Dynamic Optimization of FES and Orthosis-Based Walking Using Simple Models

Machine-learning-based coordination of powered ankle-foot orthosis and functional electrical stimulation for gait control

This study proposes a novel gait rehabilitation method that uses a hybrid system comprising a powered ankle-foot orthosis (PAFO) and FES, and presents its coordination control. The developed system provides assistance to the ankle joint in accordance with the degree of volitional participation of patients with post-stroke hemiplegia. The PAFO adopts the desired joint angle and impedance profile obtained from biomechanical simulation. The FES patterns of the tibialis anterior and soleus muscles are derived from predetermined electromyogram patterns of healthy individuals during gait and personalized stimulation parameters. The CNN-based estimation model predicts the volitional joint torque from the electromyogram of the patient, which is used to coordinate the contributions of the PAFO and FES. The effectiveness of the developed hybrid system was tested on healthy individuals during treadmill walking with and without considering the volitional muscle activity of the individual. The results showed that consideration of the volitional muscle activity significantly lowers the energy consumption by the PAFO and FES while providing adaptively assisted ankle motion depending on the volitional muscle activities of the individual. The proposed system has potential use as an assist-as-needed rehabilitation system, where it can improve the outcome of gait rehabilitation by inducing active patient participation depending on the stage of rehabilitation.

Development and Validation of a Closed-Loop Functional Electrical Stimulation-Based Controller for Gait Rehabilitation Using a Finite State Machine Model

Functional electrical stimulation (FES) can be used to initiate lower limb muscle contractions and has been widely applied in gait rehabilitation. Establishing the correct timing of FES activation during each phase of the gait (walking) cycle remains challenging as most FES systems rely on open-loop control, whereby the controller receives no feedback about joint kinematics and instead relies on predetermined/timed muscle stimulation. The objective of this study was to develop and validate a closed-loop FES-based control solution for gait rehabilitation using a finite state machine (FSM) model. A two-phased study approach was taken: (1) Experimentally-Informed Study: A neuromuscular-derived FSM model was developed to drive closed-loop FES-based control for gait rehabilitation. The finite states were determined using electromyography and joint kinematics data of 12 non-disabled adults, collected during treadmill walking. The gait cycles were divided into four states, namely: swing-to-stance, push off, pre-swing, and toe up. (2) Simulation Study: A closed-loop FES-based control solution that employed the resulting FSM model, was validated through comparisons of neuro-musculo-skeletal computer simulations of impaired versus healthy gait. This closed-loop controller yielded steadier simulated impaired gait, in comparison to an open-loop alternative. The simulation results confirmed that accurate timing of FES activation during the gait cycle, as informed by kinematics data, is important to natural gait retraining. The closed-loop FES-based solution, introduced in this study, contributes to the repository of gait rehabilitation control options and offers the advantage of being simplistic to implement. Furthermore, this control solution is expected to integrate well with powered exoskeleton technologies.

Shared Control of a Powered Exoskeleton and Functional Electrical Stimulation Using Iterative Learning

A hybrid exoskeleton comprising a powered exoskeleton and functional electrical stimulation (FES) is a promising technology for restoration of standing and walking functions after a neurological injury. Its shared control remains challenging due to the need to optimally distribute joint torques among FES and the powered exoskeleton while compensating for the FES-induced muscle fatigue and ensuring performance despite highly nonlinear and uncertain skeletal muscle behavior. This study develops a bi-level hierarchical control design for shared control of a powered exoskeleton and FES to overcome these challenges. A higher-level neural network–based iterative learning controller (NNILC) is derived to generate torques needed to drive the hybrid system. Then, a low-level model predictive control (MPC)-based allocation strategy optimally distributes the torque contributions between FES and the exoskeleton’s knee motors based on the muscle fatigue and recovery characteristics of a participant’s quadriceps muscles. A Lyapunov-like stability analysis proves global asymptotic tracking of state-dependent desired joint trajectories. The experimental results on four non-disabled participants validate the effectiveness of the proposed NNILC-MPC framework. The root mean square error (RMSE) of the knee joint and the hip joint was reduced by 71.96 and 74.57%, respectively, in the fourth iteration compared to the RMSE in the 1st sit-to-stand iteration.

