Disturbance observer enhanced variable gain …...Keywords Disturbance observer · Motion capture · Radial basis function neural networks · Teleoperation · Variable gain control

Autonomous Robotshttps://doi.org/10.1007/s10514-020-09928-7

Disturbance observer enhanced variable gain controller for robotteleoperation with motion capture using wearable armbands

Darong Huang1 · Chenguang Yang2 · Zhaojie Ju3 · Shi-Lu Dai1

Received: 11 October 2019 / Accepted: 19 June 2020© The Author(s) 2020

AbstractDisturbance observer (DOB) based controller performs well in estimating and compensating for perturbation when theexternal or internal unknown disturbance is slowly time varying. However, to some extent, robot manipulators usually workin complex environment with high-frequency disturbance. Thereby, to enhance tracking performance in a teleoperationsystem, only traditional DOB technique is insufficient. In this paper, for the purpose of constructing a feasible teleoperationscheme, we develop a novel controller that contains a variable gain scheme to deal with fast-time varying perturbation, whosegain is adjusted linearly according to human surface electromyographic signals collected from Myo wearable armband. Inaddition, for tracking the motion of operator’s arm, we derive five-joint-angle data of a moving human arm through twogroups of quaternions generated from the armbands. Besides, the radial basis function neural networks and the disturbanceobserver-based control (DOBC) approaches are fused together into the proposed controller to compensate the unknowndynamics uncertainties of the slave robot as well as environmental perturbation. Experiments and simulations are conductedto demonstrated the effectiveness of the proposed strategy.

Keywords Disturbance observer · Motion capture · Radial basis function neural networks · Teleoperation · Variable gaincontrol

1 Introduction

Robot teleoperation is a kind of advanced technology inwhich human operator/operators remotely control the far-endrobot manipulator through computer intermediary (Sheridan1995), and it plays an important role in healthcare, industrial

B Chenguang [email protected]

Darong [email protected]

Zhaojie [email protected]

Shi-Lu [email protected]

1 Key Laboratory of Autonomous Systems and NetworkedControl, School of Automation Science and Engineering,South China University of Technology, Guangzhou 510640,China

2 Bristol Robotics Laboratory, University of the West ofEngland, Bristol BS16 1QY, UK

3 School of Computing, University of Portsmouth, PortsmouthPOI 2DJ, UK

production, rescue and aerospace. One of the most popu-lar teleoperation methods is the master-salve scheme wherethe operator controls the master device directly to commandthe slave mobile robots and robotic manipulators (Luo et al.2019; Yang et al. 2016; Veras et al. 2012).

The technology of robot control has developed rapidlyin the past decades (Liu et al. 2008; Yuan and Chen 2013),and plenty of sensors are employed in teleoperation systemfor capturing human motions, such as inertial measurementunits (IMUs), vision sensors (e.g. Kinect) (Schwarz et al.2012; Xu et al. 2018), haptic devices (Phantom Omni). InYuan and Chen (2013), multiple wearable IMU sensors wereused to determine the limb joint motions and spatial locationof the human operator without external additional devices todefine the global frame. InVeras et al. (2012), to help the peo-ple with disability to perform daily tasks, a control systemwas proposed to teleoperate a robot manipulator in real-timeby PhantomOmni. However, since the device is cumbersomeand cannot be carried along by the operator, it is applicable tofew teleoperation scenarios. In Schwarz et al. (2012),with thedepth data collected by a Kinect sensor, a method of trackinghuman operator’s full-body pose was developed. However,

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Autonomous Robots

we cannot track the movements of the human operator whenthe operator is out of the sight of the Kinect sensor or whenthere is an obstacle between the operator and the Kinect sen-sor. In Xu et al. (2016), a robot manipulator was able to trackthe operator’s arm motion validly and effectively by positioncontrol when there is no external force applied on the robot.However, in practical applications, the robotic manipulatoris often subjected to uncertain external disturbance. Whenperturbation is applied on the robot, large errors will appearin the tracking task.

To deduce the effect of disturbance, researchers put for-ward many methods for different kinds of disturbance invarious systems, e.g. a hybrid scheme consisting of an itera-tive learning composite anti-disturbance structure to handlemodel uncertainties and link vibration of manipulators inQiao et al. (2019), a distributed adaptive fuzzy algorithmto cope with system nonlinear uncertainties in Sun et al.(2019), a cerebellarmodel articulation controller to tackle theeffect from parameter uncertainties and external disturbancein free-floating space manipulators (FFSMs) (Li et al. 2019),considering time delay or its effect as system uncertainties ordisturbance to be addressed in Wang et al. (2002), designinglinear filter to settle the admissible parameter uncertaintiesin Wang and Qiao (2002). Among these techniques in thescholar society, disturbance observer (DOB) is an efficientand widely-used technology in improving the tracking per-formance. TheDOB technology is proposed byOhnishi et al.(1996), and, due to the robustness, it is able to be intuitivelyadjusted in a desired bandwidth, which plays an importantrole in robust control (Sariyildiz and Ohnishi 2015). What ismore, since its efficiency in compensating the influence ofdisturbance and model uncertainties, it has been widely usedin robotics, industrial automation and automotive (Yang et al.2012; Chow and Cheung 2013). In Iida and Ohnishi (2004),DOB was first applied in teleoperation system by attenu-ating the influence of disturbance. Disturbance observer isable to compensate for the model uncertainties by estimat-ing external disturbance (Eom et al. 2001; Chen and Chen2010). A novel nonlinear disturbance observer (NDOB) forrobotic manipulator was proposed in Chen et al. (2000), andthe effectiveness of the NDOBwas demonstrated by control-ling a two link robotic arm. A three-link robotic manipulatorwas controlled by NDOB in Nikoobin and Haghighi (2009),which was the extension of Chen et al. (2000), and the stabil-ity of the NDOB was verified by Lyapunov’s direct method.In Chen et al. (2014), a scheme with adaptive fuzzy track-ing ability was designed to multi-input and multi-output(MIMO) non-linear systems under the circumstances withunknown non-symmetric input saturation, system uncertain-ties and external disturbance. DOBC owns the advantage ofsimplicity and the ability of compensation for model uncer-tainties. However, when the dynamic model is coupled with

fast-time-varying perturbation, it is not adequate to make upfor all uncertainties or disturbance.

