**1. Introduction**

Cervical spinal cord injury (SCI) may result in incomplete or complete tetraplegia and lead to paralysis of all four extremities. Upper limb onset is one of the most profound impairments that significantly degrades the life of individuals with tetraplegia by compromising independence and social interactions. Moreover, it imposes a substantial financial burden on society in the long run. While advanced medical and surgical techniques, such as stem cell therapy, nerve transfer surgery, etc., have been used to restore the upper limb functionality, in some severe cases, it is hard to achieve desired results. Emerging technologies, such as assistive robots, can provide an alternative way to facilitate individuals with physical impairments in activities of daily living (ADL) [1,2] or therapeutic exercises [3,4].

During the past few decades, upper limb exoskeletons used for power amplification and rehabilitation have attracted intensive attention from the health care and engineering sectors [5]. However, given the utility and growing demand of exoskeletons for physical assistance, the technology still faces challenges in mechanical design, controls, and human– robot interaction. Of them, the mechanical design of a shoulder exoskeleton, including kinematic and kinetic analysis, is a major issue in developing an ergonomic system [6]. Christensen et al. [7] proposed a new three degrees of freedom (DOF) spherical mechanism to comply with the human glenohumeral joint movements. The proposed mechanism takes advantage of the double parallelogram (DPL) mechanism, which connects two revolute joints to achieve a spherical workspace and maintains a remote center of motion (RCM).

**Citation:** Gull, M.A.;

Thougersen, M.; Bengtson, S.H.; Mohammadi, M.; Andreasen Struijk, L.N.S.; Moeslund, T.B.; Bak, T.; Bai, S. A 4-DOF Upper Limb Exoskeleton for Physical Assistance: Design, Modeling, Control and Performance Evaluation. *Appl. Sci.* **2021**, *11*, 5865. https://doi.org/10.3390/app11135865

Received: 19 May 2021 Accepted: 21 June 2021 Published: 24 June 2021

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The results from the biomechanical analysis of the DPL mechanism presented in [7] have shown its significance for the exoskeleton applications [1]. Similarly, Castro et al. [8] presented a novel 3-DOF curved scissor mechanism that connects two revolute joints. The proposed mechanism complies with the human shoulder movements by maintaining the instantaneous center of rotation. Since the above mechanisms can support complex shoulder movements and provide a singularity-free workspace, the passive internal rotation has made it difficult to use for individual with tetraplegia. Alternatively, several other designs, including fully active or hybrid mechanisms to comply with the shoulder anatomical movements, were proposed [9–12]. These exoskeletons support the full range of shoulder girdle movement by preserving the remote center of rotation, but their effects on supporting the physically impaired people in common ADL have not ye<sup>t</sup> been evaluated [13]. Moreover, flexible and parallel mechanisms have also been investigated to reduce inertial problem, but their size and complexity remain issues to be further addressed. Apart from the shoulder exoskeletons, exoskeletons that can support human forearm [4,14–17] and wrist movements [18–20] were developed. Among the existing mechanisms, a direct drive method and a C-ring mechanism are commonly used to support human forearm extension/flexion movements and wrist rotation, as reported in [2,5,20,21].

The feasibility of using an upper limb exoskeleton cannot only be proved by its design. Selection of a control method for improved physical human–robot interaction (pHRI) is essential for successful implementation and user acceptance. Regarding the trajectory tracking problem, proportional-derivative (PD) and proportional-integral-derivative (PID) controllers have been widely investigated for the different types of exoskeletons. Ease of implementation without having prior knowledge of robot dynamics and an ability to independently tune the control parameters have made the PD/PID control method among the most widely used control schemes [22]. However, in the PID controller, an integrator usually reduces the bandwidth of a closed loop system and removes the steady state error caused by extensive disturbance and uncertainties. Alternatively, a high value of the integrator gain may compromise the transient performance and destroys the system's stability. Therefore, many robotic manipulators, including exoskeletons, use purely PD control or PD control with relatively small integral gain [1,22–24]. It is known that a PD controller can guarantee a semi global asymptotic stability after appropriately tuning the gains [23,24].

Several studies have been conducted to modify the linear PID controller that can guarantee an asymptotic stability. For example, PD control with sliding mode compensation [25], PD-based fuzzy sliding mode control [1], PD control with neural compensation [22] and so on. It is well understood that the PD controller can guarantee the stability for the robotic manipulators, but the asymptotic stability cannot be achieved if the robot dynamic contains gravitational torque. The exoskeleton presented in this study is designed to safely support the user in their ADL, especially the C-ring mechanism designed for shoulder and wrist rotation and the worm gear used to drive the elbow joint exoskeleton to hold the output position without energy consumption because of its non-backdrivability [26]. Moreover, hard constraints in the joint mechanisms may not allow the users to move beyond the safety limits.