Feedback Control of Upright Seating with Functional Neuromuscular Stimulation during a Functional Task after Spinal Cord Injury: A Case Study

Seated stability is a major concern of individuals with trunk paralysis. Trunk paralysis is commonly caused by spinal cord injuries (SCI) at or above the thoracic spine. Current methods to improve stability restrict the movement of the user by constraining their trunk to an upright position. Feedback control of functional neuromuscular stimulation (FNS) can help maintain seated stability while still allowing the user to perform movements to accomplish functional tasks. In this study, an individual with a SCI (C7, AIS B) and an implanted stimulator capable of recruiting trunk and hip musculature unilaterally moved a weighted jar on a countertop to and from three prescribed stations directly in front, laterally, and across midline. For comparison, the tasks were performed with constant baseline stimulation and with feedback modulated stimulation based on the tilt of the trunk obtained from an external accelerometer fed into two PID controllers; one for forward trunk pitch and the other for lateral roll. The trunk pitch and roll angles were obtained through motion capture cameras and various measures of postural sway (95% fitted ellipse area, root mean squared (RMS), path length) and the repeatability (coefficient of variation (CoV), variance ratio (VR)) were calculated. Feedback control significantly increased RMS of trunk movement along the major axis of the fitted ellipse, but decreased RMS values during bending along the minor axis of motion. As a result, the fitted ellipse area decreased when deploying the jar to one of the stations and increased with the other two. The CoV indicated reduced variation in the presence of feedback controlled stimulation for all stations, and VR showed higher repeatability in trunk pitch. Plots of the trunk pitch and roll revealed a faster return to upright motion due to feedback stimulation.Clinical relevance- Feedback control in combination with FNS is a viable method to improve seated stability while still allowing dynamic movements in individuals with a SCI, thus addressing a major concern of the population.

A Tube-based Model Predictive Control Method to Regulate a Knee Joint with Functional Electrical Stimulation and Electric Motor Assist

A hybrid neuroprosthesis system is a promising rehabilitation technology to restore lower-limb function in persons with paraplegia. The technology combines functional electrical stimulation (FES) and a powered lower limb exoskeleton to produce movements for walking and standing. The main control challenge in the hybrid neuroprosthesis is to achieve an optimal coordination between FES and electric motors. Model-based optimal control methods have been suggested for the control of the hybrid neuroprosthesis. However, it is often difficult to effect robust control performance with model-based optimal control methods due to modeling uncertainties. A tube-based model predictive control (MPC) method is developed to obtain robust and optimal coordination between FES and an electric motor during a knee regulation task. An external feedback control is used to limit the error between the actual position and the MPC-computed nominal position. The tube-based MPC method is proven to have recursive feasibility, compliance to input constraints, and exponentially bounded stability. The experimental results obtained from an able-bodied participant and a participant with spinal cord injury validate the controller's ability to allocate control inputs to FES and the electric motor as well as method's robustness to modeling uncertainties.

Characterization of the Force Production Capabilities of Paralyzed Trunk Muscles Activated With Functional Neuromuscular Stimulation in Individuals With Spinal Cord Injury

Paralysis of the trunk results in seated instability leading to difficulties performing activities of daily living. Functional neuromuscular stimulation (FNS) combined with control systems have the potential to restore some dynamic functions of the trunk. However, design of multi-joint, multi-muscle control systems requires characterization of the stimulation-driven muscles responsible for movement.

OBJECTIVE

This study characterizes the input-output properties of paralyzed trunk muscles activated by FNS, and explores co-activation of muscles.

METHODS

Four participants with various spinal cord injuries (C7 AIS-B, T4 AIS-B, T5 AIS-A, C5 AIS-C) were constrained so lumbar forces were transmitted to a load cell while an implanted neuroprosthesis activated otherwise paralyzed hip and paraspinal muscles. Isometric force recruitment curves in the nominal seated position were generated by inputting the level of stimulation (pulse width modulation) while measuring the resulting muscle force. Two participants returned for a second experiment where muscles were co-activated to determine if their actions combined linearly.

