Modelling of extended deweight fuzzy control for an upperlimb exoskeleton
Siti Khadijah Ali^{1} , Masnida Hussin^{2} , M. Sukri Hadi^{3} , M. Osman Tokhi^{4}
^{1, 2}Faculty of Computer Science and Information Technology, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia
^{3}Faculty of Mechanical Engineering, Universiti Teknologi MARA Malaysia, 40450 Shah Alam, Selangor, Malaysia
^{4}Department of Electrical Engineering, London South Bank University, 103, Borough Rd, London SE1 0AA, United Kingdom
^{1}Corresponding author
Journal of Vibroengineering, Vol. 23, Issue 2, 2021, p. 459470.
https://doi.org/10.21595/jve.2020.21481
Received 18 May 2020; received in revised form 3 September 2020; accepted 11 September 2020; published 21 November 2020
Performing heavy physical tasks, overhead work and long working hours are some examples of activities that can lead to musculoskeletal problems in humans. To overcome this issue, automated robots such as the upperlimb exoskeleton is used to assist humans while performing tasks. However, several concerns in developing the exoskeleton have been raised such as the control strategies used. In this study, a control strategy known as the extended deweight fuzz was proposed to ensure that the exoskeleton could be maneuvered to the desired position with the least number of errors and minimum torque requirement. The extended deweight fuzzy is a combination of the fuzzybased PD and fuzzybased deweight controller systems. The extended deweight fuzzy was then compared with the fuzzybased PD and PID controllers, and the performances of these controllers were compared in terms of their deviations and required torques to perform tasks. The findings show that the proposed control strategy performs better than the fuzzybased PD and PID controller systems.
Keywords: upperlimb exoskeleton, fuzzybased deweight, extended fuzzybased deweight, fatigue upper arm.
1. Introduction
The exoskeleton is one example of an assistive technological innovation. Nowadays, the use of an exoskeleton is not limited to assisting or augmenting human performance [14]. In fact, the exoskeleton has been identified as one of the solutions in dealing with muscle fatigue in humans [57]. Muscle fatigue can occur at any age group and it is a condition whereby the strength required to perform the tasks is greater than the motion strength of an individual [8, 9]. Several factors that contribute to this problem are heavy physical activities, repetitive work, overhead work, and long working hours [10, 11]. Muscle fatigue can affect the quality of life for workers and there is a high risk of experiencing musculoskeletal disease (MSD) that could degrade their work performance [4, 1217].
An exoskeleton is classified into three parts, namely the upper, lowerextremity, and wholebody suits [8, 18]. There are several challenges in developing the exoskeleton, in which one of them is the development of the control system [19]. The control system is used to ensure that the exoskeleton is able to move along with the human upper limb [2022]. In addition, the control system should be able to interact and respond to movements generated by humans. Since the development of the exoskeleton in this study is to assist humans when they are experiencing fatigue, it is thus essential for the exoskeleton to be able to identify the strength of humans.
The contributions of this work are summarised as follows:
– The proposed extended deweight fuzzy controller can enhance the limitation of the fuzzybased PD controller to ensure that the movements of the upperlimb exoskeleton are accurate.
– The proposed extended deweight fuzzy controller provides an insight into the reduction of errors and torques for the upperlimb exoskeleton.
– The proposed extended deweight fuzzy controller is also capable of handling disturbance.
2. Research method
The research method comprises the modelling of the human upperlimb and exoskeleton upperlimb. In the first section, the kinematics and dynamics of the upperlimb are presented and followed by the exoskeleton upperlimb.
2.1. Kinematics and dynamics of the human arm
The development of the upperlimb exoskeleton is based on the kinematics and dynamics of the human arm during daily activities. Hence, it is important to know how movement occurs in the human body, specifically the human upper limbs. It is known that the musculoskeletal system comprising the connective tissues, muscles, and joints supports, stabilises, protects, and produces precise movements for the human body.
The human upper limb is designed as segments of linked bones that are linked by joints that have multiple degrees of freedom. The movements of the human upper limb are due to the existence of muscles. Muscles provide power or moment across the joints to enable movement. Some examples of human movements are shoulder flexion/extension, shoulder abduction/adduction, elbow flexion/extension, and wrist flexion/extension.
Fig. 1. Shoulder movements: Initial position (Extreme left), (1a) Shoulder abduction, (1b) Shoulder adduction, (2a) Shoulder extension (2b), Shoulder flexion, (3a) Shoulder internal rotation, and (3b) Shoulder external rotation
Table 1. Basic movements of the upper limb
Joints

