handling subject and model uncertainties for upper limb ... · handling subject and model...

Handling subject and model uncertainties for Upper LimbRehabilitation Robot using chattering free Sliding Mode Control

Abdul Manan KhanDepartment of Mechanical Design Engineering

Hanyang University, Sa-3 dong, AnsanKorea

[email protected]

Mian Ashfaq AliDepartment of Mechatronics Engineering

Hanyang University, Sa-3 dong, AnsanKorea

[email protected] Han*

Department of Robot EngineeringHanyang University, Sa-3 dong, Ansan

[email protected]

∗

Abstract: Need to develop human body’s posture supervised robots, gave the push to researchers to think over dex-terous design of exoskeleton robots. It requires to develop quantitative techniques to assess human motor functionand generate the command to assist in compliance with complex human motion. Upper limb rehabilitation robots,are one of those robots. These robots are used for the rehabilitation of patients having movement disorder due tospinal or brain injuries. One aspect that must be fulfilled by these robots, is to cope with uncertainties due to dif-ferent patients, without significantly degrading the performance. In this paper, we propose chattering free slidingmode control technique for this purpose. This control technique is not only able to handle matched uncertaintiesdue to different patients but also for unmatched as well. Using this technique, patients feel active assistance as theydeviate from the desired trajectory. Proposed methodology is implemented on seven degrees of freedom (DOF)upper limb rehabilitation robot. In this robot, shoulder and elbow joints are powered by electric motors while restof the joints are kept passive. Due to these active joints, robot is able to move in sagittal plane only while abductionand adduction motion in shoulder joint is kept passive. Exoskeleton performance is evaluated experimentally bya neurologically intact subjects while varying the mass properties. Results show effectiveness of proposed controlmethodology for the given scenario even having 20 % uncertain parameters in system modeling.

Keywords: Robot Control, Nonlinear Systems, Chattering Free Robust Sliding Mode Control, Upper Limb Reha-bilitation Robot, Wearable Robot

1 INTRODUCTION

There are 795,000 new strokes each year in US alone.More than 600,000 of these individuals have first timestrokes [1]. This simply means one stroke per ever 40s. In about 85% of cases, stroke is caused by hemis-paresis resulting in impairment of the upper limb anddisabilities. This requires a lot of social care whichmakes patient’s life very miserable. However, survivalrate for first time victims is over 50%. This gives hopefor the patients and demand professional health carefor recovery. For this purpose, robot-aided rehabilita-tion has been proposed for physicians [2–4].

Robots can allow patients to receive a more effec-tive and stable rehabilitation process, and therapists toreduce their workload. Robots can also offer reliabletools for functional assessment of patient progress and

∗Corresponding author

recovery by measuring physical parameters, such asspeed, direction, and strength of patient residual vol-untary activity [5]. For this purpose, much progresshas been made in this fields in different directions in-cluding robotic design, bio-mechantronics and controlsystem. However, we are still far from the desiredgoal, as existing devices have not yet been able torestore body mobility of function and especially notfully able to handle subject uncertainties. For thisour lab has developed a 7 DoFs robotic-exoskeletonto provide movement assistance in shoulder and el-bow joint. Unlike most industrial robots which canbe modeled easily and controlled by linear controltechniques, the control strategy for this type of ex-oskeleton robots is quite complex and difficult. Thisis mainly due to this nonlinear characteristic of theirdynamics model and limitations of estimating exactdynamic parameters with the wearer. In the litera-

Advances in Circuits, Systems, Signal Processing and Telecommunications

ISBN: 978-1-61804-271-2 43

ture, robotics devices have been used to provide apassive form of rehabilitation, which involved mov-ing the prson’s limb through a pre-determined trajec-tory. This has been performed using various linearapproaches, such as PD [6, 7], PID [7, 8] as well asother nonlinear control techniques such as computedtorque control [6,7] and impecance control [7,9]. It isvery important to understand that as a key requirementto provide passive rehabilitation and/or passive armmovement assistance, consistent high dynamic track-ing performance is required to maneuver the robot inan effective way. Use of linear control approaches arenot able to solve the issues associate with nonlinear-ity in modeling even if we consider these nonlinear-ities as disturbances [10]. Simple computed torquecontrol approaches are also not useful to handle themodel uncertainties which includes robust control orpassivity based robust control technique because ofdegradation of control and high jerk or slow response[10]. Jerks are especially not good for patients andstraight to the point, are dangerous. Several other con-trol techniques have been proposed including factiousgain [11], fuzzy adaptation [12], adaptive control [13].Main problem with these techniques is that, they aregood for industrial robots but not for rehabilitationrobots where system is not only interacting with hu-man but patient. This is critically important. So, pa-tient safety in case of jerking or over estimated gaintype questions are not addressed. Moreover, adap-tive control technique alway depend a lot on switchingfrequency while implementation and demands wholesystem scan within 1 micro second. Clearly, for thecomplex system, these control techniques are good inthe lab but for market point of view, it simply demandsa lot more expensive electronics.

