015) showed how the MMAC framework could be extended to address ILC through two major extensions: (1) MMAC operates from sample to sample, whereas ILC resets after each trial. We addressed this by packaging ILC as a single sample of a high dimension system, and (2) by modifying the operating point to extend the regulation problem to tracking. Both components are non-trivial, and require substantial extension of all components of the framework (i.e. the estimators, gap metric definitions, controller properties, and overall performance bounds). Unfortunately, the resulting EMMILC framework (Freeman & French, 2015) entailed intensive computational burden, limiting its practicality. It was only applied numerically to a simple problem. To solve these problems, we make the following contributions:
- 1.We propose the first multiple-model ILC framework that is both simple to apply in practice, and guarantees robust performance for general uncertainty classes. A key component is a new robust performance bound that defines the uncertainty space stabilised by existing ILC laws. Another critical component is a novel design procedure that produces a candidate model set without requiring any further model identification. This set guarantees robust stability while transparently balancing computational load and tracking accuracy.
- 2.We describe the first experimental application of EMMILC, focusing on a clinically important rehabilitation problem. We show how a model set can be designed to capture the full range of physiological variation while imposing minimal computational load. Results confirm the practical efficacy of EMMILC and opens up the possibility of translating effective FES technology to patients’ own homes for the first time.
We build on preliminary work in Zhou, Freeman, and Holderbaum (2023a) which applied EMMILC in simulation, but contained no performance bounds, identification procedures or experiments.
This paper is organised as follows: Section 2 gives an overview of ILC preliminaries and applies robust stability analysis. Section 3 introduces a multiple-model control framework together with a practical design procedure guaranteeing robust stability. Then, Section 4 defines a wrist model, and expands its identification to capture an uncertainty set. Section 5 applies the framework to rehabilitation and describes the associated hardware implementation. Results involving four healthy subjects are given in Section 6, including comparison with standard ILC to confirm its practical efficacy.
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