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

Joint Trajectory Generation and High-level Control for Patient-tailored Robotic Gait Rehabilitation

This dissertation presents a group of novel methods for robot-based gait rehabilitation which were developed aiming to offer more individualized therapies based on the specific condition of each patient, as well as to improve the overall rehabilitation experience for both patient and therapist. A novel methodology for gait pattern generation is proposed, which offers estimated hip and knee joint trajectories corresponding to healthy walking, and allows the therapist to graphically adapt the reference trajectories in order to fit better the patient's needs and disabilities. Additionally, the motion controllers for the hip and knee joints, mobile platform, and pelvic mechanism of an over-ground gait rehabilitation robotic system are also presented, as well as some proposed methods for assist as needed therapy. Two robot-patient synchronization approaches are also included in this work, together with a novel algorithm for online hip trajectory adaptation developed to reduce obstructive forces applied to the patient during therapy with compliant robotic systems. Finally, a prototype graphical user interface for the therapist is also presented

Hybrid walking therapy with fatigue management for spinal cord injured individuals

In paraplegic individuals with upper motor neuron lesions the descending path for signals from central nervous system to the muscles are lost or diminished. Motor neuroprosthesis based on electrical stimulation can be applied to induce restoration of motor function in paraplegic patients. Furthermore, electrical stimulation of such motor neuroprosthesis can be more efficiently managed and delivered if combined with powered exoskeletons that compensate the limited force in the stimulated muscles and bring additional support to the human body. Such hybrid overground gait therapy is likely to be more efficient to retrain the spinal cord in incomplete injuries than conventional, robotic or neuroprosthetic approaches. However, the control of bilateral joints is difficult due to the complexity, non-linearity and time-variance of the system involved. Also, the effects of muscle fatigue and spasticity in the stimulated muscles complicate the control task. Furthermore, a compliant joint actuation is required to allow for a cooperative control approach that is compatible with the assist-as-needed rehabilitation paradigm. These were direct motivations for this research. The overall aim was to generate the necessary knowledge to design a novel hybrid walking therapy with fatigue management for incomplete spinal cord injured subjects. Research activities were conducted towards the establishment of the required methods and (hardware and software) systems that required to proof the concept with a pilot clinical evaluation. Speciffically, a compressive analysis of the state of the art on hybrid exoskeletons revealed several challenges which were tackled by this dissertation. Firstly, assist-as-needed was implemented over the basis of a compliant control of the robotic exoskeleton and a closed-loop control of the neuroprosthesis. Both controllers are integrated within a hybrid-cooperative strategy that is able to balance the assistance of the robotic exoskeleton regarding muscle performance. This approach is supported on the monitoring of the leg-exoskeleton physical interaction. Thus the fatigue caused by neuromuscular stimulation was also subject of speciffic research. Experimental studies were conducted with paraplegic patients towards the establishment of an objective criteria for muscle fatigue estimation and management. The results of these studies were integrated in the hybrid-cooperative controller in order to detect and manage muscle fatigue while providing walking therapy. Secondly closed-loop control of the neuroprosthesis was addressed in this dissertation. The proposed control approach allowed to tailor the stimulation pattern regarding the speciffic residual motor function of the lower limb of the patient. In order to uncouple the closed-loop control from muscle performance monitoring, the hybrid-cooperative control approach implemented a sequential switch between closed-loop and open-loop control of the neuroprosthesis. Lastly, a comprehensive clinical evaluation protocol allowed to assess the impact of the hybrid walking therapy on the gait function of a sample of paraplegic patients. Results demonstrate that: 1) the hybrid controller adapts to patient residual function during walking, 2) the therapy is tolerated by patients, and 3) the walking function of patients was improved after participating in the study. In conclusion, the hybrid walking therapy holds potential for rehabilitate walking in motor incomplete paraplegic patients, guaranteeing further research on this topic. This dissertation is framed within two research projects: REHABOT (Ministerio de Ciencia e Innovación, grant DPI2008-06772-C03-02) and HYPER (Hybrid Neuroprosthetic and Neurorobotic Devices for Functional Compensation and Rehabilitation of Motor Disorders, grant CSD2009-00067 CONSOLIDER INGENIO 2010). Within these research projects, cutting-edge research is conducted in the eld of hybrid actuation and control for rehabilitation of motor disorders. This dissertation constitutes proof-of concept of the hybrid walking therapy for paraplegic individuals for these projects. ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------En individuos parapléjicos con lesiones de la motoneurona superior, la conexión descendente para la transmisión de las señales del sistema nervioso central a los músculos se ve perdida o disminuida. Las neuroprótesis motoras basadas en la estimulación eléctrica pueden ser aplicadas para inducir la restauración de la función motora en pacientes con paraplejia. Además, la estimulación eléctrica de tales neuroprótesis motoras se puede gestionar y aplicar de manera más eficiente mediante la combinación con exoesqueletos robóticos que compensen la generación limitada de fuerza de los músculos estimulados, y proporcionen soporte adicional para el cuerpo. Dicha terapia de marcha ambulatoria puede ser probablemente más eficaz para la recuperación de las funciones de la médula espinal en lesiones incompletas que las terapias convencionales, robóticas o neuroprotesicas. Sin embargo, el control bilateral de las articulaciones es difícil debido a la complejidad, no-linealidad y la variación con el tiempo de las características del sistema en cuestión. Además, la fatiga muscular y la espasticidad de los músculos estimulados complican la tarea de control. Por otra parte, se requiere una actuación robótica modulable para permitir un enfoque de control cooperativo compatible con el paradigma de rehabilitación de asistencia bajo demanda. Todo lo anterior constituyó las motivaciones directas para esta investigación. El objetivo general fue generar el conocimiento necesario para diseñar un nuevo tratamiento híbrido de rehabilitación marcha con gestión de la fatiga para lesionados medulares incompletos. Se llevaron a cabo actividades de investigación para el establecimiento de los métodos necesarios y los sistemas (hardware y software) requeridos para probar el concepto mediante una evaluación clínica piloto. Específicamente, un análisis del estado de la técnica sobre exoesqueletos híbridos reveló varios retos que fueron abordados en esta tesis. En primer lugar, el paradigma de asistencia bajo demanda se implementó sobre la base de un control adaptable del exoesqueleto robótico y un control en lazo cerrado de la neuroprótesis. Ambos controladores están integrados dentro de una estrategia híbrida cooperativa que es capaz de equilibrar la asistencia del exoesqueleto robótico en relación con el rendimiento muscular. Este enfoque se soporta sobre la monitorización de la interacción física entre la pierna y el exoesqueleto. Por tanto, la fatiga causada por la estimulación neuromuscular también fue objeto de una investigación específica. Se realizaron estudios experimentales con pacientes parapléjicos para el establecimiento de un criterio objetivo para la detección y la gestión de la fatiga muscular. Los resultados de estos estudios fueron integrados en el controlador híbrido-cooperativo con el fin de detectar y gestionar la fatiga muscular mientras se realiza la terapia híbrida de rehabilitación de la marcha. En segundo lugar, el control en lazo cerrado de la neuroprótesis fue abordado en esta tesis. El método de control propuesto permite adaptar el patrón de estimulación en relación con la funcionalidad residual específica de la extremidad inferior del paciente. Sin embargo, con el n de desacoplar el control en lazo cerrado de la monitorización del rendimiento muscular, el enfoque de control híbrido-cooperativo incorpora una conmutación secuencial entre el control en lazo cerrado y en lazo abierto de la neuropr otesis. Por último, un protocolo de evaluación clínica global permitido evaluar el impacto de la terapia híbrida de la marcha en la función de la marcha de una muestra de pacientes parapléjicos. Los resultados demuestran que: 1) el controlador híbrido se adapta a la función residual del paciente durante la marcha, 2) la terapia es tolerada por los pacientes, y 3) la funci on de marcha del paciente mejora despu es de participar en el estudio. En conclusión, la terapia de híbrida de la marcha alberga un potencial para la rehabilitación de la marcha en pacientes parapléjicos incompletos motor, garantizando realizar investigación más profunda sobre este tema. Esta tesis se enmarca dentro de los dos proyectos de investigación: REHABOT (Ministerio de Ciencia e Innovación, referencia DPI2008-06772-C03-02) y HYPER (Hybrid Neuroprosthetic and Neurorobotic Devices for Functional Compensation and Rehabilitation of Motor Disorders, referencia CSD2009-00067 CONSOLIDER INGENIO 2010). Dentro de estos proyectos se lleva a cabo investigación de vanguardia en el campo de la actuación y el control híbrido de la combinación robot-neuroprótesis para la rehabilitación de trastornos motores. Esta tesis constituye la prueba de concepto de la terapia de híbrida de la marcha para individuos parapléjicos en estos proyectos.This dissertation is framed within two research projects: REHABOT (Ministerio de Ciencia e Innovación, grant DPI2008-06772-C03-02) and HYPER (Hybrid Neuroprosthetic and Neurorobotic Devices for Functional Compensation and Rehabilitation of Motor Disorders, grant CSD2009-00067 CONSOLIDER INGENIO 2010