RESULTS

Recruitment curves of most trunk and hip muscles fit sigmoid shaped curves with a regression coefficient above 0.75, and co-activation of the muscles combined linearly across the hip and lumbar joint. Subject specific perturbation plots showed one subject is capable of resisting up to a 300N perturbation anteriorly and 125N laterally; with some subjects falling considerably below these values.

CONCLUSION

Development of a trunk stability control system can use sigmoid recruitment dynamics and assume muscle forces combine linearly.

SIGNIFICANCE

This study informs future designs of multi-muscle, and multi-dimensional FNS systems to maintain seated posture and stability.

Using Person-Specific Muscle Fatigue Characteristics to Optimally Allocate Control in a Hybrid Exoskeleton - Preliminary Results

Currently controllers that dynamically modulate functional electrical stimulation (FES) and a powered exoskeleton at the same time during standing-up movements are largely unavailable. In this paper, an optimal shared control of FES and a powered exoskeleton is designed to perform sitting to standing (STS) movements with a hybrid exoskeleton. A hierarchical control design is proposed to overcome the difficulties associated with developing an optimal real-time solution for the highly nonlinear and uncertain STS control model with multiple degrees of freedom. A higher-level robust nonlinear control design is derived to exponentially track a time-invariant desired STS movement profile. Then, a lower-level optimal control allocator is designed to distribute control between FES and the knee electric motors. The allocator uses a person's muscle fatigue and recovery dynamics to determine an optimal ratio between the FES-elicited knee torque and the exoskeleton assist. Experiments were performed on human participants, two persons without disability and one person with spinal cord injury (SCI), to validate the feedback controller and the optimal torque allocator. The muscles of the participant with SCI did not actively contract to FES, so he was only tested with the powered exoskeleton controller. The experimental results show that the proposed hierarchical control design is a promising method to effect shared control in a hybrid exoskeleton.

Computational Design of FastFES Treatment to Improve Propulsive Force Symmetry During Post-stroke Gait: A Feasibility Study

Stroke is a leading cause of long-term disability worldwide and often impairs walking ability. To improve recovery of walking function post-stroke, researchers have investigated the use of treatments such as fast functional electrical stimulation (FastFES). During FastFES treatments, individuals post-stroke walk on a treadmill at their fastest comfortable speed while electrical stimulation is delivered to two muscles of the paretic ankle, ideally to improve paretic leg propulsion and toe clearance. However, muscle selection and stimulation timing are currently standardized based on clinical intuition and a one-size-fits-all approach, which may explain in part why some patients respond to FastFES training while others do not. This study explores how personalized neuromusculoskeletal models could potentially be used to enable individual-specific selection of target muscles and stimulation timing to address unique functional limitations of individual patients post-stroke. Treadmill gait data, including EMG, surface marker positions, and ground reactions, were collected from an individual post-stroke who was a non-responder to FastFES treatment. The patient's gait data were used to personalize key aspects of a full-body neuromusculoskeletal walking model, including lower-body joint functional axes, lower-body muscle force generating properties, deformable foot-ground contact properties, and paretic and non-paretic leg neural control properties. The personalized model was utilized within a direct collocation optimal control framework to reproduce the patient's unstimulated treadmill gait data (verification problem) and to generate three stimulated walking predictions that sought to minimize inter-limb propulsive force asymmetry (prediction problems). The three predictions used: (1) Standard muscle selection (gastrocnemius and tibialis anterior) with standard stimulation timing, (2) Standard muscle selection with optimized stimulation timing, and (3) Optimized muscle selection (soleus and semimembranosus) with optimized stimulation timing. Relative to unstimulated walking, the optimal control problems predicted a 41% reduction in propulsive force asymmetry for scenario (1), a 45% reduction for scenario (2), and a 64% reduction for scenario (3), suggesting that non-standard muscle selection may be superior for this patient. Despite these predicted improvements, kinematic symmetry was not noticeably improved for any of the walking predictions. These results suggest that personalized neuromusculoskeletal models may be able to predict personalized FastFES training prescriptions that could improve propulsive force symmetry, though inclusion of kinematic requirements would be necessary to improve kinematic symmetry as well.

