Switched Kinematic and Force Control for Lower-Limb Motorized Exoskeletons and Functional Electrical Stimulation

Millions of people experience movement deficits from neurological conditions (NCs) that impair their walking ability and leg function. Exercise-based rehabilitation procedures have shown the potential to facilitate neurological reorganization and functional recovery. Lower-limb powered exoskeletons and motorized ergometers have been combined with functional electrical stimulation (FES) to provide repetitive movement, partially reduce the burden of therapists, improve range of motion, and induce therapeutic benefits. FES evokes artificial muscles contractions and can improve muscle mass and strength, and bone density in people with NCs. Stationary cycling is recommended for individuals who cannot perform load-bearing activities or have increased risks of falling. Cycling has been demonstrated to impart physiological and cardiovascular benefits. Motorized FES-cycling combines an electric motor and electrical stimulation of lower-limb muscles to facilitate coordinated, long-duration exercise, while mitigating the inherent muscle fatigue due to FES. Lower-limb exoskeletons coupled with FES, also called neuroprostheses or hybrid exoskeletons, can facilitate continuous, repetitive motion to improve gait function and build muscle capacity. The human-robot interaction during rehabilitative cycling and walking yield a mix of discrete effects (i.e., foot impact, input switching to engage lower-limb muscles and electric motors, etc.) and continuous nonlinear, uncertain, time-varying dynamics. Switching control is necessary to allocate the control inputs to lower-limb muscle groups and electric motors involved during assisted cycling and walking. Kinematic tracking has been the primary control objective for devices that combine FES and electric motors. However, there are force interactions between the machine and the human during cycling and walking that motivate the design of torque-based controllers (i.e., exploit torque or force feedback) to shape the leg dynamics through controlling joint kinematics and kinetics. Technical challenges exist to develop closed-loop feedback control strategies that integrate kinematic and force feedback in the presence of switching and discontinuous effects. The motivation in this dissertation is to design, analyze and implement switching controllers for assisted cycling and walking leveraging kinematic and force feedback while guaranteeing the stability of the human-robot closed-loop system. In Chapter 1, the motivation to design closed-loop controllers for motorized FES-cycling and powered exoskeletons is described. A survey of closed-loop kinematic and force feedback control methods is also introduced related to the tracking objectives presented in the subsequent chapters of the dissertation. In Chapter 2, the dynamics models for walking and assisted cycling are described. First, a bipedal walking system model with switched dynamics is introduced to control a powered lower-limb exoskeleton. Then, a stationary FES-cycling model with nonlinear dynamics and switched control inputs is introduced based on published literature. The muscle stimulation pattern is defined based on the kinematic effectiveness of the rider, which depends on the crank angle. The experimental setup for lower-limb exoskeleton and FES-cycling are described. In Chapter 3, a hierarchical control strategy is developed to interface a cable-driven lower-limb exoskeleton. A two-layer control system is developed to adjust cable tensions and apply torque about the knee joint using a pair of electric motors that provide knee flexion and extension. The control design is segregated into a joint-level control loop and a low-level loop using feedback of the angular positions of the electric motors to mitigate cable slacking. A Lyapunov-based stability analysis is developed to ensure exponential tracking for both control objectives. Moreover, an average dwell time analysis computes an upper bound on the number of motor switches to preserve exponential tracking. Preliminary experimental results in an able-bodied individual are depicted. The developed control strategy is extended and applied to the control of both knee and hip joints in Chapter 4 for treadmill walking. In Chapter 4, a cable-driven lower-limb exoskeleton is integrated with FES for treadmill walking at a constant speed. A nonlinear robust controller is used to activate the quadriceps and hamstrings muscle groups via FES to achieve kinematic tracking about the knee joint. Moreover, electric motors adjust the knee joint stiffness throughout the gait cycle using an integral torque feedback controller. A Lyapunov-based stability analysis is developed to ensure exponential tracking of the kinematic and torque closed-loop error systems, while guaranteeing that the control input signals remain bounded. The developed controllers were tested in real-time walking experiments on a treadmill in three able-bodied individuals at two gait speeds. The experimental results demonstrate the feasibility of coupling a cable-driven exoskeleton with FES for treadmill walking using a switching-based control strategy and exploiting both kinematic and force feedback. In Chapter 5, input-output data is exploited using a finite-time algorithm to estimate the target desired torque leveraging an estimate of the active torque produced by muscles via FES. The convergence rate of the finite-time algorithm can be adjusted by tuning selectable parameters. To achieve cadence and torque tracking for FES-cycling, nonlinear robust tracking controllers are designed for muscles and motor. A Lyapunov-based stability analysis is developed to ensure exponential tracking of the closed-loop cadence error system and global uniformly ultimate bounded (GUUB) torque tracking. A discrete-time Lyapunov-based stability analysis leveraging a recent tool for finite-time systems is developed to ensure convergence and guarantee that the finite-time algorithm is Holder continuous. The developed tracking controllers for the muscles and electric motor and finite-time algorithm to compute the desired torque are implemented in real-time during cycling experiments in seven able-bodied individuals. Multiple cycling trials are implemented with different gain parameters of the finite-time torque algorithm to compare tracking performance for all participants. Chapter 6 highlights the contributions of the developed control methods and provides recommendations for future research extensions

