61- 72 Al-Khwarizmi Engineering Journal,Vol. 1 Ant Colony Optimization Based Force Lower Limb Mohammed Y. Hassan *,** Department of *Email: (Received Abstract The aim of human lower limb rehabilitation robot is to muscles. This paper proposes the design wearable rehabilitation robot. This robot consists of a hip, knee and ankle joints to enable the patient for motion and turn in both directions. The joints are actuated by Pneumatic Muscles Actuators (PMAs). The PMAs have very great potential in medical applications because the similarity to biological muscles. Takagi-Sugeno-Kang- three- Proportional three-Proportional (3-P) controllers for force control. They are designed and simulated to improve the desired joints position specifications such as minimum overshoot, rejection during tracking the desired position medical trajectory. gains of position and force parts of the Force required specification. A comparison between the force an enhancement in the results of the second type as compared with the first one Keywords: Rehabilitation robot, Force- 1. Introduction Damage of the central nervous system or spinal cord injuries may result in such a loss of lower limb motor functions. The physical therapy and rehabilitation programs are applied to people with disability to increase their joint range, strength, power, flexibility, and coordination [1]. One type of rehabilitation robots is exoskeleton robot: “Exoskeletons are, in general, structures of rigid links, mounted on the body of some living vertebrae and following the main directions and having the main joints of the living organism’s endoskeleton” [2]. In recent years, researches on rehabilitation robot have become an important topic. There are several researches deal with this field such as Ollinger. et al. [3] in 2007 that propose for knee joint actuated by electric motor controlled by Proportional-Integral (PID) controller. Also, Akdoğan and Khwarizmi Engineering Journal,Vol. 12, No. 1, P.P. 61- 72 (201 Ant Colony Optimization Based Force-Position Control for Human Lower Limb Rehabilitation Robot Mohammed Y. Hassan* Shahad S. Ghintab of Control and Systems Engineering/ University of Technology *Email: dr.m.hassan@uotechnology.edu.iq **Email: ssswnh5@yahoo.com (Received 6 April 2015; accepted 12 September 2015) The aim of human lower limb rehabilitation robot is to regain the ability of motion and to strengthen the weak This paper proposes the design of a force-position control for a four Degree Of Freedom (4 wearable rehabilitation robot. This robot consists of a hip, knee and ankle joints to enable the patient for motion and joints are actuated by Pneumatic Muscles Actuators (PMAs). The PMAs have very great potential in medical applications because the similarity to biological muscles. Force-Position control incorporating a Proportional-Derivative like Fuzzy Logic (TSK-3-PD) Controllers for position control and P) controllers for force control. They are designed and simulated to improve the desired joints as minimum overshoot, minimum oscillation, minimum steady state error ed position medical trajectory. Ant Colony Optimization (ACO) is used to tune the gains of position and force parts of the Force-Position controllers to get the desired position tr A comparison between the force-position controllers tuned manually and tuned by f the second type as compared with the first one with an average of 39%. -Position control, lower limb, Ant Colony Optimization. the central nervous system or spinal cord injuries may result in such a loss of lower limb motor functions. The physical therapy and rehabilitation programs are applied to people with disability to increase their joint range, strength, power, flexibility, and coordination [1]. One type of rehabilitation robots is exoskeleton xoskeletons are, in general, structures of rigid links, mounted on the body of some living vertebrae and following the main directions and having the main joints of the living organism’s In recent years, researches on rehabilitation ortant topic. There are researches