Sub-optimally Solving Actuator Redundancy in a Hybrid Neuroprosthetic System with a Multi-layer Neural Network Structure

Functional electrical stimulation (FES) has recently been proposed as a supplementary torque assist in lower-limb powered exoskeletons for persons with paraplegia. In the combined system, also known as a hybrid neuroprosthesis, both FES-assist and the exoskeleton act to generate lower-limb torques to achieve standing and walking functions. Due to this actuator redundancy, we are motivated to optimally allocate FES-assist and exoskeleton torque based on a performance index that penalizes FES overuse to minimize muscle fatigue while also minimizing regulation or tracking errors. Traditional optimal control approaches need a system model to optimize; however, it is often difficult to formulate a musculoskeletal model that accurately predicts muscle responses due to FES. In this paper, we use a novel identification and control structure that contains a recurrent neural network (RNN) and several feedforward neural networks (FNNs). The RNN is trained by supervised learning to identify the system dynamics, while the FNNs are trained by a reinforcement learning method to provide sub-optimal control actions. The output layer of each FNN has its unique activation functions, so that the asymmetric constraint of FES and the symmetric constraint of exoskeleton motor control input can be realized. This new structure is experimentally validated on a seated human participant using a single joint hybrid neuroprosthesis.

Design of the Cooperative Actuation in Hybrid Orthoses: A Theoretical Approach Based on Muscle Models

Hybrid orthoses or rehabilitation exoskeletons have proven to be a powerful tool for subjects with gait disabilities due to their combined use of electromechanical actuation to provide motion and support, and functional electrical stimulation (FES) to contract muscle tissue so as to improve the rehabilitation process. In these devices, each degree of freedom is governed by two actuators. The main issue arises in the design of the two actuation profiles for there to be natural or normative gait motion in which the two actuators are transparent to each other. Hybrid exoskeleton control solutions proposed in the literature have been based on tracking the desired kinematics and applying FES to maintain the desired motion rather than to attain the values expected for physiological movement. This work proposes a muscle-model approach involving inverse dynamics optimization for the design of combined actuation in hybrid orthoses. The FES profile calculated in this way has the neurophysiological meaningfulness for the device to be able to fulfill its rehabilitative purpose. A general scheme is proposed for a hybrid hip-knee-ankle-foot orthosis. The actuation profiles, when muscle tissue is fatigued due to FES actuation are analyzed, and an integrated approach is presented for estimating the actuation profiles so as to overcome muscle peak force reduction during stimulation. The objective is to provide a stimulation profile for each muscle individually that is compatible with the desired kinematics and actuation of the orthosis. The hope is that the results may contribute to the design of subject-specific rehabilitation routines with hybrid exoskeletons, improving the exoskeleton's actuation while maintaining its rehabilitative function.

A Control Scheme That Uses Dynamic Postural Synergies to Coordinate a Hybrid Walking Neuroprosthesis: Theory and Experiments

A hybrid walking neuroprosthesis that combines functional electrical stimulation (FES) with a powered lower limb exoskeleton can be used to restore walking in persons with paraplegia. It provides therapeutic benefits of FES and torque reliability of the powered exoskeleton. Moreover, by harnessing metabolic power of muscles via FES, the hybrid combination has a potential to lower power consumption and reduce actuator size in the powered exoskeleton. Its control design, however, must overcome the challenges of actuator redundancy due to the combined use of FES and electric motor. Further, dynamic disturbances such as electromechanical delay (EMD) and muscle fatigue must be considered during the control design process. This ensures stability and control performance despite disparate dynamics of FES and electric motor. In this paper, a general framework to coordinate FES of multiple gait-governing muscles with electric motors is presented. A muscle synergy-inspired control framework is used to derive the controller and is motivated mainly to address the actuator redundancy issue. Dynamic postural synergies between FES of the muscles and the electric motors were artificially generated through optimizations and result in key dynamic postures when activated. These synergies were used in the feedforward path of the control system. A dynamic surface control technique, modified with a delay compensation term, is used as the feedback controller to address model uncertainty, the cascaded muscle activation dynamics, and EMD. To address muscle fatigue, the stimulation levels in the feedforward path were gradually increased based on a model-based fatigue estimate. A Lyapunov-based stability approach was used to derive the controller and guarantee its stability. The synergy-based controller was demonstrated experimentally on an able-bodied subject and person with an incomplete spinal cord injury.