Switching Adaptive Concurrent Learning Control for Powered Rehabilitation Machines with FES

Interfacing robotic devices with humans presents significant control challenges, as the control algorithms governing these machines must accommodate for the inherent variability among individuals. This requirement necessitates the system’s ability to adapt to changes in the environment, particularly in the context of human-in-the-loop applications, wherein the system must identify specific features of the human interacting with the machine. In the field of rehabilitation, one promising approach for exercise-based rehabilitation involves the integration of hybrid rehabilitation machines, combining robotic devices such as motorized bikes and exoskeletons with functional electrical stimulation (FES) applied on lower-limb muscles. This integrated approach offers the potential for repetitive training, reduced therapist workload, improved range of motion, and therapeutic benefits. However, conducting prolonged rehabilitation sessions to maximize functional recovery using these hybrid machines imposes several difficulties. Firstly, the design and analysis of adaptive controllers are motivated, but challenges exist in coping with the inherent switching effects associated with hybrid machines. Notably, the transitions between gait phases and the dynamic switching of inputs between active lower-limb muscles and electric motors and their incorporation in the control design remain an open problem for the research community. Secondly, the system must effectively compensate for the influence of human input, which can be viewed as an external disturbance in the closed-loop system during rehabilitation. Robust methods for understanding and adapting to the variations in human input are critical for ensuring stability and accurate control of the human-robot closed-loop system. Lastly, FES-induced muscle fatigue diminishes the human torque contribution to the rehabilitation task, leading to input saturation and potential instabilities as the duration of the exercise extends. Overcoming this challenge requires the development of control algorithms that can adapt to variations in human performance by dynamically adjusting the control parameters accordingly. Consequently, the development of rehabilitative devices that effectively interface with humans requires the design and implementation of control algorithms capable of adapting to users with varying muscle and kinematic characteristics. In this regard, adaptive-based control methods provide tools for addressing the uncertainties in human-robot dynamics within exercise-based rehabilitation using FES, while ensuring stability and robustness in the human-robot closed-loop system. This dissertation develops adaptive controllers to enhance the effectiveness of exercise-based rehabilitation using FES. The objectives include the design and evaluation of adaptive control algorithms that effectively handle the switching effects inherent in hybrid machines, adapt to compensate for human input, and account for input saturation due to muscle fatigue. The control designs leverage kinematic and torque feedback and ensure the stability of the human-robot closed-loop system. These controllers have the potential to significantly enhance the practicality and effectiveness of assistive technologies in both clinical and community settings. In Chapter 1, the motivation to design switching adaptive closed-loop controllers for motorized FES-cycling and powered exoskeletons is described. A survey of closed-loop kinematic control methods related to the tracking objectives in the subsequent chapters of the dissertation is also introduced. In Chapter 2, the dynamic models for cycling and bipedal walking are described: (i) a stationary FES-cycling model with nonlinear dynamics and switched control inputs are introduced based on published literature. The muscle stimulation pattern is defined based on the kinematic effectiveness of the rider, which depends on the crank angle. (ii) A phase-dependent bipedal walking system model with switched dynamics is introduced to control a 4-degrees-of-freedom (DoF) lower-limb exoskeleton assuming single stance support. Moreover, the experimental setup of the cycle-rider and lower-limb exoskeleton system are described. Chapter 3 presents a switched concurrent learning adaptive controller for cadence tracking using the cycle-rider model. The control design is decoupled for the muscles and electric motor. An FES controller is developed with minimal parameters, capable of generating bounded muscle responses with an adjustable saturation limit. The electric motor controller employs an adaptive-based method that estimates uncertain parameters in the cycle-rider system and leverages the muscle input as a feedforward term to improve the tracking of crank trajectories. The adaptive motor controller and saturated muscle controller are implemented in able-bodied individuals and people with movement disorders. Three cycling trials were conducted to demonstrate the feasibility of tracking different crank trajectories with the same set of control parameters across all participants. The developed adaptive controller requires minimal tuning and handles rider uncertainty while ensuring predictable and satisfactory performance. This result has the potential to facilitate the widespread implementation of adaptive closed-loop controllers for FES-cycling systems in real clinical and home-based scenarios. Chapter 4 presents an integral torque tracking controller with anti-windup compensation, which achieves the dual objectives of kinematic and torque tracking (i.e., power tracking) for FES cycling. Designing an integral torque tracking controller to avoid feedback of high-order derivatives poses a significant challenge, as the integration action in the muscle loop can induce error buildup; demanding high FES input on the muscle. This can cause discomfort and accelerate muscle fatigue, thereby limiting the practical utility of the power tracking controller. To address this issue, this chapter builds upon the adaptive control for cadence tracking developed in Chapter 3 and integrates a novel torque tracking controller that allows for input saturation in the FES controller. By doing so, the controller achieves cadence and torque tracking while preventing error buildup. The analysis rigorously considers the saturation effect, and preliminary experimental results in able-bodied individuals demonstrate its feasibility. In Chapter 5, a switched concurrent learning adaptive controller is developed to achieve kinematic tracking throughout the step cycle for treadmill-based walking with a 4-DoF lower-limb hybrid exoskeleton. The developed controller leverages a phase-dependent human-exoskeleton model presented in Chapter 2. A multiple-Lyapunov stability analysis with a dwell time condition is developed to ensure exponential kinematic tracking and parameter estimation. The controller is tested in two able-bodied individuals for a six-minute walking trial and the performance of the controller is compared with a gradient descent classical adaptive controller. Chapter 6 highlights the contributions of the developed control methods and provides recommendations for future research directions