Rotation

Translational


Flex/Ext

Abd/Add

Int/Ext

Pro/Sup

Rad/Ulnar

Up/Down

Fward/Bward


Shoulder

/

/

/

/

/


Elbow

/


Wrist

/

/

/

In this study, the development of the exoskeleton is solely based on the daily upperextremity activities, in which the activities usually comprise combinations of basic movements. The movement combinations are presented in Table 1 and shown in Figs. 13. In this study, the shoulder is attached to the body by a ball and socket joint, and this joint is responsible for shoulder flexion/extension, shoulder adduction/abduction, and shoulder internal/external movements (Fig. 1). The upper and lower arm are connected by a single rotating joint known as a revolute joint at the elbow (Fig. 2). The lower arm and the palm are also connected by a revolute joint at the wrist (Fig. 3). The region of rotation for each joint is shown in Table 2.
Fig. 2. Initial position (Extreme left) (a) Elbow flexion (b) Elbow extension (c) Forearm pronation (d) Forearm supination
Fig. 3. Initial position (Extreme left) (a) Wrist extension (b) Wrist flexion (c) Ulnar deviation (d) Radial deviation
Table 2. Range of motion and torques for human upper extremities [10, 23, 24]
Joints

Range of motion

Torque, $\mathrm{\tau}$

Shoulder flexion

0130°/180°

115°

Shoulder extension

030°/80°

110°

Shoulder abduction

0180°

134°

Shoulder adduction

050°

94°

Shoulder medial (Internal)

060°/90°

39.2°

Shoulder lateral (External)

