Direct Estimation of Wrist Joint Angular
Velocities from Surface EMGs
by Using an SDNN Function Approximator
Kazumasa Horie1 , Atsuo Suemitsu2 , Tomohiro Tanno1 , and Masahiko Morita1
1

University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, Japan,{horie|tanno|mor}@bcl.esys.tsukuba.ac.jp,
2
Sapporo University of Health Sciences, 2-1-15 Nakanuma Nishi 4, Higashi-ku,
Sapporo, Hokkaido, Japan,
sue@sapporo-hokeniryou-u.ac.jp

Abstract. The present paper proposes a method for estimating joint
angular velocities from multi-channel surface electromyogram (sEMG)
signals. This method uses a selective desensitization neural network(SDNN) as a function approximator that learns the relation between integrated sEMG signals and instantaneous joint angular velocities. A comparison experiment with a Kalman filter model shows that this method
can estimate wrist angular velocities in real time with high accuracy,
especially during rapid motion.
Keywords: Surface Electromyogram, Angular Velocity Estimation, Selective Desensitization Neural Network

1Introduction

Surface electromyograms (surface EMGs) are electrical activities recorded usingskin surface electrodes. Surface EMGs are produced by skeletal muscles andcontain information about a motion and its purpose. Recently, methods havebeen proposed for recognizing human motions from surface EMGs in order todevelop an EMG-based human-machine interface. We can classify these methods
into two types: classification of motion types and estimation of the joint angles.
Methods that can recognize complex hand motions in real time have beenproposed (e.g., [FO1]). However, these methods can recognize only the summaryof the motion purpose and classify only six to eight types of motion with highaccuracy. We cannot develop a user-friendly interface that reflects the user’s
intentions adequately with only classification methods.
Joint-angle estimation methods (e.g., [KK1]) can recognize more detailed
purposes of motion than classification methods. However, these methods cannot
estimate joint angles during rapid motion. The non-linear relationship between
the isometric muscle strength and the joint angle during rapid motion makes it
diﬃcult for these methods to model the motion. Thus, these methods cannot beapplied to a practical interface.

In addition, the estimation method of joint angles and velocities using aKalman filter (KF) [AK1] has been proposed. This method, however, was applied only to slow motion (about 30 deg/s). No method has been proposed forestimating the angular velocities of fast-moving joints such as the wrist (wrist
angular velocities may reach 1,900 deg/s at a maximum). Furthermore, the KF
may not have ability to express the dynamics of wrist rotation around the rollaxis because of the non-linearity of the relation between the surface EMGs andthe angular velocity.
In this study, we model the relationship between multichannel surface EMGs
and wrist joint angular velocities using a function approximator and estimate
the latter from the former. This method will enable an interface to use motionpurpose information which could not previously be obtained.
We choose a selective desensitization neural network (SDNN) as the function
approximator. Recent studies have shown that the SDNN has excellent learningand generalization abilities. For example, Nonaka et al. applied an SDNN to theapproximation of a two-variable function and showed that the SDNN can learn
a non-linear and discontinuous function with a small training sample [NM1].
These features will enable the proposed method to learn the complicated relation
between surface EMGs and the instantaneous joint angular velocities.
The following sections describe the SDNN and our proposed method. We
also verified the eﬃcacy of the proposed method through the estimation of wrist
angular velocities.

2

Selective Desensitization Neural Network

SDNNs are known to provide good approximations of a wide range of functions
using a small set of training data samples [NM1]. In this section, we explain how
a function y = f (x) is approximated based on an SDNN given a continuousvalued input vector x = (x1 , . . . , xm )(m >= 2).
The input layer of the SDNN consists of m neural groups. Each group has nunits that represent an input signal xi , i.e., the input signal is represented in a
distributed manner by the activity patterns of the units. If the range of possible
values for input signals is divided into q ranges, each interval corresponds todiﬀerent activity patterns which are configured using equal numbers, +1 and−1. The pattern changes gradually as the variable value changes progressively,
resulting in a high correlation between the patterns when the values are close
and a low correlation when the values are far apart. The correlation between
patterns of the values that are far apart is 0.
The middle layer comprises m(m−1) (= m P2 ) neural groups (G1,1 , G1,2 , . . . ,m,m−1G). The units in Gµ,ν are connected with both of the units in Gµ and Gν ,which are located in the input layer. This realizes a procedure called desensitization, which neutralizes the output of the units, regardless of their input andinner potential. For example, if the ith units of Gµ are desensitized by the jthunit of Gν , the output of the ith unit of Gµ,ν is given bygiµ,ν =gjν + 1 µ· gi .
2(1)where giµ is the output of the ith unit of Gµ and gjν is the output of the jth unitof Gν . This creates a pattern in which half of the units are 0 and the rest are
the same as Gm u (either +1 or −1).
The output layer of the SDNN comprises l units. Each of the units is connected to all of the units in the middle layer. The output of the ith unit in theoutput layer is calculated by(∑)
∑nµ,ν
µ,ν
yi = Hw·g+hijµ,ν(µ̸=ν)
j=1 i,j{(2)1 (u > 0)
H (u) =0 (otherwise)µ,ν
where wi,jis the synaptic weight from the jth unit of the Gµ,ν in the middlelayer and hi is a threshold. The final output y of the SDNN is determined basedon the number of units with an output of 1 in the output layer. Learning isachieved by error-correction training (the p-delta learning rule [AW1]) in thisnetwork.