Sliding mode control technique was developedto handle uncertainties especially matched ones [14].However, its chattering phenomenon due to sign func-tion, made it very difficult to use for motion con-trol equipment. Chattering phenomenon in slidingmode control is especially bad for actuators. Someresearchers developed this theory for motion controlequipment such as [15,16] but for rehabilitation robot,this theory is not discussed. Rehman.et. al has madea detail discussion about it and proposed exponen-tially reaching sliding mode control for this purpose[9]. However, robustness is still left to be handledby signum or saturation function. Another solutionto handle such problems is proposed by Xu et. al [17].We formulated our control design based on his tech-nique. In this control law, upper bounds and gains forsystem is very important. If not carefully chosen, con-troller causes chattering.

In this paper, we have developed chattering freerobust sliding mode control [17] for upper limb reha-

bilitation robot especially tuned to interact with dis-abled persons. We ensured robust convergence with-out jerking or chattering with variable mass and in-ertia properties. We also discussed methodology tooptimize the gain for the each individual patient. Pro-posed control theory is implemented on 7 degree offreedom (DOF) robot which is developed in our lab.For simplicity, we have only empowered two DOFto make the robot move in sagittal plane only. ofcourse, findings of this study can be extended for otherDOFs as well. After discussing simple robot model-ing, we have designed chattering free robust slidingmode control for our rehabilitation robot which is fol-lowed by experimental evaluation and discussion inthe end.

Rest of the paper is organized as follows. In Sec-tion 2, we have described our rehabilitation robot.Section 3 discusses chattering free robust slidingmode control for the robot. In 4 experimental eval-uation is presented. Section 5 includes discussion andconclusion.

2 Upper Limb Rehabilitation Robot

In this Section, we presents Upper Limb Rehabilita-tion Robot structure and configuration. It is a unilat-eral device and only attachment to the right arm inthis paper is studied. It consists of simple mechanicalstructure as shown in 1. Robot has the following mainparts as shown in Fig. 2.

1. A height adjustable frame to match the subject’sheight [A in Fig. 2].

2. Segment B and C [in Fig. 2] is used to allow lim-ited motion in transverse planes for the subject’sconvenience.

3. Segment D [in Fig. 2] is used to allow limitedmotion in coronal and transverse plane.

4. Segment E [in Fig. 2] is for shoulder joint andhas one DOF.

5. Segment F [in Fig. 2] is for elbow joint and alsohas one DOF with respect to shoulder joint.

6. Segment G [in Fig. 2] is for load sensors.

Moreover, xyz axis frame is also represented in Fig. 2.Passive and actuated DOFs for the robot were se-lected based on the joint ranges of motion. Majorrotations during the operation is considered in Sagit-tal plane only. Therefore, the actuated DOFs wereshoulder and forearm in Sagittal plane only. Shoulderand forearm flexion/extension maximum joint ranges


ISBN: 978-1-61804-271-2 44

were −30◦/160◦ and 0◦/120◦ respectively. All otherDOFs were for the user comfort and kept free. For theabduction/adduction motion of shoulder passive rev-olute joint was used. Robotic frame was made fromaluminum rectangular tubes to meet the strength re-quirements for the load. This frame was connectedto Human with two braces: one at shoulder sectionand other at forearm section. Motors were used forboth shoulder and forearm flexion/extension motions.These motors can provide the peak torques of 45 Nm(shoulder) and 25 Nm (elbow) which was sufficientfor the proposed application to operate the load up to3 kg.

Figure 1: Schematic Diagram of Exoskeleton Robot

Figure 2: Schematic Diagram of Exoskeleton Robot

All the hardware was controlled using LabVIEW2012 FPGA module.

Safety features were always considered criticallyimportant. For this purpose, Mechanical stops wereinstalled on shoulder and elbow joints to avoid therobot to go beyond the physiological range of motion.Moreover, in case of fast and uncontrolled movementwhole plant shut down feature is programmed. In-dependent safety circuit is also incorporated that canpower down the system in case of any danger or if thesubject’s feels discomfort.