deal with this field such as Ollinger. et al. [3] in 2007 that proposed 1-DOF for knee joint actuated by electric motor Integral-Derivative an and Şişman [4] in 2011 presented a robot mechanism with 3 DOF, flexion-extension movement for the knee and hip joints, and the abduction movement for the hip joint, for the rehabilitation of lower limbs. The system was designed to imply the patient’s muscle signals using Force feedback control method. Impedance control method was used for force control, whereas PID position control method was used for position control. Furthermore, Tu Diep and Tran 2008 introduced a 1-DOF by PMA controlled by PID with neural network. Akdo˘gan. et al. [6] in 2009 suggested an intelligent controller structure for a knee rehabilitation robot manipulator with 1 controller of the robot manipulator works based on impedance control. Also, Aminiazar. et al. [7] in 2013 proposed a 2-DOF for knee and ankle joints controlled by PD controller. It can be noticed from previous works that they deal with one or two joints of human lower limb Al-Khwarizmi Engineering Journal (2016) Position Control for Human Shahad S. Ghintab** / University of Technology regain the ability of motion and to strengthen the weak position control for a four Degree Of Freedom (4-DOF) lower limb wearable rehabilitation robot. This robot consists of a hip, knee and ankle joints to enable the patient for motion and joints are actuated by Pneumatic Muscles Actuators (PMAs). The PMAs have very great Position control incorporating a PD) Controllers for position control and P) controllers for force control. They are designed and simulated to improve the desired joints imum steady state error, and disturbance Ant Colony Optimization (ACO) is used to tune the Position controllers to get the desired position trajectory according to the position controllers tuned manually and tuned by ACO shows with an average of 39%. Position control, lower limb, Ant Colony Optimization. in 2011 presented a robot mechanism with 3- extension movement for the knee s, and the abduction-adduction movement for the hip joint, for the rehabilitation of lower limbs. The system was designed to imply the patient’s muscle signals using Force-Position feedback control method. Impedance control method was used for force control, whereas PID position control method was used for position rthermore, Tu Diep and Tran [5] in DOF for knee joint actuated by PMA controlled by PID with neural network. Akdo˘gan. et al. [6] in 2009 suggested an intelligent controller structure for a knee rehabilitation robot manipulator with 1-DOF. The controller of the robot manipulator works based Also, Aminiazar. et al. [7] DOF for knee and ankle joints controlled by PD controller. It can be noticed from previous works that they deal with one or two joints of human lower limb Mohammed Y. Hassan Al-Khwarizmi Engineering Journal, Vol. 12, No. 1, P.P. 61- 72 (2016) 62 through the design. This causes retraction in workspace and reduces the flexibility when interact with human motion. Furthermore, the robots were actuated by electric motors due to their simplicity of modeling control. The drawback of electric actuators that they often are expensive and heavy for high power applications [8]. Eelectric motor actuation significantly decreases power consumption during walking in comparison to pneumatic actuation. Friction in the robot joint, either in the actuators or in the joints mechanism and the effect of disturbances was not taken into consideration in most of the previous works. In this work, Force-Position controllers are designed to overcome the nonlinearity inherent in 4-DOF lower limb wearable rehabilitation robot [9]. The detailed design and modelling of the 4- DOF lower limb wearable rehabilitation robot actuated by Pneumatic Muscles Actuators (PMAs) has been explained in details in reference [9]. The design of the Force-Position controllers for the joints of the robot incorporates three- Proportional-Derivative (TSK-3-PD) like FLC for position control and three-Proportional (3-P) controllers for force control. These types of controllers are used to deal with the forces that have an effect on the robot links by the patient limb. Force-Position controllers are designed to improve the desired position specification such as minimum overshoot, minimization of oscillation, minimum steady state error, and disturbance rejection during tracking the desired position medical trajectory. Ant Colony Optimization (ACO) is used to tune the gains of position and force parts of the Force-Position controllers to get the desired position trajectory according to the required specification. 2. Force-Position Controllers The force-position control is the successful execution of an interaction task without jeopardizing itself or the environment. Such an interaction requires the control of both, motion and interaction forces. As presented by Karam [10], the objective of the Force-Position control is that the robot’s end-effector responds to forces applied externally, according to some well- defined dynamics. More specifically, the desired dynamic relationship between the end effector position � ∈ �� and the vector of contact forces � ∈ �� are specified as follows [10]: F� − F = K��X� − X� + B��X� � − X� � + M��X� � − X� � … (1) Where the parameter �� ∈ ��×� is the stiffness diagonal matrix, �� ∈ ��×� is the damping diagonal matrix and �� ∈ ��×� is the inertia diagonal matrix. �� are the desired joint forces applying to the robot joints in (N). �, ��, �� are the position, velocity and acceleration of the robot system in the Cartesian space respectively. The control law of the force that is applied to the dynamic model of robot is [10]: � = ����� �!�"� − "� + �#�"�� − "� � + ����$ + %� − �$�& + ' … (2) Where � ∈ �( is the control law applied to robot model, ���� ∈ ��×( is the Jacobean matrix and, �!, �# )*+ �$ ∈ ��×� are the position, velocity and force gain matrices respectively. "� = [-+. -+/ -+0]� are the desired trajectory position (in m), �� = [�+. �+/ �+0]� are the joint forces applied to the robot joints (in N), 23 = [24 25 26 27]�are the measured angle from each joint (in degree), � = [�. �/ �0]� are the generated force vector (in N), �$ = [�$. �$/ �$0]� are the joint gains and 8 = [8. 8/ 80]�are the outputs of fuzzy controller. In this work, tuned the gains of force- position controllers depend on the Ant Colony Optimization (ACO) algorithm [11]. However, Fig. 1 shows the block diagram for the closed loop dynamic model controlled by Force-Position controllers. The parameters of force part and position part of the controllers are tuned by ACO. Mohammed Y. Hassan Al-Khwarizmi Engineering Journal, Vol. 12, No. 1, P.P. 61- 72 (2016) 63 Fig. 1. Closed loop Force-Position controlled system tuned by ACO. 3. Design of Force-Position Rehabilitation Robot Since the 4-DOF rehabilitation robot and PMA have high nonlinearity, a Force-Position controller has the ability to deal with this nonlinearity to achieve good tracking response. The front view and side view of proposed structure (the schematic diagram of the robot mechanism) are shown in Fig. 2. A TSK PD-like Fuzzy type is designed as a position controller. The inputs of the controller are the (error (e) and rate of error (9�� ), where the control signal is: 8�:� = ;<39�:� + ;=39��:� … (3) The input and output scaling factors are defined as: Proportional gain, �kp�, derivative gain �kv�, and output gain �ko�. Seven triangular shaped membership functions are selected for each input, Fig. 3. The linguistic variables of the membership functions of the FLC are; NB (Negative Big), NM (Negative Medium), NS (Negative Small), Z (Zero), PS (Positive Small), PM (Positive Medium), and PB (Positive Big). The universe of discourse for (e, 9�) is taken within (-1, 1) since the error has positive and negative values while the output universe of discourse is within the range (0, 1) since the valve takes positive values of voltage as input. The values of output membership functions (constant type), of TSK are listed in Table 1. A typical rule in a Sugeno