Human-Robot Interaction Strategies for Walker-Assisted Locomotion

Neurological and age-related diseases affect human mobility at different levels causing partial or total loss of such faculty. There is a significant need to improve safe and efficient ambulation of patients with gait impairments. In this context, walkers present important benefits for human mobility, improving balance and reducing the load on their lower limbs. Most importantly, walkers induce the use of patients residual mobility capacities in different environments. In the field of robotic technologies for gait assistance, a new category of walkers has emerged, integrating robotic technology, electronics and mechanics. Such devices are known as robotic walkers, intelligent walkers or smart walkers One of the specific and important common aspects to the field of assistive technologies and rehabilitation robotics is the intrinsic interaction between the human and the robot. In this thesis, the concept of Human-Robot Interaction (HRI) for human locomotion assistance is explored. This interaction is composed of two interdependent components. On the one hand, the key role of a robot in a Physical HRI (pHRI) is the generation of supplementary forces to empower the human locomotion. This involves a net flux of power between both actors. On the other hand, one of the crucial roles of a Cognitive HRI (cHRI) is to make the human aware of the possibilities of the robot while allowing him to maintain control of the robot at all times. This doctoral thesis presents a new multimodal human-robot interface for testing and validating control strategies applied to a robotic walkers for assisting human mobility and gait rehabilitation. This interface extracts navigation intentions from a novel sensor fusion method that combines: (i) a Laser Range Finder (LRF) sensor to estimate the users legs kinematics, (ii) wearable Inertial Measurement Unit (IMU) sensors to capture the human and robot orientations and (iii) force sensors measure the physical interaction between the humans upper limbs and the robotic walker. Two close control loops were developed to naturally adapt the walker position and to perform body weight support strategies. First, a force interaction controller generates velocity outputs to the walker based on the upper-limbs physical interaction. Second, a inverse kinematic controller keeps the walker within a desired position to the human improving such interaction. The proposed control strategies are suitable for natural human-robot interaction as shown during the experimental validation. Moreover, methods for sensor fusion to estimate the control inputs were presented and validated. In the experimental studies, the parameters estimation was precise and unbiased. It also showed repeatability when speed changes and continuous turns were performed

Design of a new approach to register biomechanical gait data, when combining lower limb powered exoskeletons controlled by neural machine interfaces and transcutaneous spinal current stimulation