3 Dynamic Modeling and ControlDesign

For this study, we kept our rehabilitation robot sim-ple for control algorithm evaluation. It has two activedegree of freedoms (DOFs) with five passive DOFs.Passive DOFs are designed for future enhancementand fore increased range of motion. It is important tomention that robot and human arm, is considered assingle rigid body. Dynamic behavior of overall struc-ture can be expressed as [10]

M(q)¨q +C( ˙q, q) ˙q +G(q) +F (q, ˙q) = τ − τh (1)

where q ∈ Rn and ˙q represents joint angles andits time derivatives in radians respectively. M(q) ∈Rn×n, C( ˙q, q) ∈ Rn×n, G(q) ∈ Rn, F (q) are In-ertial, Coriolis, Gravitational and friction matrices forthe rehabilitation robots. τ represents the joint actu-ator torques while τh represents human applied forceinteracting with robot.

We can re-write above equation as

¨q = M−1(q)(τ − η(q, ˙q)− (τh)) (2)

where η(q, ˙q) is defined as

η(q, ˙q) = C(q, ˙q) ˙q +G(q) + F ( ˙q) (3)

In a similar fashion, we can represent predicted modelas

¨q = M−1(q)

(τ − ˆη(q, ˙q)− τh

)(4)

where (·) represents predicted information. To con-trol the predicted system, we propose following con-trol [17] as

τ = M(q)

(¨qd + M−1(ˆη(q, ˙q) + τh)

−Cgλ˙q −Ks

)(5)


ISBN: 978-1-61804-271-2 45

where s represents the sliding surface as

s = ˙q +Cgλ˜q (6)

˜q = q − qd (7)

Assumptions

In our study, main assumptions are about matched andunmatched uncertainty. We assume that both matchedand unmatched uncertainties are bounded by some up-per bound which is the practical scenario.

A1

First assumption is that unmatched uncertainties arebounded such as

|M−1(q)ˆη(q, ˙q)−M−1(q)η(q, ˙q)| ≤ h(q) (8)

A2

Second assumption tells that matched uncertaintiesin system modeling are bounded by D ∈ Rn×n asM(q) = (I −∆(q))M(q), |∆ij | ≤ Dij < 1 wherei, j = 1, 2.

It is important to note that upper bounds h(q, ˙q)and D(q) are function of joint angles q and joint ve-locity ˙q which makes our control law very unique. Weassume that in our system, parametric uncertainty likeinertia, center of mass and mass distribution is not ac-curately known. Therefore, our control law emphasizeon these parameters.

To find the controller gain K, we can formulate(detail of the equation is provided in proof)

h(q) +D∣∣∣¨qd + M−1(ˆη(q, ˙q) + τh)−Cgλ

˙q∣∣∣

+ µs = Ks−D|Ks| (9)

where we can find K by solving the following equa-tion as

hi +Dii

∣∣∣qdi + (M−1(ˆη + τh))i − λiei

∣∣∣+µiisi = Kiisi −Dii |Kiisi| if si > 0

Kii = 0 if si = 0

hi +Dii

∣∣∣qdi(M−1(η + τh))i − λiei

∣∣∣−µiisi = −Kiisi −Dii |Kiisi| if si < 0

(10)

Proof

To prove the closed loop convergence, we define Lya-punov function as

V = sT s (11)

Defining ˙s as

˙s = ¨q − ¨qd +Cgλ˙q (12)

Using (2), we can rewrite above equation as

˙s =M−1(q)(τ − η(q, ˙q)− (τh)) (13)

− ¨qd +Cgλ˙q (14)

Now, using (5) in above equation, we can have

˙s =M−1(q)

(M(q)

(¨qd + M−1(ˆη(q, ˙q) + τh)

−Cgλ˙q −Ks

)− η(q, ˙q)

− (τh)

)− ¨qd +Cgλ

˙q (15)

from assumption A2, we know that

MM−1 = (I + ∆) (16)

using above relation, we can simplify (15) as

˙s =∆¨qd + f − ˆf −∆ ˆf −∆Cgλ˙q (17)

(I + ∆)Ks (18)

where

f = −η(q, ˙q)− (τh)

ˆf = −ˆη(q, ˙q)− (τh) (19)