fuzzy model has the form: If Input 1 = x and Input 2 = y, then Output is z = a.x + b.y + c. … (4) For a zero-order Sugeno model, the output level z is a constant (a=b =0). However, the rules of the FLC are listed in Table 2 and selected by several trials to reach the best position response. The parameters of the Force controller incorporating in the Force- Position control, equation (1), are selected as; ��=3000 (N/m), ��=200 (N· s/m) and ��=5 (kg). These values are representing a second order reference model with damping ratio and un-damped natural frequency of ζ=0.8164 and wn=24.49 (rad/sec) respectively [12]. The Simulink of the force and position controllers is shown in Fig. 4 and the Simulink of the complete Force-Position controlled system for lower limb rehabilitation robot is shown in Fig. 5. It consists of sub blocks of the dynamic model, PMA, the position controller, the force controller and the reference trajectory. Table 1, Constant membership functions for the output. NB=0.3 NM=0.4 NS=0.527 Z=0.647 PS=0.7 PM=0.83 PB=0.99 Mohammed Y. Hassan Al-Khwarizmi Engineering Journal, Vol. 12, No. 1, P.P. 61- 72 (2016) 64 (a) Front view (b) Side view Fig. 2. The Proposed Structure of the Lower Limb Wearable Rehabilitation Robot. Table 2, Rules of PD-like position FLC. Fig. 3. Inputs Membership functions. B/B∙ NB NM NS Z PS PM PB NB NB NB NB NB NM NS Z NM NB NB NB NM NS Z PS NS NB NB NM NS Z PS PM Z NB NM NS Z PS PM PB PS NM NS Z PS PM PB PB PM NS Z PS PM PB PB PB PB Z PS PM PB PB PB PB Mohammed Y. Hassan Al-Khwarizmi Engineering Journal, Vol. 12, No. 1, P.P. 61- 72 (2016) 65 Fig. 4. The force and position controllers. Mohammed Y. Hassan Al-Khwarizmi Engineering Journal, Vol. 12, No. 1, P.P. 61- 72 (2016) 66 Fig. 5. The Simulink of Force-Position controlled system for the lower limb rehabilitation. 4. Simulation Results In this work, the elliptic trajectory which enable the patient to move in x and y axes is applied. The desired trajectory is given by [13]: ���:� = 0.614 − 0.015 . cos�0.2N . : − N� … (5) O��:� = −0.1 . sin �0.2N . : − 2N� … (6) Where 0 ≤ : ≤ 20 seconds. By applying the reference position trajectory, the gains of the PD- FLC and the proportional gain ��$� of the force controller for each joint are manually tuned using several trials and error and the best values are illustrated in Table 3. The response for each axis and the position trajectory are shown in Fig. 6 and Fig. 7 respectively. In this work, the criterion selected to measure the goodness of results as a performance index is Root Mean Square Error (RMSE) [14]: ��ST = 4U ∑ W9.5�X� + 9/5�X� + 905�X�U4 … �7� Where 9.5�X� is the trajectory error in x-axis, 9/5�X�is the trajectory error in y-axis and 905�X� is the trajectory error in z-axis. N is the number of samples. The performance index for first position trajectory without disturbance is calculated and equals to 0.0547. During rehabilitation exercises, many interior factors, such as position changes and even coughing, usually cause some disturbance to the rehabilitation system. A disturbance of 4*sin (10.π.t) N.m is applied [15]. Based on the characteristics of a tremor the value of above disturbance is sufficient to describe the convulsions for human lower leg. The gains of the controller listed in Table 3 are used for the elliptic trajectory with disturbance. The response for each axis and the position trajectory are shown in Fig. 8 and Fig. 9 respectively. The performance index for position reference trajectory with disturbance is calculated and equals to 0.0652. Table 3, PD-like Force-Position FLC gains for the first (elliptic) trajectory. Gain Kp1 Kd1 Ko1 Kp2 Kd2 Ko2 Kp3 Kd3 Ko3 Value 0.23 0.54 3.6 1.5 0.7 6.8 0.04 0.008 0.4 Kf1 Kf2 Kf3 6.4 7.85 5.27 Mohammed Y. Hassan Al-Khwarizmi Engineering Journal, Vol. 12, No. 1, P.P. 61- 72 (2016) 67 Fig. 6. Position response for the x and y axes of the elliptic reference position trajectory without disturbance. Fig. 7. Position trajectory response without disturbance in the (x-y) axes. Fig. 8. Position response for the x and