3

Proposed method

Our proposed method has three components: surface EMG acquisition, signal
preprocessing, and function approximation (Figure 3.1).
3.1

Surface EMG Acquisition

The surface EMGs are measured at 10 points on the forearms (Figure 3.1). A
relatively large number of sensors is required, but it is not necessary to positionthe sensors accurately on specific muscles. The surface EMGs are measured
and sampled at 1 kHz using Personal-EMG (Oisaka Electronic Device Ltd.)equipment and a 12-bit A/D converter.
3.2

Signal Preprocessing

Surface EMGs are not suitable for use as input signals because of their fluctuations. Thus, it is necessary to extract features by signal preprocessing. In theproposed method, the integral of the surface EMG (IEMG) and its mean overthe previous 300 ms (average IEMG: AIEMG) are obtained as features.
IEMGs can be obtained easily with little time lag using a low-pass filter.
Thus, the IEMG is well-suited for a human-machine interface that requires arapid response. Unfortunately, this signal is not directly related to joint angularvelocities; it is related to the force generated by muscles. It is diﬃcult to achieve
accurate estimation with only IEMGs. AIEMG is the mean of the IEMG over the(a) Thumb side(b) Small finger side
Fig. 2. Arrangement of EMG sensors.
Fig. 1. Structure of the proposed method.

previous 300 ms. We consider that the AIEMG corresponds to muscle contraction
speed. AIEMG is well-suited for estimation of joint angular velocities. However,there is a large time lag between the AIEMGs and the actual joint angularvelocity itself. Therefore, the combined use of both of these features can be
expected to enhance the accuracy and reduce the adverse eﬀects of the time lag
between the AIEMGs and the actual angular velocities.
In the proposed method, a filter box (Oisaka Electronic Device Ltd.) and asimple-moving-average (SMA) filter are used to convert the surface EMGs intofeatures. Both features are normalized against their maximum values during eachtime step before being used as inputs for the SDNN.
3.3

Function Approximation

As a component of function approximation, the SDNN models the relation between the features and the joint angular velocities. The SDNN is constructed asshown in Figure 4.1 and used as a function approximator. Note that the SDNN
is prepared for each axis of rotation, but all SDNNs have the same structure andparameters.
The input layer comprises 10 neural groups (G1 , · · · , G10 ) and 10 other neural groups (G11 , · · · , G20 ), which represent the IEMGs and the AIEMGs, respectively. The activity patterns of the units are determined from the input signals
using the parameters n = 96, q = 96.
The middle layer has two parts P1 and P2 , which comprise 90 and 20 neuralgroups, respectively. The units of the neural groups in P1 are connected with theunits of two neural groups from G1 , · · · , G10 . In P2 the units of the neural groups

are connected with the units in the corresponding pair of the neural groups((G1 , G11 ), · · · , (G10 , G20 )). In the middle layer, half of the units are desensitizedby the corresponding units in the input layer.
The output layer comprises 140 units and calculates the final output of theSDNN by 0.01k − 0.2 ([-0.2, 1.2]), where k is the number of units with outputsof 1 in the output layer. The output represents the normalized joint angularvelocity, which is calculated byVn (t) =Vm (t)+ 0.5
2 · maxt′ |Vm (t′ )|(3)where Vn (t) and Vm (t) are the normalized and measured joint angular velocities
at time t, respectively. The output range of the SDNN is wider than that of
the normalized joint angular velocity, which enhances the learning ability of theSDNN. According to the error-correction training algorithm (the p-delta learning
rule [AW1]), the SDNN repeats the training process until the root mean squared
error (RMSE) is suﬃciently low or a specific number of iterations have beencompleted.