To tackle the problems concerning robot dynamics uncer-tainties, the human limb’s stiffness transfer schemes andadaptive control techniques have been utilized in Yang et al.(2006), Ajoudani et al. (2012), whereas human limb’s stiff-ness transfer and adaptive control might not do well intransient performance or cannot address the influence result-ing from unparameterizable external disturbances throughparameter adaptation algorithm. To overcome the high-frequency perturbation, in Li et al. (2016b), the authorsproposed the control strategy that integrated robot automaticcontrol and human operated impedance control using stiff-ness byDOBbased adaptive control technique.However, thismethod does not take advantage of the motion skills of thehuman, and the movement of telerobot is not able to be con-trolled. In Zhang et al. (2016), to control the variable stiffnessjoints robot, the DOB based adaptive neural network controlis proposed.

In this paper, the main contributions lie in:

(i) A novel variable gain control scheme in teleoperationis proposed, in which the Myo wearable armband isemployed to collect human arm’s surface electromyo-graphic (sEMG) signals to generate suitable control gainas well as to collect human arm’s motion to produce thedesired trajectory for tele-robot to follow (Xu et al. 2016).In this way, the stiffness and the dexterity of humanarm can be transferred to the tele-robot. Through thisapproach, humanoperator can easily tune the control gainby adjusting his forearmmuscle strength, according to hisjudgment on whether a high or low gain is needed undercurrent teleoperation task.

(ii) An integration of radial basis function neural networks(RBFNN) algorithm and DOB theory is formulated, bywhich the one of the main part of the controller isconstructed, whose function is to minimize the influ-ence of the potential adverse effect brought by thesystem dynamics uncertainties or the perturbation fromexternal environment or internal friction, sensormeasure-ment noise, etc.. Through the introduction of integralLyapunov–Krasovskii function, the system stability isguaranteed.

In the following sections, we show the proposed teleoper-ation system configuration in Sect. 2, in which the usageof Myo armbands and the mapping from operator’s armmotion to the slave robot’s 5 joint angles are illustrated.We then introduce the proposed controller in Sect. 3, wherewe develop the variable gain control scheme according tohuman arm sEMG signals and derive a novel combinationof the RBFNN algorithm and the DOB theory. We show theexperiments, simulations and the corresponding results in

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Fig. 1 The structure of the whole system

Sect. 4. Finally, we summarize our contributions and outlinethe future work in Sect. 5.

2 Teleoperation system configuration

A brief structure of the proposed control system is shown inFig. 1. The two Myo armbands worn on operator’s arm (oneon upper arm and the other on forearm as shown in Fig. 5)work independently and generate their own rotating data (agroup of quaternions) as operator moves his arm, which canbe then transferred tomaster computer via bluetooth commu-nication technique. By combining two groups of quaternionscollected from the built-in IMU ofMyo armbands, we derive5 joint angles data in real time, which is considered to be theraw reference trajectory for a tele-robot (namely the slaverobot) to follow. At the meanwhile, the sEMG signals arecollected from 8 sensors of every armband to adjust the con-trol gain according to certain rule (discussed in the Sect. 3).

2.1 Introduction of the structure of a human upperlimb

There are seven degrees of freedoms (DOFs) in a humanupper limb, containing three DOFs in the shoulder joint,two in the elbow joint and two in the wrist joint. The kine-matic model of an upper limb can be depicted in Fig. 2in accordance with the standard Denavit-Hartenberg (DH)model (Craig 2009). Though it is said to be able to capture7 joint angles via two Myo armbands (Xu et al. 2016), inthis paper, we only employ 5 joints (3 in shoulder and 2 inelbow) to demonstrate the proposed scheme, and the 5 jointsDH parameters are shown in Table 1 (Ding and Fang 2013),where L1 and L2 represent the lengths of the operator’s upperarm and forearm, respectively.

2.2 Motion capture

First of all, to capture motion of human arm for teleopera-tion, we need a rotationmatrix derived from a unit quaternion(Hamilton 1848) produced by each armband in every sam-pling time, presenting in the form of (1), then, combine two

Fig. 2 DHmodel of a human arms (including shoulder joints and elbowjoints only)

Table 1 Standard DHparameters of kinematics modelfor human arm

i θi di ai αi

1 0◦ 0 0 90◦

2 90◦ 0 0 90◦

3 −90◦ L1 0 90◦

4 180◦ 0 0 90◦

5 90◦ L2 0 90◦

armbands data together to compute the joint angles for robotmanipulator.

q = q0 + q1 i + q2 j + q3k (1)

According to Rodrigues’ rotation formula, we derive arotation matrix relevant to every quaternion.

R =⎡⎣1 − 2q22 − 2q23 2q1q2 − 2q0q3 2q1q3 + 2q0q22q1q2 + 2q0q3 1 − 2q21 − 2q23 2q2q3 − 2q0q12q1q3 − 2q0q2 2q2q3 + 2q0q1 1 − 2q21 − 2q22

⎤⎦ (2)

Secondary, since armbands work independently to eachother, after they randomly starting up at a random place, onearmband does not know the pose of the other armband. There-fore, the primary task, is to establish the relation between twoarmbands. Seen from Fig. 3a, we can formulate (3), unify-ing a whole coordinate system for the two rotation matrixindicating two armband poses.