y axes of the elliptic reference position trajectory with disturbance. Fig. 9. Position trajectory response with disturbance in (x-y) axes 0 2 4 6 8 10 12 14 16 18 20 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 time (second) x- ax is ( m et er ) x-axis response desired actual 0 2 4 6 8 10 12 14 16 18 20 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 time (second) y- ax is ( m et er ) y-axis response desired actual 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 x-axis (meter) y- ax is ( m et er ) first trajectory (manual tuning) desired actual 0 2 4 6 8 10 12 14 16 18 20 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 x-axis response time (second) x- ax is ( m et er ) desired actual 0 2 4 6 8 10 12 14 16 18 20 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 time (second) y- ax is ( m et er ) y-axis response desired actual 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 x-axis (meter) y- ax is ( m et er ) first trajectory w ith distubance (manual tuning) desired actual Mohammed Y. Hassan Al-Khwarizmi Engineering Journal, Vol. 12, No. 1, P.P. 61- 72 (2016) 68 It is difficult to enhance position tracking performance using the controller tuned manually. The process of tuning the gains of the controllers consumes time and efforts. In this research, ACO algorithm is used to tune the gains of the controllers in order to reach the best position performance. To get more accurate position responses, the values of the gains �kp, kv, Ko and kf� for each controller are tuned by ACO to achieve the desired specifications. The number of iterations for position trajectory is 40 iterations. The algorithm stops iterating either when an ant found a solution or when a maximum number of iterations have been performed. Table 4 lists the parameters of Force-Position controllers obtained by ACO tuning to follow the reference position trajectory without disturbance. The performance index for the elliptic trajectory without disturbance is calculated and equals to 0.036. However, the response of each axis and the position tracking responses in the x, y Cartesian space are shown in Figs. 10 and 11 respectively. Moreover, Fig. 12 shows the performance index obtained by ACO. Here the disturbance of 4*sin (10.π.t) is applied. The same parameters listed in Table 4 are used for trajectory with disturbance. The performance index for position trajectory with disturbance is calculated and equals to 0.0362. However, the position tracking responses in the x, y Cartesian space are shown in Figs. 13 and 14 respectively. Table 4, PD-like Force-Position FLC gains for the elliptic trajectory tuned ACO. Gain Kp1 Kd1 Ko1 Kp2 Kd2 Ko2 Kp3 Kd3 Ko3 Value 0.0081 0.0029 4.6456 0.0496 0.0067 4.557 0.001 0.001 0.0065 Kf1 Kf2 Kf3 2.381 4.6962 0.0055 Fig. 10. Position response for the x and y axes of the elliptic reference Position trajectory tuned by ACO without disturbance. 0 2 4 6 8 10 12 14 16 18 20 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 time (second) x- ax is ( m et er ) x-axis response desired actual 0 2 4 6 8 10 12 14 16 18 20 -0.1 -0.05 0 0.05 0.1 time (second) y- ax is ( m et er ) y-axis response desired actual Mohammed Y. Hassan Al-Khwarizmi Engineering Journal, Vol. 12, No. 1, P.P. 61- 72 (2016) 69 Fig. 11. Position trajectory response without disturbance. Fig. 12. ACO performance index response. Fig. 13. Position response for the x and y axes of the elliptic reference position trajectory with disturbance. 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 -0.1 -0.05 0 0.05 0.1 x-axis (meter) y- ax is ( m et er ) first trajectory w ithout disturbance (ACO tuning) desired actual 0 5 10 15 20 25 30 35 40 0.034 0.036 0.038 0.04 0.042 0.044 0.046 0.048 fitness response for the first trajectory (elliptic) iteration fi tn es s 0 2 4 6 8 10 12 14 16 18 20 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 x-axis response time (second) x- ax is ( m et er ) desire actual 0 2 4 6 8 10 12 14 16 18 20 -0.1 -0.05 0 0.05 0.1 time (second) y- ax is ( m et er ) y-axis response desired actual Mohammed Y. Hassan Al-Khwarizmi Engineering Journal, Vol. 12, No. 1, P.P. 61- 72 (2016) 70 Fig. 14. Position trajectory response with disturbance. 