4Experiment

To evaluate the proposed method, we performed a comparison experiment with aKalman filter (KF) model [AK1]. The KF model did not use the AIEMGs as input because a preliminary experiment showed that they decrease the estimation
accuracy. To implement the KF model, Matlab and the System Identification
Toolbox were used.
4.1

MethodA three-axis gyroscope (MP-G3-2000B, MicroStone Co. Ltd.) was used to measure the wrist angular velocities. The gyroscope was mounted on the back of theright hand (Figure 4) and measured the angular velocities around the pitch androll axes. The velocities were normalized against the maximum values during
each time step.
To obtain measurements of wrist angular velocities and surface EMGs, eightmale subjects (24 ± 2 years old) were asked to execute flexion-extension andsupination-pronation repeatedly at diﬀerent speeds for 10 s. The subjects repeated this task nine times for each motion, and finally, we obtained 18 (2motions × 9 repetitions) samples in total. Next, we selected six samples (threesamples for each motion) to train the corresponding SDNN and performed threefold cross-validation.
4.2

Results

The experimental results are summarized in Table 1. The RMSE values aroundthe pitch axis (corresponding to flexion and extension) with the proposed method

Fig. 4. Installed gyroscope.
Fig. 3. Structure of the SDNN used in theproposed method.

and the KF model were 79.7 and 97.7 deg/s, respectively. Each system could
estimate the approximate angular velocities around the pitch axis. There wereno significant diﬀerences between the methods. In contrast, the RMSE aroundthe roll axis (corresponding to supination and pronation) with the KF model(232.8 deg/s) were two times higher than those obtained with the proposed
method (p < 0.01: Wilcoxon signed-rank test).
Figures 5 and 6 show the example of the estimated angular velocities withthe proposed method and the KF model, respectively. Figure 6(b) demonstrates
that the KF model could not estimate the angular velocity around the roll axis,
especially during rapid motion.
The estimation accuracy of the KF model depends on the linearity of therelation between the IEMG signals and the angular velocities. The relation between the signals and the joint angular velocities around the roll axis may bevery complicated because pronation and supination require the coordination ofmultiple muscles (flexor carpi radialis, pronator teres, etc.), making it diﬃcult
for the KF model to solve this problem.
In contrast, the SDNN has adequate ability to learn the non-linearity relationship. Thus, the proposed methods can handle rapid motion or rotation
around the roll axis. The diﬀerence in learning ability between the KF and theSDNN caused the variation in estimation accuracy.

5Conclusion

In this study, we proposed a method for directly estimating the wrist angularvelocities around the pitch and roll axes from multichannel surface EMGs using

1500
500-500 0

1234567896789-1500(a) Flexion-Extension
1500
500-500 0

12345-1500
me (sec)
MeasuredEs mated(b) Supination-Pronation
Fig. 5. Example of joint angular velocity estimation with the proposed method.
1500
500-500 0

1234567896789-1500(a) Flexion-Extension
1500500-500 012345-1500
me (sec)
MeasuredEs mated(b) Supination-Pronation
Fig. 6. Example of joint angular velocity estimation with the KF.

Table 1. Root mean squared error among the estimated angular speeds (deg/s).

(a) Around the pitch axis
AB

C

Subject
DEFG

H

Ave.

SDNN 63.9 60.0 84.8 89.5 76.3 60.4 113.3 89.6 79.7
KF 91.7 43.1 137.1 142.5 108.7 49.9 127.3 81.4 97.7(b) Around the roll axis
AB

C

Subject
DEF

GH

Ave.

SDNN 115.3 105.7 122.4 140.1 124.3 133.6 134.8 100.5 121.9
KF 243.3 150.9 265.8 247.9 220.5 272.0 285.0 176.7 232.8

SDNNs. The experimental results show that the proposed method can estimate
the approximate angular velocities of the wrist. The proposed method will be
useful for recognizing the purpose of the rapid motion.
In future research, we aim to improve the estimation accuracy and to implement an EMG-based device using the proposed method.

Acknowledgment
This work was supported partly by JSPS KAKENHI grant numbers 22300079
and 24700593 and by Tateishi Science and Technology Foundation grant number
2157011.

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