Designing a backstepping sliding mode controller for an assistant human knee exoskeleton based on nonlinear disturbance observer☆
Introduction
The knee exoskeleton is a simple exoskeleton which add power to the knee so as to assist flexion and extension of the knee in the sagittal plane [1]. This exoskeleton consists of a linear series elastic actuator (SEA) connected to the upper and lower portions of the knee brace [2]. By applying power to the knee joint, this device can allow greater control on gains, while exhibiting a physically low-impedance interface to the wearer, and remaining safe to the operator. Moreover, the knee exoskeleton is used in cases with musculoskeletal disorders at the knee joint . This kind of exoskeleton can be used for rehabilitation or assistance purposes to strengthen or aid damaged limb function [3]. As an example, in patients with osteoarthritis, which affects the ligaments or cartilages, this exoskeleton can be used to strengthen the muscles, reduce the stiffness and provide joint stabilization. Similarly, after total arthroplasty, the knee exoskeleton is used to reduce knee stiffness and increase knee range of motion by performing static progressive stretch. Furthermore, patients who have had a stroke, or those with spinal cord or traumatic injuries can use an exoskeleton to regain control of their limbs and perform daily activities [4].
A single axis knee joint is a common structure in existing knee exoskeletons [5], [6]. Regarding single-joint artificial orthotics, a simple hinge structure is used that can be constructed easily and have good durability. However, it can only control the swing phase and cannot control the stance phase sufficiently. In real human knee joints, when the knee joint moves with a polycentric motion, the center of rotation changes during the rotation [7]. Due to this characteristic, a single-joint exoskeleton cannot completely track the human knee-joint motion. In addition, this center misalignment results in loss of energy. Currently, a four-bar linkage is used in assisting devices [8], [9]. However, the features that the four-bar linkage is used for in assisting devices is different from those of prostheses. The relative motion between the wearer and the assistive device can be reduced by using the four-bar linkage, since it can provide a polycentric motion similar to that of a human knee joint. If the relative motion is not reduced, the resulting friction will cause skin abrasion and become a source of loose binding force. Thus, four bar linkages can minimize these problems and, due to the similarity of their motion to human knee joints, improve comfort during wearing the exoskeleton. In this research, a four-bar linkage based on the study by Norton [10] for the designed knee joint was selected and implemented .
To date, many researches have been attracted to the field of control strategies in the lower limb exoskeleton [11]. Some earlier works in this field will be presented in this section. Roboknee assists the thigh muscle during flexion and extension to enhance the wearer’s performance by using a proportional controller [12]. To evaluate the user’s contribution, two load cells are, normally, placed in the users shoes to measure the ground vertical reaction force. However, the users effort was determined in the study by Fleischer and Hommel [13] using electromyogram (EMG) electrodes placed at his/her thigh and linked to the knee joint. The desired behavior of the system composed of the lower limb and the exoskeleton is defined by the term adaptability of the exoskeleton parameters.
The systems stiffness is reduced by adding an elastic brace parallel to the knee joint, and this causes the raise in running abilities [14]. Then, damping and inertia parameters of the system are modulated with respect to the wearers intention. In fact, the knee exoskeleton system inertia, viscous/damping coefficients and the subject’s properties (e.g. mass and height) vary in the time that from a subject to another [15]. In addition to this, there are parameter uncertainties in the whole system such as errors in parameter identification, and external disturbances such as involuntary movements performed by the wearer as well as external interactions with the environment. Therefore, the use of a robust controller is an obligation. To date, different robust controllers have been proposed in this regards. The First Order Sliding Mode Controller (FOSMC) has been used by Jezernik et al. to drive the Lokomat system for the restoration process of a dependent subject’s lower limbs movements [16]. Tzu-Hao Huang used the same control strategy (FOSMC) to drive a Lower Limb Exoskeleton. Besides, determining the sliding control law and the optimal sliding surface, the genetic algorithm (GA) was applied to progress the effect of SMC [17]. A robust terminal sliding mode control (RTSMC) method combined with a nonlinear disturbance observer (NDO) is also used to reduce the required time for eliminating external disturbances [18].
This study proposed a control method of a designed knee exoskeleton, that has one revolute joint in the sagittal plane and can assist patients in strengthening their muscles in the sitting position. A nonlinear disturbance observer was presented to estimate the muscular torque developed by the wearer and the uncertainties of the modeling [20]. Moreover, a robust Backstepping Sliding Control (SBC) with NDO was proposed, instead of a basic sliding mode controller that can estimate the external disturbance, improve the tracking precision and extend the control bandwidth, which is a major disadvantage of the basic sliding mode. To validate the proposed controller, first, it is simulated in OpenSim and MATLAB, and then, it is compared with four published methods (basic SMC, NDO based SMC, and RTSMC). Finally, the proposed controller is applied to the knee exoskeleton designed based on the four-bar linkage at the knee joint.
The paper is organized as follows. In Section 2, the knee exoskeleton design and its mechanical structure is presented. The nonlinear knee exoskeleton motion mathematical model with disturbance is established in Section 3. The NDO-based SBC approaches and analysis of its stability by means of Lyapunov theory are presented in Section 4. In Section 5, the identification parameter of the knee-exoskeleton is described. The simulation results are presented in Section 6 followed by experimental results, discussions and conclusions.