Now, defining V = ˙ss

V =(∆¨qd + f − ˆf −∆ ˆf −∆Cgλ

˙q (20)

(I + ∆)Ks)s (21)

Now, applying upper bounds for [s1, s2]T > [0, 0]T ,

as mentioned in A1, we have

V ≤(h+D

∣∣∣¨qd − ˆf −Cgλ˙q∣∣∣

−Ks+ ∆|Ks|)s (22)

Above equation can be proven negative definite, if wecan chooseK such that

−KsT s+(h+D

∣∣∣¨qd − ˆf −Cgλ˙q∣∣∣

+ ∆|Ks|)s = −µsT s < 0 (23)


ISBN: 978-1-61804-271-2 46

which means that for [s1, s2]T > [0, 0]T , we can cal-

culateK as

h+D∣∣∣¨qd − ˆf −Cgλ

˙q∣∣∣+ µs = Ks−D|Ks|

(24)

while the above situation is equally valid for s1 > 0while s2 < 0 in individual level as described in (10).

In a very similarly way, we can arrange equationfor [s1, s2]

T < [0, 0]T as

−KsT s+(− h−D

∣∣∣¨qd − ˆf −Cgλ˙q∣∣∣

−∆|Ks|)s = −µsT s < 0 (25)

and we can calculate controller gain as

−h−D∣∣∣¨qd − ˆf −Cgλ

˙q∣∣∣+ µs = Ks+D|Ks|

(26)

It is important to note that due to the conditionsfor s > 0 and s < 0 causes chattering phenomenon.However, it significantly reduced one term of chatter-ing reducing over all chattering phenomenon [18].

4 Experimental Evaluation

For experimental purpose robot (Fig. 1 ) with the hu-man is considered as single rigid body.

Arm length l1 = 0.32 m and forearm lengthl2 = 0.30 m is taken. Similarly, masses of arm andforearm are initialized to m1 = 6 kg and m2 = 5kg respectively. All the initial conditions for shoulderand elbow joints are taken as zero including veloci-ties. For the structure uncertainties maximum param-eter error for 20% is considered.

Human upper limb parameters like segment mass,center of mass and lengths are calculated by subject’sgender, body weight, height and age as described in[19, 20].

For the experiments, ten healthy neuorologicallyintact male subjects (age 25-30 years) are selected(Table 1). All participants are given written consentapporved by the University Committee and performedexperiment are reviewed by the Institutional ReviewBoard (IRB). Detailed procedural steps for experi-ments are explained below.

Results show that variation in mass of the forearmdoes not effect the trajectory tracking. Moreover, ap-plied torque τ remains within the limits. Fig. 3 andFig. 4 represents the shoulder and elbow join trajec-tory tracking for subject 1. Small chattering in finalcould be due to sensor noise as torque signal in Fig.5is very smooth.

Table 1: Subjects Parameters used in ExperimentAge 25 to 30Gender MaleBody Weight 62 to 80Height (m) 1.7 to 1.80

Figure 3: Average Shoulder Joint Angle(q1) trajectoryfor Subject 1

Figure 4: Average elbow Joint Angle(q2) trajectoryfor Subject 1

Figure 5: Shoulder and Elbow Joint Torques for Sub-ject 1

Figures 6 and 7 shows average shoulder and el-bow joint angle trajectory tracking for subject 2 whileFig.8 represents joint torque. It is evident from thefigures that desired controller tracks the given trajec-tory without chattering and oscillation. Smooth con-trol signal in Fig8 ensures the controller performance.

Figures 9 and 10 represents average shoulderand elbow joint angle trajectory tracking for subject


ISBN: 978-1-61804-271-2 47




3. These figures just endorse the results obtainedfrom the last two subjects. Moreover, chattering freesmooth torque signal in Fig8 depicts the effectivenessof proposed methodology for application.

5 Conclusion

In this paper, we have discussed issues and controlchallenges for upper limb rehabilitation robot partic-ularly in concerned with patients comfort. We haveproposed chattering free robust sliding mode controlfor upper limb rehabilitation robot with high uncer-tainty in patient body parameters. Proposed method-ology is implemented on 7 degree of freedom robotwith two active and five passive joints. These active




joints make the robot able to move in saigttal planonly. We have tested our control algorithm with hu-man subjects and we have successfully handled up to20 % uncertainty in subject body parameters. Exper-imental findings confirms effectiveness of proposedmethodology for rehabilitation robots.

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handling subject and model uncertainties for upper limb ... · handling subject and model...

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