(a) Knowing their randomly start-up coordinate OU0 andOF0, representing the initial coordinate of the armband wornon upper arm and forearm, respectively; (b) Recording one oftheir real-time poses RU0 and RF0 with a certain arm motionat a certain sampling time; (c) Knowing their poses RU1

and RF1 regarding to their start-up coordinates; (d) Then,we obtain the two important rotation matrices RU2 and RF2,which take certain poses RU0 and RF0 as their initial coordi-nate frames

RU2 = RU1R−1U0 , RF2 = RF1R

−1F0 (3)

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Fig. 3 a Unify two armbands’ coordinate frames. b Description for 5joint angles generated by Myo armbands

By now, the two rotation matrices are still disconnectedbut can be unified to one coordinate frame basing on (4).Then, the armband poses on forearm (R∗

F2) takes OU2 as thereference coordinate frame.

R∗F2 = RT

U2RF2 (4)

Then, according to Craig (2009), the Euler angles arederived as

β = arctan(−rU31,√r2U11 + r2U21) (5)

α = arctan(rU21/cosβ, rU11/cosβ) (6)

γ = arctan(rU32/cosβ, rU33/cosβ) (7)

η = acos(rF∗11) (8)

ε = acos(rF∗33) (9)

where r represents an element of a rotation matrix, its sub-script “U” and “F” denoting RU2 and R∗

F2 respectively andsubscript numbers “ij” (i, j = 1, 2, 3) means the element posi-tion in thematrix; besides,meanings of thoseGreek alphabetsare shown in Fig. 3b. By exploiting differential theory, thecorresponding velocities and accelerations of the 5 joints arederived.

2.3 sEMG signals and control gains

There are eight built-in electrodes in everyMyo armband andevery channel of the eight produces a sEMG signal value inevery sampling time.We integrate the N channels values intoone by summing them up, and adopt their average, as (10)describes.

u(k) = 1

N

N∑i=1

|ui (k)| (10)

where N ≤ 8, k represents sampling time and ui is the real-time sEMG value. Due to measurement noise, we employ asliding window filter, as described in (11), to gain a smoothercurve.

u f (k) =

⎧⎪⎪⎪⎨⎪⎪⎪⎩

1

k

∑kj=0 u( j), k < w,

1

w

∑kj=k−w u( j), k ≥ w.

(11)

where u f (k) is the filtered sEMG value, w is the width ofthe sliding window filter.

According to Potvin et al. (1996) and Han et al. (2015),supposing that sEMG equals to electromyographic (EMG),we obtain the muscle activity a(k)

a(k) = eAu f (k) − 1

eA − 1(12)

where A is a coefficient chosen from interval (-3, 0). ToEnsure the stability of the system, the range of the controlgain can be constrained to be (Gmin , Gmax ). Then, the linearrelation between sEMG signals and the control gain can beestablished as (13) shown.

G(k) = Gmin + (Gmax − Gmin)(a(k) − amin)

(amax − amin)(13)

3 Variable gain control scheme based onDOB and RBFNN

As it is known, to obtain a precise non-linear dynamicsmodelof a robot manipulator is nearly impossible. Even if an accu-ratemodel is obtained at the first time, daily usage of the robotwill damage its accuracy due to abrasion in joints, ageing ofparts, etc., which are hardly measurable. In addition, whenrobot manipulator carries out tasks, for instance, loadingheavy objects, grabbing an alive animal with dynamic move-ment, or working in a temperature-fluctuating environment,etc., the trajectory tracking performance of the manipulatorcan be affected. Therefore, we proposed an effective schemeto resist and compensate for these uncertainties and distur-bances.

Generally, the dynamics model of a series robot manipu-lator can be expressed in Lagrange Dynamics Equation (14),

M(θ)θ + C(θ, θ )θ + G(θ) + fint = τ − fext (14)

where θ , θ and θ ∈ Rn×1 represents joint angles, velocitiesand accelerations of a series robot manipulator, M ∈ Rn×n isthe inertia matrix, C(θ, θ )θ ∈ Rn×1 is Coriolis and centrifu-gal torque, G(θ) ∈ Rn×1 denotes gravitational force, fintand fext are internal and external disturbance respectivelyand τ ∈ Rn×1 is the motor torque vector.

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Then it can be transformed into a state-space equation

⎧⎨⎩x1 = x2x2 = M−1 [F(x) + d(t) + τ ]y = x1

(15)

where x1 = [θ1, θ2, . . . , θn]T , x2 = [θ1, θ2, . . . , θn]T ,F(x) =−C(θ, θ )θ − G(θ), d(t) = − fint − fext .

From the above equations, we can conclude that to executea mission with high quality, obtaining an accurate dynamicsmodel, precisely measuring the disturbance are inevitable.However, due to difficulties mentioned before, to be feasi-bly, we need to try another way. That is the purpose of thepaper: designing a controller combining the adaptive neuralnetwork scheme and the DOB technology to approximate theinfluence caused by dynamics uncertainties and disturbance,which is discussed in the following subsections.

Before that, we do some preliminary formulation.We define Md ∈ Rn×n as a diagonal matrix with diag-

onal elements mdii (x) > 0, which represents parts of thedynamics-model and can be easily obtained but has no needfor high precision. Then, there must exits an unknownmatrixΔM making equation Md +ΔM = M . Considering (15), wehave

Md x2 = (M − ΔM )x2= (M − ΔM )M−1[F(x) + d(t) + τ ]= τ − ΔMM−1τ + (I − ΔMM−1)d(t)

+ (I − ΔMM−1)F(x)= τ + g(τ ) + r(d) + F(x)

(16)

where g(τ ) = −ΔMM−1τ , r(d) = (I − ΔMM−1)d(t) andF(x) = (I − ΔMM−1)F(x).

Remark 1 Generally, according to the saturation of systeminput, the motor torque of a normal robotic or mechani-cal system are assumed to be bounded, therefore, g(τ ) =−ΔMM−1τ is considered bounded.

Assumption 1 The unknown internal and external distur-bance d(t) is assumed to be bounded, namely there existsan unknown positive constant dm making d(t) ≤ dm.