Model-Based Dynamic Control Allocation in a Hybrid Neuroprosthesis

A hybrid neuroprosthesis that combines human muscle power, elicited through functional electrical stimulation (FES), with a powered orthosis may be advantageous over a sole FES or a powered exoskeleton-based rehabilitation system. The hybrid system can conceivably overcome torque reduction due to FES-induced muscle fatigue by complementarily using torque from the powered exoskeleton. The second advantage of the hybrid system is that the use of human muscle power can supplement the powered exoskeleton's power (motor torque) requirements; thus, potentially reducing the size and weight of a walking restoration system. To realize these advantages, however, it is unknown how to concurrently optimize desired control performance and allocation of control inputs between FES and electric motor. In this paper, a model predictive control-based dynamic control allocation (DCA) is used to allocate control between FES and the electric motor that simultaneously maintain a desired knee angle. The experimental results, depicting the performance of the DCA method while the muscle fatigues, are presented for an able-bodied participant and a participant with spinal cord injury. The experimental results showed that the motor torque recruited by the hybrid system was less than that recruited by the motor-only system, the algorithm can be easily used to allocate more control input to the electric motor as the muscle fatigues, and the muscle fatigue induced by the hybrid system was found to be less than the fatigue induced by sole FES. These results validate the aforementioned advantages of the hybrid system; thus implying the hybrid technology's potential use in walking rehabilitation.

A Nonlinear Dynamics-Based Estimator for Functional Electrical Stimulation: Preliminary Results From Lower-Leg Extension Experiments

Miniature inertial measurement units (IMUs) are wearable sensors that measure limb segment or joint angles during dynamic movements. However, IMUs are generally prone to drift, external magnetic interference, and measurement noise. This paper presents a new class of nonlinear state estimation technique called state-dependent coefficient (SDC) estimation to accurately predict joint angles from IMU measurements. The SDC estimation method uses limb dynamics, instead of limb kinematics, to estimate the limb state. Importantly, the nonlinear limb dynamic model is formulated into state-dependent matrices that facilitate the estimator design without performing a Jacobian linearization. The estimation method is experimentally demonstrated to predict knee joint angle measurements during functional electrical stimulation of the quadriceps muscle. The nonlinear knee musculoskeletal model was identified through a series of experiments. The SDC estimator was then compared with an extended kalman filter (EKF), which uses a Jacobian linearization and a rotation matrix method, which uses a kinematic model instead of the dynamic model. Each estimator's performance was evaluated against the true value of the joint angle, which was measured through a rotary encoder. The experimental results showed that the SDC estimator, the rotation matrix method, and EKF had root mean square errors of 2.70°, 2.86°, and 4.42°, respectively. Our preliminary experimental results show the new estimator's advantage over the EKF method but a slight advantage over the rotation matrix method. However, the information from the dynamic model allows the SDC method to use only one IMU to measure the knee angle compared with the rotation matrix method that uses two IMUs to estimate the angle.

Muscle Synergies Facilitate Computational Prediction of Subject-Specific Walking Motions