090°

39.2°

Elbow flexion

0160°

72°

Elbow extension

0140°/146°

42°

Forearm pronation

080°

9°

Forearm supination

085°

7°

Wrist flexion

090°

–

Wrist extension

080°

–

Wrist abduction

030°/40°

–

Wrist adduction

0150°

–

2.2. Mechanical design of the upperlimb exoskeleton
The design of the exoskeleton used in this study was inspired by the TitanArm due to the simplicity of its design. Moreover, it is capable of powered use and data transmission on a mobile platform [9]. The material used to design the exoskeleton is aluminium as it is a lowdensity material with reasonable strength characteristics. As mentioned in Section 2.1, the shoulder joint in this study has three degrees of freedom, while the elbow and wrist joints have one degree of freedom, respectively (Fig. 4).
2.2.1. Kinematics of the exoskeleton
Fig. 5 shows the schematic diagram of the exoskeleton and the DenavitHartenberg Table for shoulder adduction/abduction movements. The ${0}_{1}$, ${0}_{2}$, ${0}_{3}$, and ${0}_{4}$ values represent the base for shoulder internal/external, shoulder extension/flexion, elbow extension/flexion, and the endpoint of the exoskeleton. The homogenous transformation matrix Eq. (1) is used to obtain the position and orientation of the endeffector (${0}_{4}$), with respect to the fixed reference frame (${0}_{0}$):
$=\left[\begin{array}{c}\begin{array}{c}\mathrm{cos}{\theta}_{i}\mathrm{sin}{\theta}_{i}\mathrm{cos}{\alpha}_{i}\mathit{}\mathrm{sin}{\theta}_{i}\mathrm{sin}{\alpha}_{i}{a}_{i}\mathrm{cos}{\theta}_{i}\\ \mathrm{sin}{\theta}_{i}\mathrm{cos}{\theta}_{i}\mathrm{cos}{\alpha}_{i}\mathrm{cos}{\theta}_{i}\mathrm{cos}{\alpha}_{i}{a}_{i}\mathrm{sin}{\theta}_{i}\end{array}\\ 0\mathrm{sin}{\alpha}_{i}\mathrm{cos}{\theta}_{i}{d}_{i}\\ 0001\end{array}\right].$
Fig. 4. View of the exoskeleton from three perspectives
a) Front view
b) Right view
c) Perspective view
Fig. 5. a) Schematic diagram of exoskeleton, b) DenavitHartenberg table
a)
b)
2.2.2. Dynamics of the exoskeleton
The dynamics of the upperlimb exoskeleton was developed using the EulerLagrange approach as it is frequently used for the modelling of rigid robotic systems. Euler Lagrange is derived from Lagrangian ($\mathcal{L}$). Lagrangian is the difference between the kinetic ($\mathcal{T}$) and potential ($\mathcal{V}$) energy:
The total kinetic and potential energy for the whole system is presented as follows:
$\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}+\frac{1}{2}({I}_{1}{\dot{\theta}}_{1}^{2}+{I}_{2}({{\dot{\theta}}_{1}+{\dot{\theta}}_{2})}^{2}+{I}_{3}({{\dot{\theta}}_{1}+{\dot{\theta}}_{2}+{\dot{\theta}}_{3})}^{2}+{I}_{4}({{\dot{\theta}}_{1}+{\dot{\theta}}_{2}+{\dot{\theta}}_{3}+{\dot{\theta}}_{4})}^{2},$
By applying the partial derivative to Eqs. (3, 4), the dynamic of the whole system is obtained and presented as follows:
The $M\left(q\right)$ is the exoskeleton inertia matrix, $C\left(q,\dot{q}\right)$ is a matrix containing Coriolis and Centrifugal terms, $G\left(q\right)$ is a vector containing the gravity term, and $\tau $ is the vector of external torques acting on the actuated degreeoffreedom (DOF). The $q$, $\dot{q},$ and $\ddot{q}$ are positions, angular velocities, and angular accelerations of the revolute joints.
The dynamic model of the whole system was validated by comparing the generated torques between Eq. (5) with the SimMechanics model (Fig. 6). The input to the system is the angular positions of the shoulder and elbow joints for both the flexion and extension movements. The results for the validation process are presented in Section 4.
Fig. 6. Validation approach
3. Control strategy
The control design of this study is presented in Fig. 7. A detailed description of the control design is provided in [1, 2].
Fig. 7. Control design of the upperlimb exoskeleton
The proposed controller has been previously tested on humans with different strength [1]. In this study, the proposed controller was evaluated with the inclusion of disturbance. The performance of the proposed controller was compared with PID and fuzzybased PD control. In the next section, the implementation of the PID, fuzzybased PD, and the deweight fuzzy controllers are described.
3.1. Implementation of PID control
The PID control was selected as a reference point for comparison as it was simple to implement and reliable. The input to the PID controller is the error of the trajectory. The error is obtained by comparing the actual trajectory from the desired trajectory. The error is then fed into the controller and the necessary torque is generated by the controller. The generated torque is then sent to the motor joint to move or to achieve the desired trajectory (Fig. 8).
Fig. 8. Implementation of the exoskeleton with PID control
3.2. Implementation of fuzzybased PD control
The implementation of the fuzzybased PD control for the exoskeleton is presented in Fig. 9. The combination of fuzzybased PD was selected due to the ability of PD to minimise the steadystate error and the rise time, thus requiring less power consumption.
The inputs to the fuzzybased PD control are the trajectory error ($e$) and the rate of change of error ($\dot{e}$). The error is obtained by measuring the difference between the actual trajectory and the desired trajectory, while the rate of change of error is calculated by the derivative of the error. The controller will generate the torque according to the inputs to ensure that the motor joint moves to the desired trajectory.
Fig. 9. Implementation of the exoskeleton with fuzzybased PD control
3.3. Implementation of an extended deweight fuzzy control
The extended deweight fuzzy controller consists of fuzzybased PD and fuzzybased deweighting control (Fig. 10). The fuzzybased PD assists the motor joint to move to the desired trajectory, whilst the fuzzybased deweighting is used to compensate the gravity torque to increase the smoothness of the movement. The inputs for the fuzzybased PD is similar to those described in Section 3.2. The inputs for the fuzzybased deweight are position error ($e$) and the current position of the motor joint ($a$). The torques generated from the fuzzybased PD and fuzzybased deweight are summed up and sent to the motor joint. For both fuzzybased PD and extended deweight fuzzy, a saturation block is included to ensure that the inserted torque is within the range of the human torque [22, 23].
Fig. 10. Implementation of the exoskeleton with extended deweight fuzzy control
4. Results and discussion
The experiments and simulations were performed using Simulink and SimMechanics. A computer with an Intel Core i7 @ 2.6GHz processing system with 4G RAM was used to run the experiments and simulations.
4.1. Validation of the dynamic model
As previously described in Section 2.2.2, the inputs to the system were the angular positions of the shoulder and elbow joint. Flexion and extension movements were applied to both joints (Fig. 11).
Fig. 11. Angular positions of flexion and extension for shoulder and elbow joints
Fig. 12(ab) shows that although the movement patterns of the velocity and torque required for each joint were similar, they had different values. The torque generated from the mathematical representation (Simulink) was slightly higher than the value obtained from SimMechanics. This could be due to minor differences in the geometrical model built into SimMechanics and parameters described in the mathematical equation [10].
4.2. Observation of control strategies
As previously mentioned in Section 3, three types of controllers were used, and their performances were compared. During the experiments, a disturbance was included to validate the stability and robustness of the system. The external forces or disturbance at 1000 Nm were applied at the position shown in Fig. 13 from 2.5 s until 10 s. The external force applied at the forearm was expected to affect the movement of the elbow joint.
Fig. 12. Flexion and extension movements: a) velocity and b) torque required
a)
b)
The control parameters used for PID, fuzzybased PD, and extended deweight fuzzy are shown in Table 3. These parameters were obtained by heuristic tuning. In general, all the controllers were able to track the desired movements even if a high disturbance was applied to the forearm of the exoskeleton (Figs. 1416), thus indicating that all the controllers were stable and robust. As mentioned previously, joint 4 was the most affected as the disturbance was applied at the forearm. The observations were performed in two stages. Firstly, the PID and fuzzyPD controllers in terms of root mean square (RMS) and maximum absolute error (MAE) (Table 4) were observed. As shown in Table 4, the RMS of Joint 4 for PID was slightly higher as compared to fuzzyPD. In addition, the MAE of PID was almost 50 % higher than the fuzzyPD. This indicates that the maximum difference between the desired and actual trajectory for fuzzyPD is better than PID, despite the high disturbance applied to the system.
Secondly, the fuzzyPD was compared with the control proposed in this study, namely the extended deweight fuzzy.
Table 3. Control parameters for PID, fuzzyPD, and extendeddeweight fuzzy systems
Control parameters