Feedback control of cycling in spinal cord injury using functional electrical stimulation

This thesis is concerned with the realisation of leg cycling by means of FES in SCI individuals with complete paraplegia. FES lower-limb cycling can be safely performed by paraplegics on static ergometers or recumbent tricycles. In this work, different FES cycling systems were developed for clinical and home use. Two design approaches have been followed. The first is based on the adaptation of commercially available recumbent tricycles. This results in devices which can be used as static trainers or for mobile cycling. The second design approach utilises a commercially available motorised ergometer which can be operated while sitting in a wheelchair. The developed FES cycling systems can be operated in isotonic (constant cycling resistance) or isokinetic mode (constant cadence) when used as static trainers. This represents a novelty compared to existing FES cycling systems. In order to realise isokinetic cycling, an electric motor is needed to assist or resist the cycling movement to maintain a constant cadence. Repetitive control technology is applied to the motor in this context to virtually eliminate disturbance caused by the FES activated musculature which are periodic with respect to the cadence. Furthermore, new methods for feedback control of the patient’s work rate have been introduced. A one year pilot study on FES cycling with paraplegic subjects has been carried out. Effective indoor cycling on a trainer setup could be achieved for long periods up to an hour, and mobile outdoor cycling was performed over useful distances. Power output of FES cycling was in the range of 15 to 20 W for two of the three subjects at the end of the pilot study. A muscle strengthening programme was carried out prior and concurrent to the FES cycling. Feedback control of FES assisted weight lifting exercises by quadriceps stimulation has been studied in this context

