A Nonlinear Optimal Control Approach for a Lower-Limb Robotic Exoskeleton

The use of robotic limb exoskeletons is growing fast either for rehabilitation purposes or in an aim to enhance human ability for lifting heavy objects or for walking for long distances without fatigue. The paper proposes a nonlinear optimal control approach for a lower-limb robotic exoskeleton. The method has been successfully tested so far on the control problem of several types of robotic manipulators and this paper shows that it can also provide an optimal solution to the control problem of limb robotic exoskeletons. To implement this control scheme, the state-space model of the lower-limb robotic exoskeleton undergoes first approximate linearization around a temporary operating point, through first-order Taylor series expansion and through the computation of the associated Jacobian matrices. To select the feedback gains of the H-infinity controller an algebraic Riccati equation is solved at each time-step of the control method. The global stability properties of the control loop are proven through Lyapunov analysis. Finally, to implement state estimation-based feedback control, the H-infinity Kalman Filter is used as a robust state estimator

Two-link lower limb exoskeleton model control enhancement using computed torque

Robotic technology has recently been used to help stroke patients with gait and balance rehabilitation. Rehabilitation robots such as gait trainers are designed to assist patients in systematic, repetitive training sessions to speed up their recovery from injuries. Several control algorithms are commonly used on exoskeletons, such as proportional, integral and derivative (PID) as linear control. However, linear control has several disadvantages when applied to the exoskeleton, which has the problem of uncertainties such as load and stiffness variations of the patient’s lower limb. To improve the lower limb exoskeleton for the gait trainer, the computed torque controller (CTC) is introduced as a control approach in this study. When the dynamic properties of the system are only partially known, the computed torque controller is an essential nonlinear controller. A mathematical model forms the foundation of this controller. The suggested control approach’s effectiveness is evaluated using a model or scaled-down variation of the method. The performance of the suggested calculated torque control technique is then evaluated and contrasted with that of the PID controller. Because of this, the PID controller’s steady-state error in the downward direction can reach 5.6%, but the CTC can lower it to 2.125%

Second Order Integral Fuzzy Logic Control Based Rocket Tracking Control

Fuzzy logic is a logic that has a degree of membership in the vulnerable 0 to 1. Fuzzy logic is used to translate a quantity that is expressed using language. Fuzzy logic is used as a control system because this control process is relatively easy and flexible to design without involving complex mathematical models of the system to be controlled. The purpose of this paper is to present a fuzzy control system implemented in a rocket tracking control system. The fuzzy control system is used to keep the rocket on track and traveling at a certain speed. The signal from the fuzzy logic control system is used to control the rocket thrust. The fuzzy Logic System was chosen as the controller because it is able to work well on non-linear systems and offers convenience in program design. Fuzzy logic systems have a weakness when working on systems that require very fast control such as rockets. With this problem, fuzzy logic is modified by adding second-order integral control to the modified fuzzy logic. The proposed algorithm shows that the missile can slide according to the ramp path at 12 m altitude of 12.78 at 12 seconds with a steady-state error of 0.78 under FLC control, at 10 m altitude of 10.68 at 10 seconds with a steady-state error of 0.68 with control integral FCL, at a height of 4 m is 4.689 at 4 seconds with a steady-state error of 0.689 with a second-order integral control of FCL. The missile can also slide according to the parabolic path with the second-order integral control of FCL at an altitude of 15.47 in the 4th minute with a steady-state error of 0

Disturbance Observer-based Robust Control and Its Applications: 35th Anniversary Overview

Disturbance Observer has been one of the most widely used robust control tools since it was proposed in 1983. This paper introduces the origins of Disturbance Observer and presents a survey of the major results on Disturbance Observer-based robust control in the last thirty-five years. Furthermore, it explains the analysis and synthesis techniques of Disturbance Observer-based robust control for linear and nonlinear systems by using a unified framework. In the last section, this paper presents concluding remarks on Disturbance Observer-based robust control and its engineering applications.Comment: 12 pages, 4 figure

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

Design, modeling, and control of a variable stiffness elbow joint

New technological advances are changing the way robotics are designed for safe and dependable physical human–robot interaction and human-like prosthesis. Outstanding examples are the adoption of soft covers, compliant transmission elements, and motion control laws that allow compliant behavior in the event of collisions while preserving accuracy and performance during motion in free space. In this scenario, there is growing interest in variable stiffness actuators (VSAs). Herein, we present a new design of an anthropomorphic elbow VSA based on an architecture we developed previously. A robust dynamic feedback linearization algorithm is used to achieve simultaneous control of the output link position and stiffness. This actuation system makes use of two compliant transmission elements, characterized by a nonlinear relation between deflection and applied torque. Static feedback control algorithms have been proposed in literature considering purely elastic transmission; however, viscoelasticity is often observed in practice. This phenomenon may harm the performance of static feedback linearization algorithms, particularly in the case of trajectory tracking. To overcome this limitation, we propose a dynamic feedback linearization algorithm that explicitly considers the viscoelasticity of the transmission elements, and validate it through simulations and experimental studies. The results are compared with the static feedback case to showcase the improvement in trajectory tracking, even in the case of parameter uncertainty

Configuration-Dependent Optimal Impedance Control of an Upper Extremity Stroke Rehabilitation Manipulandum

Robots are becoming a popular means of rehabilitation since they can decrease the laborious work of a therapist, and associated costs, and provide well-controlled repeatable tasks. Many researchers have postulated that human motor control can be mathematically represented using optimal control theories, whereby some cost function is effectively maximized or minimized. However, such abilities are compromised in stroke patients. In this study, to promote rehabilitation of the stroke patient, a rehabilitation robot has been developed using optimal control theory. Despite numerous studies of control strategies for rehabilitation, there is a limited number of rehabilitation robots using optimal control theory. The main idea of this work is to show that impedance control gains cannot be kept constant for optimal performance of the robot using a feedback linearization approach. Hence, a general method for the real-time and optimal impedance control of an end-effector-based rehabilitation robot is proposed. The controller is developed for a 2 degree-of-freedom upper extremity stroke rehabilitation robot, and compared to a feedback linearization approach that uses the standard optimal impedance derived from covariance propagation equations. The new method will assign optimal impedance gains at each configuration of the robot while performing a rehabilitation task. The proposed controller is a linear quadratic regulator mapped from the operational space to the joint space. Parameters of the two controllers have been tuned using a unified biomechatronic model of the human and robot. The performances of the controllers were compared while operating the robot under four conditions of human movements (impaired, healthy, delayed, and time-advanced) along a reference trajectory, both in simulations and experiments. Despite the idealized and approximate nature of the human-robot model, the proposed controller worked well in experiments. Simulation and experimental results with the two controllers showed that, compared to the standard optimal controller, the rehabilitation system with the proposed optimal controller is assisting more in the active-assist therapy while resisting in active-constrained case. Furthermore, in passive therapy, the proposed optimal controller maintains the position error and interaction forces in safer regions. This is the result of updating the impedance in the operational space using a linear time-variant impedance model