Joint 1

Joint 2

Joint 3

Joint 4

${K}_{p}$

10

1.0

10

100

${K}_{I}$

5.0

1.0

5.0

70

${K}_{D}$

$1.0{e}^{1}$

$1.0{e}^{1}$

0.1

4.0

${K}_{e}$

$2.0{e}^{2}$

$1.0{e}^{4}$

$1.0{e}^{2}$

1.0

${K}_{\dot{e}}$

$2.5{e}^{5}$

$1.0{e}^{6}$

$1.0{e}^{6}$

0

$K$

1000

1000

500

500

${K}_{e}$

$2.0{e}^{2}$

$1.0{e}^{4}$

$1.0{e}^{2}$

1.0

${K}_{\dot{e}}$

$2.5{e}^{5}$

$1.0{e}^{6}$

$1.0{e}^{6}$

0

${K}_{1}$

1000

500

500

500

${K}_{e}$

1.0

1.0

5.0

20.0

${K}_{a}$

$1.0{e}^{4}$

$1.0{e}^{4}$

$1.0{e}^{3}$

$1.0{e}^{3}$

${K}_{1}$

5

50

3

500

Fig. 13. Exoskeleton: a) exoskeleton movement and b) external disturbance
Table 4. RMS and MAE of Joint 4
Controller/Joint

RMS

MAE

PID

0.3825

1.598

Fuzzy PD

0.3386

0.8735

Extended deweight

0.01802

0.03872

Fig. 14. Performance of PID controller with external force (1000 Nm)
Based on Table 4, the RMS and MAE values for the extended deweight fuzzy were lesser as compared to fuzzyPD. This indicates that the combination of fuzzybased PD and deweight fuzzy provides a more stable and robust system as compared to the previous study [1, 2]. This observation could be due to the algorithm of the extended deweight fuzzy itself, in which the value of the actual movements and the error is considered and subsequently added as inputs to the fuzzy. Therefore, when the disturbance was applied, the system could identify that there was a slight uncommon movement from the actual trajectory and hence, corrected the uncommon movement.
Fig. 15. Performance of fuzzyPD controller with external force (1000 Nm)
Fig. 16. Performance of extended deweight fuzzy controller with external force (1000 Nm)
5. Conclusions
In this study, an extended deweight control approach of an upperlimb exoskeleton with control saturation was developed for the joint angle position tracking objective. The deweight fuzzy control was added to the fuzzybased PD to compensate for the gravity torque to increase the smoothness of the movement. The robustness of the system was evaluated in this study. Simulation experiments including a comparison with PID and fuzzybased PD controllers were performed, in which the proposed approach demonstrated satisfactory tracking performance and interaction torque reduction when high amounts of disturbance were applied. Based on these aspects, the performance of the proposed controller outperforms PID and fuzzybased PD controller. In future experiments, the human fatigue model will be included to observe the robustness of the proposed control system.
Acknowledgements
This work was supported by Universiti Putra Malaysia and the Malaysian Ministry of Education through Geran Putra – Inisiatif Putra Muda (GPIPM) (Vot: 9671000) and FRGS/1/2019/ICT02/UPM/02/3.
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