Control strategies for functional electrical stimulation induced cycling

Functional Electrical Stimulation cycling ergometers and mobile cycling systems have been developed over a number of years to allow Spinal Cord Injured persons to exercise. Standard able bodied exercise tests are adapted and applied to paraplegic cyclists. A modified recumbent tricycle is instrumentated with an electric motor and sensors to measure cadence and the power produced by the cyclist at the crank. They are then integrated to a stimulator and a laptop computer. The tricycle is mounted on an indoor cycling trainer to provide a novel test bed for the implementation of exercise testing. Controllers are desired to control cadence and power during cycling. Identification of input-output data for the cadence-motor loop and the power-stimulation loop is undertaken. Three muscle groups are stimulated on a paraplegic subject to produce power. Models are identified of the power and cadence systems. Thereafter controllers are designed, via polynomial methods. The results show that the controllers are robust during cadence tracking, power tracking and for disturbance rejection. The controllers can be accurately applied to exercise testing protocols. The concept of VO2 control is induced. VO2 is the rate of oxygen uptake during exercise. VO2-power dynamics are identified and as before a model is fitted to the measured data. Controllers are designed and further modified, as the understanding of the VO2 dynamics is developed. This is through a series of tests to improve the accuracy of the control. The results illustrate that VO2 control is a novel and practical application. These findings develop the field of functional Electrical Stimulation Induced Cycling within the laboratory. However further work is required to develop this application outside laboratory conditions

Robust Compensation of Electromechanical Delay during Neuromuscular Electrical Stimulation of Antagonistic Muscles

Neuromuscular electrical stimulation (NMES) can potentially be used to restore the limb function in persons with neurological disorders, such as spinal cord injury (SCI), stroke, etc. Researches on control system design has so far focused on relatively simple unidirectional NMES applications requiring stimulation of single muscle group. However, for some advanced tasks such as pedaling or walking, stimulation of multiple muscles is required. For example, to extend as well as flex a limb joint requires electrical stimulation of an antagonistic muscle pair. This is due to the fact that muscles are unidirectional actuators. The control challenge is to allocate control inputs to antagonist muscles based on the system output, usually a limb angle error to achieve a smooth and precise transition between antagonistic muscles without causing discontinuities. Furthermore, NMES input to each muscle is delayed by an electromechanical delay (EMD), which arises due to the time lag between the electrical excitation and the force development in muscle. And EMD is known to cause instability or performance loss during closed-loop control of NMES. In this thesis, a robust delay compensation controller for EMDs in antagonistic muscles is presented. A Lyapunov stability analysis yields uniformly ultimately bounded tracking for a human limb joint actuated by antagonistic muscles. The simulation results indicate that the controller is robust and effective in switching between antagonistic muscles and compensating EMDs during a simulated NMES task. Further experiments on a dual motor testbed shows its feasibility as an NMES controller for human antagonistic muscles

The application of estimation and control techniques in 2 modes of exercise for the spinal cord injured

A spinal cord injury (SCI) can result in a loss of sensory and motor capacity, dysfunction of the autonomic nervous system and also in a number of secondary health conditions including muscular atrophy, cardiovascular disease and osteoporosis. The impact of these secondary health conditions may be reduced through exercise which loads the muscles, skeleton and central cardiovascular system. A number of new exercise methods are emerging in the field of rehabilitation. Functional electrical stimulation (FES) is a technique for inducing artificial muscular contractions that has been applied to facilitate cycling amongst adults with a spinal cord injury. Preliminary data has demonstrated the feasibility of FES cycling in the paediatric SCI population. The use of an electric motor to provide torque assistance where required allows the exercise to continue for longer periods and over a wider range of cadences. In this thesis, a feedback control system is devised whereby the cadence can be automatically controlled to reference levels using such a motor, and tested during FES cycling of children with an SCI. The use of robot-assisted body weight supported devices is gaining popularity in the rehabilitation world. Their application has thus far been focused on rehabilitation of gait via neural re-learning. However, robot-assisted gait can also elicit a significant cardiovascular response and thus has potential as a tool for exercise training and testing. In this thesis, a method for estimating the work rate contributed by an exercising subject is developed and then incorporated into a feedback control scheme where the objective is to regulate the work rate to reference values. This enables specific work rate profiles to be performed during robot-assisted gait as is often required for standard exercise tests and training. In addition to controlling the mechanical variables during exercise, it is also possible to control some of the physiological variables. A feedback system whose goal is to control the rate of oxygen uptake rate is developed which also incorporates the work rate control method. This allows a predetermined level of physiological response to be achieved so that the training is of sufficient intensity to promote improvements in physical capacity and fitness. This thesis examines the application of estimation and control techniques in two exercise modes for the spinal cord injured. The ultimate aim of the exercise is to reduce the severity of the secondary health conditions that spinal cord injured people face. The estimation and control algorithms allow the exercise to be regulated with respect to speed and intensity and therefore have utility in both training and testing applications

