Compliant adaptive control of human upper-limb exoskeleton robot with unknown dynamics based on a Modified Function Approximation Technique (MFAT)

Highlights

• A new compliance control is developed allows the exoskeleton robot to cooperate with humans.

• Detection of the desired movement intention (DMI) of the subject.

• A Modified Function Approximation Technique (MFAT).

• Active functional therapy training.

Abstract

Rehabilitation robots have shown a high potential for improving the patients’ mobility, improving their functional movements and assisting in daily activities. However, this technology is still an emerging field and suffers from several challenges like compliance control and dynamic uncertain caused by the human–robot collaboration. The main challenge addressed in this paper is to ensure that the exoskeleton robot provides a suitable compliance control that allows it to cooperate perfectly with humans even if the dynamic model of the exoskeleton robot is uncertain. To achieve that, an adaptive tracking controller based on Modified Function Approximation Technique (FAT) is proposed to approximate the dynamic model of the exoskeleton robot. Unlike a conventional FAT, the required use of basis functions in estimations law of dynamic model and the acceleration feedback is eliminated in the proposed modified FAT. Additionally, the desired trajectory is designed based on the designer’s prediction of the motion intention of the human, using the Damped Least Square method in order to reduce the error between the actual position of the robot and the motion intention of the human which help the subject move the exoskeleton arm easily in active rehabilitation tasks. The stability analysis is formulated and demonstrated based on Lyapunov function. An experimental physiotherapy session and comparison study with a healthy subject was performed to test the effectiveness and robustness of the proposed adaptive control.

Introduction

Rehabilitation robots are a new technology dedicated to the physiotherapy and assistance motion and has prompted large interest in the scientific community. This importance comes from its medical benefit to people with neurologic impairments [1], [2], [3]. These robots are still an open field of research because of its complex mechanical design (created to be comfortable for human use), the variety of assistance strategies (for different types of patients having different degrees of impairments), and the sensitivity of the interaction with different human conditions [4]. Human safety and reliable performance are among the major required criteria in robotic rehabilitation training. For instance, a force controller was introduced in [5] for an exoskeleton which allows the human–robot system to realize motor exercise based on muscle activity recognition. A computed torque controller was presented in [6] for tracking the trajectory of an upper-limb exoskeleton robot based on its dynamic model. The sliding mode controller with exponential reaching law is introduced in [7] to reduce the chattering dilemma. Nevertheless, in previously cited papers, control schemes are model-based, in which the control loop requires the full dynamic model of the exoskeleton.

To control an exoskeleton robot to perform human-like motion is one of the principal purposes of the control systems implemented to these kinds of robots. As mentioned above, these robots are distinguished by a highly nonlinear dynamics because of their complex mechanical design and arduous nonlinearities, such as nonlinear friction forces, backlash, etc. Besides, the collaboration between the human and the robot makes the robot system subject to unknown and external disturbances because of different physiological conditions of each subject. These conditions involve non-linear biomechanical properties of the musculoskeletal system, its payload, and the possibility of the existence of spasticity, etc. It is consequently imperative for us to design an adaptive controller that approximates the dynamic model of the exoskeleton robot and minimizes the non-smooth nonlinear constraints effects, while maintaining the stability of the exoskeleton robot at the same time.

The adaptive control design for the dynamic parameters is one of the challenging problems in robotics, particularly, when the number of degrees of freedom (DOFs) is high. Several approaches have been proposed to approximate the dynamic parameters. Some of the strategies use the linear parameterization of the robots’ dynamic model to get the regressor matrix needed in the updated control law [8], [9]. Although, when the number of DOFs of the robot increases, it is not easy to get all dynamic parameters of robot [10]. There are new methods designed to approximate the dynamic model without the computation of the regressor matrix, such as a Function Approximation Technique (FAT) [11], [12]. FAT strategy employs a finite linear combination of orthonormal basis functions to approximate the dynamic parameters of the robot, providing good performance [11]. Although this approach does not need the measure of the joint acceleration, nor the inversion of the estimated inertia matrix, it nevertheless suffers from the need of the basis functions in parameters estimation. The choice and the number of these basis functions influence directly the accurate estimation of the parameters and the online computation time. Time Delay Estimation technique is able to approximate the unknown uncertain of the dynamics of the robot [13], [14], [15], [16], [17]. It suffices to delay the system one time step to approximate the unknown dynamics accurately. Nevertheless, because of noisy measurements and nonlinearity of signals along the sampling time, a Time Delay Error subsists, which would influence negatively the robustness and the precision of the control system. Recently, approximation-based control strategies like fuzzy logic and neural networks [18], [19], [20], [21] have been used to learn the exoskeleton dynamic model. However, through these approaches only uniformly ultimate boundedness of the tracking errors was achieved. Meanwhile, the estimated weights were not reached to their actual values. This might reduce convergence speed during weights training operation, which stops the approximation-based control for real-time implementation.

Motivated by the previous observations, we propose an adaptive tracking control based on modified Function Approximation Technique (FAT). Unlike a conventional FAT approach, the need to use basis functions in the estimation law of the dynamic model is eliminated; the acceleration feedback is also eliminated in the proposed modified FAT approach. In this investigation, the predefined task trajectory is given directly by the subject that wears the exoskeleton robot, which is unknown to the control scheme. In this case, the human consumes much energy to move the exoskeleton arm if the error between the actual position of the robot and the motion intention of the human was much larger. As a promising solution, the desired trajectory can be designed based on the designer’s prediction of the motion intention of the human. To achieve that, it is necessary to detect the desired intention of the subject’s motion (DIM) using indirect force control loop [22]. By using Damped Least Square approach (DLS) [23], the detection of DIM can be achieved. This approach has been successfully used extensively in the application of many technologies [24], [25]. The DLS technique intends to present a trade-off between robustness and precision of the control system. In fact, the detection DIM of the subject is a helpful option to minimize the effort of the subject in his moving with the exoskeleton robot. So, the proposed adaptive compliant control aims to make the exoskeleton robot to move forward actively to the desired position according to the force exerted by its wearer in the absence of total knowledge about the dynamic model of the exoskeleton robot. The stability analysis is formulated and proved based on Lyapunov theory. Besides, the proposed control is evaluated experimentally with healthy subjects.

This paper is designed as follows. The exoskeleton’s dynamics model and problem statement are exhibited in the next section. The proposed control approach is explained in Section 3. Experimental results with healthy subjects are given in Section 4. The conclusion and future work are given in Section 5.