In this paper, we present a PD control in the joint space to control the four degrees of freedom (DOF) upper limb exoskeleton robot [2] and investigate its effect as an assistive device to support individuals with physical impairments of the upper limbs in a set of ADLs. The contribution of the article can be summarized as follows.

1. The proposed design can support the human upper limb musculoskeletal structure in basic ADL by providing a kinematically safe and singularity-free workspace. The deign along with the PD control is able to provide a satisfactory tracking performance. It is hypothesized that the trajectory tracking for C-ring mechanism and worm gear mechanism is less prone to the variation in payload, weight of human arm, and exoskeleton due to its ability to hold the output position without energy consumption. 2. The integration of the upper limb exoskeleton with the CarbonHand glove (BioServo Technologies AB, Kista, Sweden) offers a new paradigm that not only supports the user in manipulation but facilitates them also in hand opening and closing. The experimental evaluation has shown that the proposed design with the PD control scheme is appropriate in performing several ADLs, such as eating/drinking.

The paper is organized as follows. The mechanical design of a wheelchair exoskeleton is presented in Section 2 together with the kinematic modeling required to fulfil the task requirements in operational space. The dynamic model of the upper limb exoskeleton along with the PD control scheme is presented in Section 3. Moreover, the PD controller implementation along with the experimental results on the wheelchair exoskeletons is illustrated in Section 4. Subsequently, a discussion on the exoskeleton performance and its potential future directions are presented in Section 5. The work is finally concluded in Section 6.

#### **2. Upper Limb Exoskeleton Robot**

### *2.1. Mechanical Design*

This section presents a design of an adaptive 4-DOF upper limb wheelchair mounted exoskeleton that can actively support the wearer in performing their activities of daily living, such as eating and drinking. The exoskeleton was designed after carefully analyzing the human upper limb biomechanics. To reduce the complexity of the human biomechanics, several studies have modeled the human arm as 7 degrees of freedom kinematics system by enforcing the simplifications to the upper limb joints and segments [27]. However, we have noticed that the 4-DOF exoskeleton is sufficient for the most common ADLs and keeps the workspace of the human upper extremity intact.

The exoskeleton in Figure 1b is designed as an open-chain structure to replicate the anatomy of human right upper limb and provides a controllable assistive torque to each joint. To describe the design and complete functioning of a robotic exoskeleton, we have separated the design into three sub-modules, i.e., shoulder joint mechanism, elbow module and a wrist module.

(**a**)

(**b**)

**Figure 1.** Overview of a 4-DOF wheelchair exoskeleton. (**a**) Mechanical model of 4-DOF upper limb exoskeleton. (**b**) A prototype of a wheel chair exoskeleton with carbon hand developed from SEM glove (Supplementary Materials).

The human shoulder (Glenohumeral) joint is modeled as a 3-DOF spherical joint that describes the orientation of the human upper arm. These three successive rotations are abduction/adduction, extension/flexion, and internal/external rotation. Hence, an open chain serial mechanism with three revolute joints whose axes of rotation intersect at a common point is kinematically equivalent to a spherical joint. Based on this observation, we have designed a shoulder mechanism that can actively support the 2-DOF glenohumeral joint movements such as shoulder extension/flexion movement and shoulder internal/external rotation, as shown in Figure 1a. The shoulder abduction/adduction movement is passively adjustable. Locking the upper arm abduction movement will prevent the user from moving beyond the wheelchair workspace, causing uncomfortable interaction with an external environment. The complete design of the shoulder mechanism, shown in Figure 1a, is able to preserve the dynamic center of rotation throughout its workspace. The exoskeleton's extension/flexion is achieved by a direct drive brushless DC motor (EC-i40) and a CSD-17-80-2A-R harmonic drive to amplify the motor torque. A dovetail C-ring mechanism is used to actively support the human upper arm internal/external rotation. Furthermore, a 4 pole EC Maxon motor and a speed reducer drive the C-ring mechanism through a spur gear set.

The elbow joint module consists of a normal revolute joint. A Maxon EC-4 pole motor with a speed reducer located near the elbow joint controls the forearm extension/flexion through a worm gear set. The length of the exoskeleton's upper link is adjustable to adapt the user with different anthropomorphic parameters. Moreover, an upper arm support prevents the offset between the exoskeleton and human anatomical joints, i.e., shoulder and elbow joint, causing an uncomfortable interaction between the two systems. Finally, the wrist module consists of a C-ring mechanism that is designed to support the human wrist rotation (radial/ulnar deviation). A 4 pole EC Maxon motor and a speed reducer located along the forearm likewise actuate the C-ring of the wrist joint.