Then, we define another item, filtered tracking error siSlotine et al. (1991):

si =(d

dt+ λi

)n−1

ei

= e(n−1)i + C1

n−1λ1i e

(n−2)i + C2

n−1λ2i e

(n−3)i

+ · · · + λn−1i ei , i = 1, 2, . . . , n.

(17)

In (17), Cba denotes mathematical combination, lambda =

diag[λ1, λ2, . . . , λn] with λi (i = 1, 2, . . . , n) being posi-

tive constant to be designed, and e = [e1, e2, . . . , en] withei = xi − xdi . It is easy to confirm ei converges to 0 with siconverging to 0. Moreover, the “n” represents the state-spacedimension, and to be specifically, n = 2 in this paper as wehave only two state x1 and x2. Therefore, we have

s = e + λe (18)

and

s = e + λe= x2 − yd + λe= M−1

d [τ + g(τ ) + r(d) + F(x)] + ν

(19)

with ν = −ydi + λe.

3.1 Introduction of integral Lyapunov–Krasovskiifunction

Before introducing the designed controller, referring to Liet al. (2016a), we firstly present an integral Lyapunov–Krasovskii (20), to facilitate the design of the controller later,which is capable in avoiding singularity problem of a con-troller.

V1 = sT Mϑ s (20)

where Mϑ = ∫ 10 ϑMα dϑ = diag

[∫ 10 ϑMαi i (xi ) dϑ

],

with Mα = Mdα = diag[Mdiiαi i ]n×n . And the matrixα = diag[α11, α22, . . . , αnn]. To be simple for analyz-ing, we define α11 = α22 = · · · = αnn . And the xiis defined as xi = [xT1 , xT2 , . . . , xTn−1, xn1, xn2, . . . , ϑsi +ζi , . . . , xnm]T ∈ Rnm , with ζ = y(n−1)

di − ξi and ξi =λi1e

n−2i + · · · + λi,n−1ei . ϑ is an independent scalar to xi ,

including s and ζ . It is important to choose suitable Md andα such that Mdiiαi i > 0. Then we can write

V1 =m∑i=1

s2i

∫ 1

0ϑMαi i (xi , ϑsi + ζi ) dϑ (21)

Applying the symmetric nature of Mα and Mϑ , the partialderivation of (20) with respect to time can be derived

V1 = sT[2Mϑ s +

(∂Mϑ

∂ss)s +

(∂Mϑ

∂xx)s

+(

∂Mϑ

∂ζζ

)s]

(22)

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with⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

∂Mϑ

∂ss = diag

[1∫0

ϑ∂Mαi i

∂sisi dϑ

]

∂Mϑ

∂xx = diag

[1∫0

ϑ∑n

j=1∂Mαi i∂x j

x j dϑ

]

∂Mϑ

∂ζζ = diag

[1∫0

ϑ∂Mαi i

∂ζiζi dϑ

]

(23)

For

diag

[∫ 1

0ϑ

∂Mαi i

∂sisi dϑ

]=

∫ 1

0ϑ2 ∂Mα

∂ϑdϑ, (24)

we derive

sT(

∂Mϑ

∂ss)s = sT

([ϑMα] |10 − 2

∫ 1

0ϑBαdϑ

)s

= sT Mα s − 2sT Mϑ s (25)

For

diag

[∫ 1

0ϑ

∂Mαi i

∂ζisi dϑ

]=

∫ 1

0ϑ

∂Mα

∂ϑdϑ, (26)

and ζi = −νi , we have

sT(

∂Mϑ

∂ζζ

)s = sT

(−

∫ 1

0ϑ

∂Mα

∂ϑdϑ

)

= −sMαν + sT (27)

Then,

V1 = sT Mα s − sT Mαν

+sT[(

∂Mϑ

∂xx)

+∫ 1

0Mανdϑ

]. (28)

Substituting s with (19), we obtain

V1 = sT MαM−1d [τ + g(τ ) + r(d) + F(x)]

+sT[(

∂Mϑ

∂xx)s +

∫ 1

0Mανdϑ

](29)

Utilizing the symmetric property of α, Md and Mdα, thefollowing equation makes sense.

MαM−1d = MdαM

−1d = α (30)

Applying (30), we have

V1 = sTα [τ + g(τ ) + r(d) + F(x) + Θ] (31)

where

Θ =∫ 1

0ϑ

(∂Md

∂xx

)sdϑ +

∫ 1

0Mdνdϑ (32)

with

∂Md

∂xx = diag

⎡⎣

n∑j=1

∂Mdii

∂x jx j

⎤⎦ (i = 1, 2, . . . , n) (33)

3.2 Controller design

The controller design can be divided into two parts. Refer-ring to Zhang et al. (2016), for one, the DOB technologyis employed to estimate the internal or external unmeasur-able uncertainties and disturbance; for the other, the RBFNNis applied to approximate the residual uncertainties of therobot manipulator. Firstly, we define D as the estimation ofunknown disturbance D, with

D + D = D = g(τ ) + r(d) (34)

where D is the estimation error.Secondly, Applying RBFNN to approximate the rest

unknown dynamics uncertainties, we define

F(x) + D = −WT S(X) (35)

whereW is the NN weight and S(X) is the radial basis func-tion output, which is supposed to be bounded ||S(X)|| ≤Smax with input X = [xT1 , xT2 ]T . For the radial basis func-tion, we choose Gaussian function

Si (X) = exp

[−(X − ci )T (X − ci )

b2i

](36)

with ci = [ci1, ci2, . . . , ci,m] is the center and bi is the widthof the Gaussian function. In general, theoretically, RBFNNhas the ability to smoothly approximate all continuous func-tion. However, here in practice, errors always occur duringupdating weight and we define it to be

W = W − W (37)

with W is the updating weight in real time.Then, we can write

Md x2 = τ + D − WS (38)

To complete the formulation of DOB, an auxiliary equa-tion is designed as

z = D − K x2 (39)

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with K = KT > 0 is diagonal matrix and all its elementsare positive constants.