To analyze the effect of robotic-aided gait rehabilitation controlled with brain-machine interfaces, it is necessary to ensure a strategy to assess gait biomechanics recording data that is not disturbed by the rehabilitation technologies. To this end, a protocol to measure the kinematics of the lower extremities on the three planes based on Inertial Measurement Units (IMUs) is developed. To evaluate the IMUs system accuracy and reliability, it is validated with a high-precision reference device, an optoelectronic system. The validation of the protocol is performed in one healthy subject in two steps: 1) testing four different configurations of the IMUs to identify the optimal gait data registration model, including the number and location of sensors, since these affect the system's output, and 2) validation of IMUs with Vicon through synchronously walking records (Condition 1) and exoskeleton-assisted walking (Condition 2). The within-day multiple correlation coefficients (CMCw) from Kadaba and its reformulation, the inter-protocol CMC (CMCp), are used respectively for Part 1 and Part 2 to assess the waveform similarity of each lower limb joint angle, removing the between-gait-cycle variability. In addition, other parameters are studied to assess the technological error and the differences between the biomechanical models, such as Pearson's correlation, range of motion, offset, and the Root Mean Square Error. For Part 1, it is concluded that the optimal configuration for the rest of the project is Model 2, showing good CMCw values for every joint angle (CMCw ≥ 0.8). During the walking test (Part 2, Condition 1) the CMCp shows that gait kinematics measured by both systems for the right limb are equivalent, demonstrating IMUs accuracy, for the hip and the knee flexion/extension (CMCp = 1), and for the knee adduction/abduction (CMCp = 0.91). For exoskeleton-assisted walking (Part 2, Condition 2), after adjusting the position of the IMUs located at the ankles, the gait kinematics for the right limb are equivalent for every joint in the sagittal plane (CMCp ≥ 0.9), for the knee and the ankle in frontal plane (CMCp ≥ 0.95), and for the hip in transversal plane (CMCp = 0.99)Para analizar el efecto de la rehabilitación de la marcha asistida por robots controlada con interfaces cerebro-máquina, es necesario garantizar una estrategia para evaluar los datos de registro de la biomecánica de la marcha de forma que no estén alterados por las tecnologías de rehabilitación. Para ello, se desarrolla un protocolo para medir la cinemática de las extremidades inferiores en los tres planos basado en Unidades de Medición Inercial (IMUs). Para evaluar la precisión y fiabilidad del sistema de IMUs, se valida con un dispositivo de referencia de alta precisión, un sistema optoelectrónico. La validación del protocolo se realiza en un sujeto sano en dos pasos: 1) prueba de cuatro configuraciones diferentes de las IMUs para identificar el modelo óptimo de registro de datos de la marcha, incluyendo el número y la ubicación de los sensores, ya que estos afectan a la salida del sistema, y 2) validación de las IMUs con Vicon a través de registros sincronizados de marcha (Condición 1) y marcha asistida por exoesqueleto (Condición 2). Los coeficientes de correlación múltiple dentro del día (CMCw) de Kadaba y su reformulación, el CMC interprotocolo (CMCp), se utilizan respectivamente en la Parte 1 y la Parte 2 para evaluar la similitud de la forma de onda de cada ángulo articular de la extremidad inferior, eliminando la variabilidad entre ciclos de la marcha. Además, se estudian otros parámetros para evaluar el error tecnológico y las diferencias entre los modelos biomecánicos, como la correlación de Pearson, el rango de movimiento, el desplazamiento y el error cuadrático medio. Para la Parte 1, se concluye que la configuración óptima para el resto del proyecto es el Modelo 2, mostrando buenos valores de CMCw para cada ángulo articular (CMCw ≥ 0.8). Durante la prueba de marcha (Parte 2, Condición 1), el CMCp muestra que la cinemática de la marcha medida por ambos sistemas para la extremidad derecha es equivalente, demostrando la precisión de las IMUs, para la flexo-extensión de la cadera y la rodilla (CMCp = 1), y para la aducción/abducción de la rodilla (CMCp = 0.91). Para la marcha asistida por exoesqueleto (Parte 2, Condición 2), tras ajustar la posición de las IMUs situadas en los tobillos, la cinemática de la marcha para la extremidad derecha es equivalente para cada articulación en el plano sagital (CMCp ≥ 0.9), para la rodilla y el tobillo en el plano frontal (CMCp ≥ 0.95), y para la cadera en el plano transversal (CMCp = 0.99)Per analitzar l'efecte de la rehabilitació de la marxa assistida per robòtica controlada amb interfícies cervell-màquina, cal garantir una estratègia per avaluar la biomecànica de la marxa registrant dades que no es vegi alterada per les tecnologies de rehabilitació. Amb aquesta finalitat, es desenvolupa un protocol per mesurar la cinemàtica de les extremitats inferiors en els tres plans basat en Unitats de Mesurament Inercial (IMU). Per avaluar la precisió i la fiabilitat del sistema IMU, es valida amb un dispositiu de referència d'alta precisió, un sistema optoelectrònic. La validació del protocol es realitza en un subjecte sa en dos passos: 1) provant quatre configuracions diferents de les IMU per identificar el model òptim de registre de dades de la marxa, inclòs el nombre i la ubicació dels sensors, ja que aquests afecten la sortida del sistema, i 2 ) validació de les IMU amb Vicon mitjançant registres de marxa sincrònica (Condició 1) i caminada assistida per exoesquelet (Condició 2). Els coeficients de correlació múltiple d'un dia (CMCw) de Kadaba i la seva reformulació, el CMC interprotocol (CMCp), s'utilitzen respectivament per a la part 1 i la part 2 per avaluar la similitud de la forma d'ona de cada angle d'articulació de l'extremitat inferior, eliminant l'entre- variabilitat del cicle de la marxa. A més, s'estudien altres paràmetres per avaluar l'error tecnològic i les diferències entre els models biomecànics, com ara la correlació de Pearson, el rang de moviment, l'offset i l'error quadràtic mitjà. Per a la part 1, es conclou que la configuració òptima per a la resta del projecte és el model 2, que mostra bons valors de CMCw per a cada angle d'articulació (CMCw ≥ 0,8). Durant la prova de marxa (part 2, condició 1), el CMCp mostra que la cinemàtica de la marxa mesurada pels dos sistemes per a l'extremitat dreta és equivalent, demostrant la precisió de les IMU, per al maluc i la flexió/extensió del genoll (CMCp = 1) i per a la adducció/abducció del genoll (CMCp = 0,91). Per a la marxa assistida per exoesquelet (Part 2, Condició 2), després d'ajustar la posició de les IMU situades als turmells, la cinemàtica de la marxa de l'extremitat dreta és equivalent per a cada articulació del pla sagital (CMCp ≥ 0,9), per al genoll. i el turmell en pla frontal (CMCp ≥ 0,95), i per al maluc en pla transversal (CMCp = 0,99