5. Conclusions Force-Position controllers were designed to control the proposed robot. Result showed that: 1. The proposed controller using manual tuning could not overcome the nonlinearity of dynamic model, nonlinearity of PMA, effects of frictions, and disturbances. 2. ACO algorithm was used to tune the gains of the force part and position part of force- position controllers to satisfy the desired specification. Results of applying the medical trajectory show an average enhancement in the position trajectory. 3. (Without disturbance and with disturbance) for elliptic trajectory (39 %). 4. For the proposed Force-Position controllers tuned by ACO, the results of the elliptic trajectory were compared with the results of reference 11. The percentage of enhancement for x and y axes are 50 % and 85 % respectively. 5. The proposed force-position controllers tuned by ACO had achieved the desired performance and compensated the nonlinearity of frictions, external disturbance and any other nonlinearity in the proposed model. List of Symbols Symbols Definition Unit. �� Damping diagonal matrix ^. _/` F Generated force ^ �� The desired joint forces applying to the robot joints N �� Stiffness diagonal matrix ^/` �� Inertia diagonal matrix ;a � The position �� The velocity �<3 Proportional gains of ith controller �=3 Velocity gains of ith Controller �b3 Output gains of ith controller �$3 The force gain of ith controller J Jacobean matrix U Voltage input Volt 23 Joint angle of link i +9ac99 d Damping ratio e( Un-damped natural Frequency c)+/_ 9.�X� The trajectory error in x- axis ` 9/�X� The trajectory error in y- axis ` 90�X� The trajectory error in z- axis ` 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 -0.1 -0.05 0 0.05 0.1 x-axis (meter) y- ax is ( m et er ) first trajectory w ith disturbance (ACO) tuning desired actual Mohammed Y. Hassan Al-Khwarizmi Engineering Journal, Vol. 12, No. 1, P.P. 61- 72 (2016) 71 6. References [1] Nef, T.; Mihelj, M.; Riener, R.: ARMin: A Robot for Patient-Cooperative Arm Therapy. Medical and Biological Engineering and Computing, International Federation for Medical and Biological Engineering, 45, 887- 900, 1 July (2007). [2] Rocon, E.; Pons, J. L.: Exoskeletons in Rehabilitation Robotics, Springer-Verlag Berlin Heidelberg, 1–20, (2011). [3] Ollinger, G. A.; Colgate, J. E.; Peshkin, M. A.; Goswami, A.: Active-Impedance Control of a Lower-Limb Assistive Exoskeleton. IEEE 10th International Conference on Rehabilitation Robotics, June 12-15, Noordwijk, Netherlands, 188-195, 12-15 June (2007). [4] Akdoğan, E.; Şişman, Z.: A Muscular Activation Controlled Rehabilitation Robot System”, Springer-Verlag Berlin Heidelberg, 271–279, 2011. [5] Thanh, T. D. C.; Phuc, T. T.: Neural Network Control of Pneumatic Artificial Muscle Manipulator for Knee Rehabilitation. Science & Technology Development, 11, 03, 16-29, (2008). [6] Akdo˘gan, E.; Taçgın, E.; Adli, M. 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Hindawi Publishing Corporation Applied Computational Intelligence and Soft Computing Journal, 1-7, (2012). [12] Wang, J.; Li , Y.: Hybrid Impedance Control of a 3-DOF Robotic Arm Used for Rehabilitation Treatment. 6th Annual IEEE Conference on Automation Science and Engineering Toronto, Ontario, Canada, 768- 773, Aug. (2010). [13] Chang M. K.; Liou, J. J.: T-S Fuzzy Controller Applied to Lower Limb Rehabilitation Robot Actuated by Pneumatic Muscle Actuators. CACS International Automatic Control Conference, National Taipei University of Technology, Taipei, Taiwan, November 27-29, (2009). [14] Karam, Z. A.: Design and Implementation of Rehabilitation Robot Arm, M.Sc. thesis, University of Technology, control and system Eng. Dept., Dec. (2013). [15] Pan, L.; Song, A.; Xu, G.; Li, H.; Xu, B.: Safety Supervisory Strategy for an Upper- Limb Rehabilitation Robot Based on Impedance Control. 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