Considering (38), we calculate the derivative of z regard-ing to time

z = D − K x2 (40)

= D − KM−1d

[τ + D − WT S

](41)

Combining Remark 1 and Assumption 1, we assume thatthe system disturbance is slowly time varying. Thus, theremust exists an constant dm so as to

||D|| ≤ dm (42)

Therefore, (40) can be updated to be

˙z = −KM−1d

[τ + D − W T S

](43)

Consequently, the z can be updated as in every samplingtime, and the estimation value of D can be obtained as well

D = z + K x2 (44)

Finally, let us design the DOB and RBFNN based controllaw:

τ = −Gαs − D + W T S(X) − Θ (45)

whereG is the variable control gain partially computed from(13).

The RBFNN weight updating law is

˙Wi = −Γi

[Si (X)αi i si + δi Wi

](46)

where Γi ∈ Rn is one of a series of symmetric positivedefinite constant matrices and δi is one of a series positiveconstants.

Employing the above-mentioned Integral Lyapunov–Krasovskii Function, we take the following Lyapunov func-tion as candidate:

V2 = V1 + 1

2DT D + 1

2

n∑i=1

W Ti Γ −1

i Wi (47)

With the help of (31), (35) and (46), substituting D,WT Sand τ , the derivative of V2 can be written as

V2 = sT[−Gαs + D + W S(X)

]

+DT ˙D +n∑

i=1

W Ti Γ −1

i˙Wi (48)

Thanks to the following facts

D = D − D = z − z = z (49)

˙D = ˙z = z − ˙z= D − KM−1

d

[D + W T S

](50)

sTα D ≤ sααs2

+ DT D

2(51)

DT ≤ DT D

2+ ||D||2

2(52)

n∑i=1

W Ti Si (X)siαi i = sTαW T S(X) (53)

DT KM−1d W T S(X) ≤ ||D||2

2+ KM−1

d S(X)||W ||22

(54)

− δW Ti Wi = −δ||W ||2i − δW T

i (55)

Wi ≤ −δ||Wi ||22

+ δ||Wi ||22

(56)

we derive

V2 ≤ −sTα

(G − 1

2In×n

)αs

− DT(KM−1

d − 2In×n

)D

− δ − KM−1d Smax

2

n∑i=1

W Ti Wi

+ dm2

+ δ||W ||22

(57)

For further proving, we need to choose positive definitevariable gain matrixG, K and δ in order to make the follow-ing inequalities.

λmin

(α

(G − 1

2In×n

)α

)≥

∫ 2

0ϑλ (Mα) dϑ (58)

KM−1d − 2In×n > 0 (59)

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Fig. 4 Experimental setup

δ − KM−1d Smax > 0 (60)

Then, by enlarging the right side of inequality (57), to beexactly, the first three terms, we can establish

V2 ≤ −kV2 + C (61)

with

k = min

(λmin

(KM−1

d − 2In×n

),δ − KM−1

d Smax∑mi=1 Γ −1

i

, 1

)

(62)

C = dm2

+ δ||W ||22

(63)

Bya similarway to solve a differential equation, inequality(61) can be mathematically “solved” to be

V2 ≤(V2|t=0 − C

k

)e−kt + C

k(64)

where t denotes time. It is apparent that the right side of

inequality (64) exponentially converge toC

k, proving V2 to

be bounded, therefore, s, D and W are bounded.

4 Experimental study

The flow chart of the whole experimental setup is shownin Fig. 4. In such framework, we design the followingexperiments and simulations to verified the performance ofthe proposed teleoperation scheme and the proposed con-troller. Section 4.1 shows the strategy that human operatorwear two Myo armbands, using them to generate trajecto-ries and sEMG for the controller to control a tele-robot.Section 4.2 demonstrates the feasibility of the proposedcontroller, including the tacking performance of the pro-posed controller as well as the functionality of RBFNN inSect. 4.2.1 and the effectiveness of the variable gain approachin Sect. 4.2.2.

Fig. 5 Sample frames which depicts that Baxter’s left arm copiesmotions of operator’s left arm, confirming the feasibility of the pro-posed motion capturing scheme

Fig. 6 a Raw sEMG signals and filtered sEMG signals. bMotion cap-tured with operator stretching out his arm and drawing circles with hishand

4.1 Humanmotion capturing and sEMG signalscollecting

In this section, we demonstrate the feasibility of humanmotion capturing and human sEMG collecting.

Above all, the wireless hardware, twoMyo armbands, areworn on human operator’s arm (refer to Figs. 3b, 5) to collectmovements (quaternion) and sEMG signal (eight channels)data of operator, which are then transferred to the mastercomputer via Bluetooth technique. These data is processedin real-time and transformed into the joint position for thetele-robot manipulator (Baxter) and the gain increment forthe proposed controller.

Firstly,with operatorwearing twoarmbands onupper limb[one on upper arm and the other on forearm (Fig. 5)], employ-ing the theory developed in Sect. 2.2, the joint angles areobtained at the meanwhile when the operator moves his arm.They are converted to slave computer connecting to Baxterrobot. By employing the left arm of Baxter and command-ing it to move its first five joints (from shoulder to elbow)to match the received angles data by executing joint positioncontrol mode, we can intuitively see that the left arm of Bax-ter follows the human well, referring to Fig. 5, which depictsthat Baxter’s left arm copies motions of operator’s left arm.