Cadence and range of motion modulate pedal force in a rat model of motorized cycling after spinal cord injury.

Motorized cycling (MC) can be utilized post-spinal cord injury (SCI) in patients who lack the strength and/or stability to participate in traditional physical exercise interventions. MC has been applied with the goal of improving locomotor function or cardiovascular health in both human and animal models of SCI. However, a discrepancy exists between the results of human and animal studies of MC, particularly regarding cardiovascular outcomes. Despite the abundance of studies in both humans and animals, the mechanism behind the improvements in cardiovascular function following MC are poorly understood. We posited that increased venous return during MC is likely due to the skeletal muscle pump, where muscle activity during MC would be triggered by stretch reflexes. As stretch reflexes are dependent on both rate and length of muscle stretch, we hypothesized that cycling cadence and crank length could modulate muscle activity and therefore hindlimb loading during cycling. Initial studies testing the development of the instrumented pedals noted spasticity that was represented in the force traces, and a filtering technique was developed to separate spastic from non-spastic forces. Results using this technique combined with EMG of a knee flexor and extensor suggest that higher cadences (≥30 RPM) increased RMS EMG and non-spastic forces, while lower cadences (≤15 RPM) increased spastic forces. Furthermore, large spastic events were associated with a decrease in BP, while high cadence cycling with limited spasticity appeared to elevate BP and HR above baseline levels. These results suggest that MC in rats may constitute a mild eccentric training regimen; clinical translation may therefore be dependent on the ability to reflexively generate muscle contraction in patients during cycling

Mechanisms of Sensorimotor Impairment in Multiple Sclerosis

Sensorimotor impairments in people with multiple sclerosis (MS) might alter coordination and balance strategy during functional movements. People with MS often have symptoms such as weakness and discoordination in the lower limbs, resulting in poor walking and balance function. This decrease in function can result in falls, decreased community activity, unemployment, and reduced quality of life. As MS is a progressive disease resulting in a range of dysfunction, the amount of lower limb impairment can cause changes to walking and balance strategies to maintain functional performance. The overall objective of this dissertation was to quantify the impairment at the hip and ankle, and characterize the effects of impairment on walking and balance in MS. To quantify the lower limb impairment, a custom-built robot was used to impose movement to the legs about the hip and ankle joint separately. Joint torque and work done were used as quantitative measures of strength during isometric contraction and coordination during subject assisted leg movements in MS and healthy control subjects. To characterize the effect of impairment on functional movements, motion analysis was used to record kinematic and kinetic parameters during overground walking and during a challenging arm tracking task in standing. Hip and ankle sagittal moments were used to quantify the contribution of each joint to functional movement. The findings from these studies suggest that there is a greater sensorimotor impairment at the ankle than the hip in MS, resulting in a reduced reliance on the ankle during walking and an increased hip versus ankle strategy during upper body movements. This was observed by increased negative work at the ankle during assisted bilateral leg movements, reduced ankle moments during stance in gait, and increased hip versus ankle contribution during arm tracking movements in standing. These results indicate that differential impairment between the hip and ankle can drive changes to walking and balance strategy to maintain functional performance, highlighting the importance of joint specific rehabilitation methods in improving function in MS