Researchers have explored a variety of neurorehabilitation approaches to restore normal walking function following a stroke. However, there is currently no objective means for prescribing and implementing treatments that are likely to maximize recovery of walking function for any particular patient. As a first step toward optimizing neurorehabilitation effectiveness, this study develops and evaluates a patient-specific synergy-controlled neuromusculoskeletal simulation framework that can predict walking motions for an individual post-stroke. The main question we addressed was whether driving a subject-specific neuromusculoskeletal model with muscle synergy controls (5 per leg) facilitates generation of accurate walking predictions compared to a model driven by muscle activation controls (35 per leg) or joint torque controls (5 per leg). To explore this question, we developed a subject-specific neuromusculoskeletal model of a single high-functioning hemiparetic subject using instrumented treadmill walking data collected at the subject's self-selected speed of 0.5 m/s. The model included subject-specific representations of lower-body kinematic structure, foot-ground contact behavior, electromyography-driven muscle force generation, and neural control limitations and remaining capabilities. Using direct collocation optimal control and the subject-specific model, we evaluated the ability of the three control approaches to predict the subject's walking kinematics and kinetics at two speeds (0.5 and 0.8 m/s) for which experimental data were available from the subject. We also evaluated whether synergy controls could predict a physically realistic gait period at one speed (1.1 m/s) for which no experimental data were available. All three control approaches predicted the subject's walking kinematics and kinetics (including ground reaction forces) well for the model calibration speed of 0.5 m/s. However, only activation and synergy controls could predict the subject's walking kinematics and kinetics well for the faster non-calibration speed of 0.8 m/s, with synergy controls predicting the new gait period the most accurately. When used to predict how the subject would walk at 1.1 m/s, synergy controls predicted a gait period close to that estimated from the linear relationship between gait speed and stride length. These findings suggest that our neuromusculoskeletal simulation framework may be able to bridge the gap between patient-specific muscle synergy information and resulting functional capabilities and limitations.

A Muscle Synergy-Inspired Adaptive Control Scheme for a Hybrid Walking Neuroprosthesis

A hybrid neuroprosthesis that uses an electric motor-based wearable exoskeleton and functional electrical stimulation (FES) has a promising potential to restore walking in persons with paraplegia. A hybrid actuation structure introduces effector redundancy, making its automatic control a challenging task because multiple muscles and additional electric motor need to be coordinated. Inspired by the muscle synergy principle, we designed a low dimensional controller to control multiple effectors: FES of multiple muscles and electric motors. The resulting control system may be less complex and easier to control. To obtain the muscle synergy-inspired low dimensional control, a subject-specific gait model was optimized to compute optimal control signals for the multiple effectors. The optimal control signals were then dimensionally reduced by using principal component analysis to extract synergies. Then, an adaptive feedforward controller with an update law for the synergy activation was designed. In addition, feedback control was used to provide stability and robustness to the control design. The adaptive-feedforward and feedback control structure makes the low dimensional controller more robust to disturbances and variations in the model parameters and may help to compensate for other time-varying phenomena (e.g., muscle fatigue). This is proven by using a Lyapunov stability analysis, which yielded semi-global uniformly ultimately bounded tracking. Computer simulations were performed to test the new controller on a 4-degree of freedom gait model.

A semi-active hybrid neuroprosthesis for restoring lower limb function in paraplegics

Through the application of functional electrical stimulation (FES) individuals with paraplegia can regain lost walking function. However, due to the rapid onset of muscle fatigue, the walking duration obtained with an FES-based neuroprosthesis is often relatively short. The rapid muscle fatigue can be compensated for by using a hybrid system that uses both FES and an active orthosis. In this paper, we demonstrate the initial testing of a semi-active hybrid walking neuroprosthesis. The semi-active hybrid orthosis (SEAHO) supports a user during the stance phase and standing while the electric motors attached to the hip section of the orthosis are used to generate hip flexion/extension. FES in SEAHO is mainly used to actuate knee flexion/extension and plantar flexion of the foot. SEAHO is controlled by a finite state machine that uses a recently developed nonlinear controller for position tracking control of the hip motors and cues from the hip angle to actuate FES and other components.

Further Results on Predictor-Based Control of Neuromuscular Electrical Stimulation

Electromechanical delay (EMD) and uncertain nonlinear muscle dynamics can cause destabilizing effects and performance loss during closed-loop control of neuromuscular electrical stimulation (NMES). Linear control methods for NMES often perform poorly due to these technical challenges. A new predictor-based closed-loop controller called proportional integral derivative controller with delay compensation (PID-DC) is presented in this paper. The PID-DC controller was designed to compensate for EMDs during NMES. Further, the robust controller can be implemented despite uncertainties or in the absence of model knowledge of the nonlinear musculoskeletal dynamics. Lyapunov stability analysis was used to synthesize the new controller. The effectiveness of the new controller was validated and compared with two recently developed nonlinear NMES controllers, through a series of closed-loop control experiments on four able-bodied human subjects. Experimental results depict statistically significant improved performance with PID-DC. The new controller is shown to be robust to variations in an estimated EMD value.