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Fig. 7 This is the state of 0 position of all joints of Baxter left arm.The first two joints are selected as controlled object, while the othersare viewed as disturbance

Secondly, the sEMG signals can be extracted from bothMyos in any channel of the 16. In this experimental study,for the purpose of simplicity, we recorded sEMG data in onechannel on the Myo on the forearm (the MYO 2 in Fig. 6a),and the raw and the filtered time-series of sEMG amplitudeare shown in Fig. 6a. This data is then used to estimate humanarm’s muscle activity and transformed into the increment forthe control gain. In Fig. 6a, the human operator tensed (alittle) his arm muscle at around 33 s and tensed (tightly)and persist for a while from 43 to 48 s, while in the othertime, he remain his arm relax. Apparently, the sEMG signalare available and controllable: its amplitude climbs up asthe operator tense his muscle and stay to a minor value asthe operator relax his arm. Then, through the formulation inSect. 2.3, we obtain the filtered sEMG signal, and then thevariable control gain.

From the above figures and explanation, we see the fea-sibility for the proposed teleoperation scheme, including awireless way for human motion capturing and muscle activ-ity estimating.

4.2 Tracking performance verification

The tracking performance is verified through the followingexperiments and simulations.

In this verification, without loss of generality, we uti-lized the first two joints of the Baxter robot (“left_s0” and“left_s1”), while other joints are not considered a part of thecontrol object but viewed as a payload attached to the joint“left_s1” as well as disturbance, illustrated in Fig. 7.

4.2.1 Performance of different controllers

In this part, we collected trajectories using the proposedscheme developed in Sect. 2.2. These trajectories were col-lected when human operator stretched out his arm anddrew non-regular circles with his hand, depicted in Fig. 6b.The generated trajectories are shown in Fig. 8a with note“θ1d” and “θ2d”. Then, we utilized them for the two above-

mentioned joints of the Baxter to track, while other five jointswere forced to keep to 0 position with a widely-used Pro-portional Derivative (PD) controller. Here, it is important topoint out that the coupling dynamics of the last five linkscan be viewed as time varying stochastic disturbance, affect-ing the tracking performance of the first two joints. It can beexplained by figures from Fig. 8e–i that the last five jointsand links moved and collided sometimes as the first twolinks drawing circles, which certainly contributed to coupledynamical influence “attached” to the first two links. Tra-jectories were obtained offline and the tracking test wereconducted via the Baxter in the Robot Operating System(ROS) Gazebo platform.

For the purpose of a proper comparison between our pro-posed controller and the others, we referred to a traditionalPD controller, which is popularly employed in robot control,and a PD controller integrated with a NDOB proposed byChen et al. (2000).

The selected PD controller is: τ = −K1d e − K1pe, withK1d = diag[30, 29] and K1p = diag[225, 220].

The chosen PD controller with NDOB is:

τ = −K2d e − K2pe − d

d = z + p(θ, θ )

z = −L(θ, θ )z + L(θ, θ )(G(θ, θ ) − T − p(θ, θ ))

G(θ, θ ) = CNDOB + GNDOB

L(θ, θ ) = c

[1 01 1

]M−1

NDOB

p(θ, θ ) = c

[θ1

θ1 + θ2

](65)

where c = 0.01, K2d = diag[22, 20], K2p = diag[215, 215]and MNDOB, CNDOB and GNDOB are the first two linksdynamics model of Baxter robot, which can be nominallyobtained through Smith et al. (2016).

As far as to the proposed controller, Md was chosenas diag[0.05, 0.05], denoting that we did not know muchinformation about the controlled object model. And othervariables are listed in Table 2. In this part, the sEMG signalwas not yet involved and the control gain stayed constant.

Besides the three controllers mentioned above, to demon-strate the functionality of the RBFNN in the proposedcontroller, we simply remove the RBF item in the proposedcontroller (the third item in Eq. (45)) and form another con-troller to be compared. Hence, four controllers were involvedin this comparison.

The experimental results are shown in Fig. 8. Figure 8a,b show the desired and the real-time recorded trajectoriesand the tracking errors of the four controllers. Figure 8c, ddepict the control outputs and the norm of RBFNN weights.Figure 8e–i are the positions and torques in joint 3–joint 7,

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0 2 4 6 8 10 12 14 16 18 20Time (s)

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t 1 p

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Four controllers performance comparison in joint 1θ1,raw

θ1dθ1dθ1dθ1-PDθ1-PD with NDOBθ1-Proposed, without RBFθ1-Proposed

9.2 9.6 10

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θ2dθ2dθ2dθ2-PDθ2-PD with NDOBθ2-Proposed, without RBFθ2-Proposed 15.5 16 16.5

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oint

4 (

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θ4dθ4

Collision

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τ4

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6 (

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τ6

(h)

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ition

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oint

7 (

rad)


θ7dθ7

0 2 4 6 8 10 12 14 16 18 20

Time (s)

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0

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0.4

Tor

que

in jo

int 7

(N

m)


τ6

(i)

Fig. 8 Experimental results of the performance comparison of three controllers

Table 2 Variables of theproposed controller

Parameters Value Parameters Value

Sampling rate 100 Hz Node centres Combination of θ1(0.1, 0.9), θ2(−0.9,−0.1),θ1(−0.24, 0.24) and θ2(−0.24, 0.24)

Control rate 100 Hz λ diag[17.5, 16]No. of RBF nodes 16 G diag[17.5, 16]Node variance 1 K diag[0.1, 0.1]Initial weight 0

which certainly raise constant (the weight of the five linksand joints), time-varying and stochastic (coupling dynamics,even some collision in joint 4, see Fig. 8f) disturbance to thecontrolled object, the first two joints.

Based on these results, especially on Fig. 8a, b, we see twofacts: (i) comparing to the proposed controller, the trackingtrajectory and errors fluctuate more sever when the RBFNNitem is cut off, and (ii) tracking errors keep to minimumin most time when the proposed controller was employed.

Therefore, we can conclude that: (i) without RBFNN, thesystem become less stable, and in anotherwords, theRBFNNintegrated to the proposed controller has the ability to atten-uate the affect caused by model uncertainties, and (ii) theproposed controller can perform well even under such asever circumstance with hardly measurable disturbance, sur-passing the PD controller and the PD controller with aNDOB. This simulation confirms the feasibility of the pro-pose scheme of integrating the RBFNN algorithm and DOB

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Fig. 9 Disturbance is created through driving the sixth joint to track asine curve, while the first two joints are controlled to stay in 0 position

technology in the controller to attenuate the adverse influencecaused by model uncertainties and disturbance.