Section snippets
Knee exoskeleton design
The designed exoskeleton consists of two main segments related along by a four bar mechanism and a curved one. One segment of it is connected to the human thigh whereas the other is attached to the shank using braces (Fig. 1). This system is designed to carry out the flexionextension movement of the human knee joint. Two main supports (lower and upper) are fixed on the leg by means of velcro closures that tighten themselves over a soft rubber part. The soft part provides comfort and prevents
Knee-exoskeleton modeling
A subject wearing the designed knee exoskeleton with the shank freely moving around the knee joint is illustrated in Fig. 3. Since the exoskeleton is fixed to the human leg in such a way that both have the same rotational axis at the knee joint, the exoskeleton and the leg are assumed coupled. The angle of the knee, and therefore, the exoskeleton, is shown in Fig. 3. In the following, the subscripts s and e refer to the shank and exoskeleton, respectively.
Design of knee exoskeleton sliding backstepping controller with NDO
The control objective of the knee exoskeleton controller is to cause the output y of the system Eq. (14) to asymptotically track a desired trajectory by designing the control law U, while keeping all the closed-loop signals bounded. As the knee exoskeleton dynamics are influenced by unpredictable environmental disturbances and the subject’s variable properties, the output of the controller will be larger than what is expected if the sliding backstepping controller is directly designed for the
Parameters identification
As the shank-exoskeleton system is composed of the shank and the exoskeleton, their parameters should be identified in some separate identification processes. In order to make identification possible, the knee exoskeleton can be implemented within the OpenSim simulator [28] while being controlled by a controller realized in MATLAB. The former is a biomechanical simulator developed at Stanford University and allows the simulation of a complex body model. The simulator makes two main analyses
Validation of the exoskeleton and its design procedures
The design procedure is validated in three steps. First, the identification of the shank and exoskeleton is verified. In the second step, the designed controller is simulated and its superiority to some other published methods is shown. In the last step, the whole system is verified by applying a desired trajectory to the system and measuring the tracking error.
Simulation results of the controllers
In order to evaluate the quality of the proposed method of sliding backstepping with NDO, MATLAB. is employed. The knee exoskeleton has been simulated coupled with the model of the lower limbs of the human body for a flexion/extension knee task. Fig. 8 shows its Simulink model. In this model, the reference trajectory was a sinusoidal curve with the frequency of 0.3 Hz. The controller and NDO blocks determine the control law, then, with the help of the OpenSim-MATLAB interface and by using the
Experimental results
The knee exoskeleton prototype was utilized in all implemented experiments of the third step in the validation process, as shown in Fig. 15. The exoskeleton has a single degree of freedom at the knee joint level and is attached to the shank and thigh by means of straps. The exoskeleton is equipped with an incremental encoder that measures the knee joint angle. Furthermore, a current sensor is used to measure the current of the motor. All computations are performed using a dSPACE board. The
Discussions
As shown in the simulations, NDO-based SBC reduces the RMS error where there exist some external disturbances in comparison to NDOSMC; however, simultaneously, the properties of the control outputs remain the same. Moreover, its amount of energy conception is lower than that of the NDO-based RTSMC. The RMS of its tracking error is about 0.0125 without external disturbance and 0.02 with external disturbance which is about one-third of the lowest RMS error in the other three methods (SMC,
Conclusions
In this paper, a model of a knee exoskeleton was exposed and its parameters were estimated using some optimization algorithms. A nonlinear disturbance observer based on sliding backstepping control scheme was proposed for the knee exoskeleton to solve its nonlinearity, uncertainty and external disturbance problems. A NDO was utilized to estimate the disturbances occurred in the system. Sliding mode backstepping method was used to solve the uncertainty and nonlinearity that NDO cannot observe.
Conflict of interest
There are no conflicts of interest.
Acknowledgments
The authors are grateful to the university of Isfahan for supporting this research.
Maryam Khamar received her M.Sc. degree from Isfahan University of Technology, Isfahan, Iran, in 2013. She is currently a Ph.D. candidate in Control Engineering at University of Isfahan, Isfahan, Iran. Her research interests include control system and rehabilitation robotics.
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Maryam Khamar received her M.Sc. degree from Isfahan University of Technology, Isfahan, Iran, in 2013. She is currently a Ph.D. candidate in Control Engineering at University of Isfahan, Isfahan, Iran. Her research interests include control system and rehabilitation robotics.
Mehdi Edrisi is currently an assistant professor at Electrical Engineering Department, University of Isfahan, Isfahan, Iran. He received his B.Sc. from Isfahan University of Technology, M.Sc. from University of New South Wales, Australia and Ph.D. form University of South Australia. He has been in Biomedical Engineering department from 2000 to 2012. He served as the chairman of IT Department for seven years. He has been the Chair of the Intelligent Systems Research Group at the University of Isfahan since 2012. He is now the head of Processing and Intelligent Systems Research Center. His main research fields are robotics and fuzzy control.
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This paper was recommended for publication by Associate Editor Dr. J Bae.