4.2.2 Effectiveness of variable gain control

Let us imagine a scenario where we need to teleoperate arobot to rescue a pet and the tele-robot needs to hold it andput it into a safe box, but the animal is scared and strug-gling to escape from the robot end effector. In such cases, weneed a strategy to keep the end effector closed to the desiredposition under such condition with unknown and fast time-varying disturbance. Hence, we proposed this variable gaincontrol scheme. Through this method, we can do it easily:the control gain can be convenientlymodified by the operatorthrough tensing or relaxing his arm muscles, which is practi-cal in robot teleoperation. The following study demonstratesits effectiveness.

To verify the anti-disturbance performance of the pro-posed variable control gain scheme, firstly, we collectedsEMG time series. The collected sEMG was employedoffline, simply supposing that the operator began to tenseor relax his arm muscles when he realized the teleoperationsituation required him to modify the control gain. Secondly,we created different disturbances with different frequenciesand amplitudes through the method depicted in Fig. 9 wherethe sixth joint of Baxter is driven to follow a sine wave:θ6d = nsin(2mπ t); Thirdly, we employed the developedvariable gain method to try to keep the first two joint ofBaxter (in Gazebo) to 0 position under circumstances withdifferent disturbances.

In this part, the parameters we utilized are the same asthose listed in Table 2 except for those in Table 3

For the part of creating disturbance, we forced the sixthjoint to track a sine wave with different frequencies in a fixeddirection, the 45◦ in Fig. 9. Such direction ensures that thiskind of dynamical disturbance generated by the sixth jointinfluences the first two joints.

Table 3 Parameters utilized in variable gain control tests

Parameters Value

Node centers Combination of θ1(−0.4, 0.4),θ2(−0.4, 0.4), θ1(−0.56, 0.56) andθ2(−0.56, 0.56)

G Gmax = diag[30, 28], Gmin = diag[15.5, 15]A −0.04

N 1

(n, m) in Fig. 9 (± 0.8, 1)

Then we conducted the simulations under different kindsof circumstances. One result of them is shown in Fig. 10,while the others are in Table 4.

In every minipage of Fig. 10, we divide the results into5 stages, which are marked out alternately by two kinds ofgray background colour.

Stage 1 is from0s to 5s and the first two joints are free fromfast-time-varying disturbance. They normally stay to the 0position, see Fig. 10a. We can see the controller functionswell in such peaceful environment, though the “attached”static disturbance (payload of the last five joints) never dis-appears.

Stage 2 is from 5 to 15 s and the fast-time-varying distur-bance starts, see Fig. 10h, but the sEMG is not yet employed.We can see the influence of the movement of joint 6 onjoint 1 and joint 2: the tracking errors of joint 1 and joint2 increase up to around ± 0.6 rad and ± 0.5 rad respec-tively, see Fig. 10a, b. Though theRBFNNstartsworking, seeFig. 10f, theDOB is of no use to this kind of fast-time-varyingand asymmetrical disturbance. The asymmetry property ofdisturbance can be reflected by the unsymmetrical errors,which mainly results from the particular movement limit ofjoint 4.

Stage 3 is from 15 to 30 s, where the sEMGbegins to workand the control gainG11 andG22 are lightlymodified because(suppose) the operator still does not notice the disturbance,see Fig. 10e, and no changing of the tracking errors of joint1 and joint 2 can be noticed.

Stage 4 is from 30 to 45 s, and (suppose) the operatorrealizes the disturbance and keeps his muscle tensed at thefirst time. In this stage, the tracking errors of joint 1 and joint2 apparently decrease (Fig. 10b) as control gain increases(Fig. 10e).

Stage 5 is from 45 to 60 s, where the movement of joint6 keeps going but the control gain moves to another higherstate, which results in the minimum errors in joint 1 and joint2 among all stages, see Fig. 10a, b.

The other minipages in Fig. 10 without being mentionedabove also describe some information of the procedure, espe-cially in Fig. 10c, we can see the increase of the controlleroutputs (control torques) as sEMG climbs up.

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The root mean square errors (RMSE) are also computed:RMSE1,1 (joint 1, 17.5–27.5 s) = 0.00127, RMSE1,2 (joint1, 32.5–42.5 s) = 0.00104, RMSE1,3 (joint 1, 47.5–57.5 s)= 0.00079, and likewise, RMSE2,1 = 0.00120, RMSE2,2 =0.00103, RMSE2,3 = 0.00080. They, in another aspect, con-tribute to the verification of the effectiveness of the variablegain control scheme.

In Table 4, another 12 simulation results are given, inwhich all conditions in every single No. are the same to theaforementioned simulation except for thosemarked out in thesecond column. Similarly, all RMSE results reveal the factthat as the operator tenses his forearm muscles, the trackingerrors of joint 1 and joint 2 tend to decrease, nomatter chang-ing the disturbances, modifying the control gain intervals oradjusting different amplitudes of the operator’s arm musclesEMG (note: these sEMG series were obtained when opera-tor regularly relax-tense his arm muscles alike Fig. 10e).

Therefore, we yield a brief summary that the proposedvariable gain control scheme is practical and able to resistsuch fast-time-varying disturbance.

5 Conclusion

This paper mainly introduces a novel, simple and possiblescheme for robot teleoperation. By utilizing Myo armbandsin capturing humanmotion and collecting arm sEMGsignals,

human motion can be transferred to a tele-robot manip-ulator, making it work more flexibly as a human being.This wireless way has advantages such as being availableto captured human motion anywhere (comparing to thosemachine-vision methods that might be blocked by obsta-cles) and being simpler and more comfortable for operators(comparing to those EMG-extracted technique that requiresoperator to wear complex sensors). In addition, by utilizingthe proposed controller, integrating the DOB technology, theRBFNN algorithm and the variable gain strategy, the tra-jectory tracking performance of robot manipulator is fine,compared to those mentioned controllers. Model dynamicsuncertainty problems are out of account, since the proposedcombination of DOB and RBFNN reduces the reliability ofconstructing a precise dynamics non-linear model. And thevariable gain control scheme is practical and verified to beeffective in resisting the fast-time-varying disturbances tosome extent. Experimental and simulation results demon-strate the merits of the proposed approach which enables thetele-robot manipulator to copy human arm motions, and toresist low and high-frequency disturbances.

Though good results in the paper demonstrate the feasi-bility of the proposed method, we still have a long way togo to improve the system in the future. For instance, we aregoing to find out more suitable ways to generate position,velocity and acceleration trajectories without using slidingwindow filter, for which actually brought about many side

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Table 4 Variable gain control tests results

No. Changed condition RMSE results

RMSE1,1 RMSE1,2 RMSE1,3RMSE2,1 RMSE2,2 RMSE2,3

1 m = 1.1 0.00135 0.00118 0.00097

0.00126 0.00111 0.00092

2 m = 0.9 0.00111 0.00082 0.00064

0.00105 0.00081 0.00067

3 m = 0.8 0.00082 0.00059 0.00047

0.00074 0.00056 0.00046

4 n = ±1 0.00125 0.00099 0.00084

0.00119 0.00096 0.00086

5 n = ±0.9 0.00126 0.00103 0.00086

0.00122 0.00102 0.00085

6 n = ±0.7 0.00125 0.00100 0.00081

0.00119 0.00098 0.00082

7 Gmax = Gmax + 2 0.00131 0.00099 0.00080

0.00125 0.00096 0.00082

8 Gmin = Gmin − 2 0.00140 0.00109 0.00082

Gmax = Gmax + 2 0.00131 0.00106 0.00087

9 Gmin = Gmin − 2 0.00137 0.00112 0.00087

Gmax = Gmax − 2 0.00130 0.00110 0.00088

10 sEMG series 1 0.00131 0.00124 0.00096

0.00125 0.00120 0.00096

11 sEMG series 2 0.00130 0.00120 0.00097

0.00126 0.00116 0.00095

12 sEMG series 3 0.00129 0.00105 0.00084

0.00123 0.00103 0.00085

effects, such as lagging of the trajectories, and causing themissing of actual peak values, etc..

Acknowledgements This work was partially supported by Engineer-ing and Physical Sciences Research Council (EPSRC) under GrantEP/S001913, and partially by the National Natural Science Foundationof China under Grant 51575412.

Open Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing, adap-tation, distribution and reproduction in any medium or format, aslong as you give appropriate credit to the original author(s) and thesource, provide a link to the Creative Commons licence, and indi-cate if changes were made. The images or other third party materialin this article are included in the article’s Creative Commons licence,unless indicated otherwise in a credit line to the material. If materialis not included in the article’s Creative Commons licence and yourintended use is not permitted by statutory regulation or exceeds thepermitted use, youwill need to obtain permission directly from the copy-right holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Publisher’s Note Springer Nature remains neutral with regard to juris-dictional claims in published maps and institutional affiliations.

Darong Huang is currently pur-suing the Ph.D. degree under thesuccessive postgraduate and doc-toral study program in South ChinaUniversity of Technology, China,and major in control science andengineering. His current researchinterest lies in intelligent controlstrategy, robot teleoperation andhuman–robot interaction.

Chenguang Yang (M’10–SM’16)is a Professor of Robotics. Hereceived the Ph.D. degree in con-trol engineering from the NationalUniversity of Singapore, Singa-pore, in 2010 and performed post-doctoral research in human roboticsat Imperial College London, Lon-don, UK from 2009 to 2010. Hehas been awarded EUMarie CurieInternational Incoming Fellowship,UK EPSRC UKRI Innovation Fel-lowship, and the Best Paper Awardof the IEEE Transactions on Roboticsas well as over ten conference

Best Paper Awards. His research interest lies in human robot interac-tion and intelligent system design.

Zhaojie Ju (M’08–SM’16) receivedthe B.S. degree in automatic con-trol and the M.S. degree in intelli-gent robotics from the HuazhongUniversity of Science and Tech-nology, Wuhan, China, and thePh.D. degree in intelligent roboticswith the University of Portsmouth,Portsmouth, U.K. He is currentlya Reader in machine learning androbotics with the School of Com-puting, University of Portsmouth.His current research interests incl--ude machine intelligence, patternrecognition and their applications

on human motion analysis, human–robot interaction and collabora-tion, and robot skill learning. He has authored or co-authored over110 publications in journals, book chapters, and conference proceed-ings. Dr. Ju was a recipient of the four Best Paper Awards and oneBest AE Award in ICRA2018. He is an Associate Editor of the IEEETRANSACTIONS ON CYBERNETICS and the International Journalof Humanoid Robotics.

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Shi-Lu Dai (S’09–M’11) receivedthe B.Eng. degree in thermal engi-neering and the M.Eng. and Ph.D.degrees in control science and engi-neering from Northeastern Uni-versity, Shenyang, China, in 2002,2006, and 2010, respectively. From2007 to 2009, he was a Visit-ing Student with the Departmentof Electrical and Computer Engi-neering, National University of Sin-gapore, Singapore. From 2015 to2016, he was a Visiting Scholarwith the Department of ElectricalEngineering, University of Notre

Dame, Notre Dame, IN, USA. Since 2010, he has been with theSchool of Automation Science and Engineering, South China Univer-sity of Technology, Guangzhou, China, where he is currently a Pro-fessor. His research interests include adaptive and learning control anddistributed cooperative systems.

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Disturbance observer enhanced variable gain …...Keywords Disturbance observer · Motion capture · Radial basis function neural networks · Teleoperation · Variable gain control