The Estimation of Knee Joint Angle Using Generalized Regression Neural Network

(GRNN)based on Generalized Regression Neural Network (GRNN) and Neural Network (NN) With

Wavelet FeaturesSubtitle as needed (paper subtitle)

Tanvir Anwar (Author)School of Elec, Mech and

Mechatronic system University of Technology, Sydney

Sydney, Australiatanvir.anwar@student.uts.edu.au

Yee Mon AungSchool of Elec, Mech and

Mechatronic system University of Technology, Sydney

Sydney, Australiayee.m.aung@student.uts.edu.au

Adel Al Jumaily School of Elec, Mech and

Mechatronic systemUniversity of Technology, Sydney

Sydney, AustraliaAdel.Al-Jumaily@uts.edu.au

Abstract— To capture Capturing of the intended action of the patient and provide assistance as needed is required in, the robotic rehabilitation devices. shouldThe intended action data that can be be able to extract from sEMG signal extract from sEMG signal can include the intended posture, intended torque, intended knee joint angle and intended desired impedance of the patient. Utilizing such data to driven robotics assistive devices , like Thus an exoskeleton, device requires a multilayer control mechanism to achieve a smooth Human Machine Interaction force. It is very important that the controller for gait assistive device is able to extract as many information as possible from the patient muscle with impaired limb and identify different parameters associated with gait cycle. This paper proposes a new technique based on sEMG signal to predict knee flexion and extension postures as well as Knee Joint angles of two postures. Gait cycle of lower limb consists of flexion and extension postures at knee, hip and ankle joints respectively. Knee joint flexion has an operational range of 50o and extension has an operational range of 90°. The sEMG data has been collected from healthy person who completed knee joint (flexion and extension) motion in 2s, 3s, 4s and 5s. The feature data of raw sEMG data have been filtered with a second order digital filter and then input to the Neural Network (NN), ) and to Generalized Regression Neural Network (GRNN) to estimate the angle of flexion and extension. The GRNN and NN have been tested with RMS, LOG, MAV, IAV, Hjorth, VAR and MSWT features. MSWT feature has ensured 1.5704 Mean Square Error which is very promising. The SVM has been used to predict postures (flexion and extension). The SVM has classified flexion and extension with 100% accuracy.

Keywords— EMG, Flexion, Extension, Interaction Force, NN, GRNN.

I. INTRODUCTION (HEADING 1)

The conventional Robotic Rehabilitation Device (RRD) is in the pattern of industrial robot which still behaves like master-slave manner (MIT-MANUS). One of the main objectives of a RRD is to obtain a smooth human machine interaction in different phases of gait cycle at the patient exoskeleton interaction point. The control interface between the paralysed and rehabilitation exoskeleton is most of the times unidirectional. Research is taking place to make the human machine interaction bidirectional to achieve a very effective wearable exoskeleton for rehabilitation purpose. At the interaction point patient and exoskeleton need to share the control of joint torque, angle and postures (flexion and extension) together. In human body, brain is the controller that generates necessary signal for actuator and muscle is the actuator. In the exoskeleton device, Robot is the controller and generates necessary signal for the actuator. When patient’s brain is affected due to stroke or any other injury then brain cannot generate necessary signal for limb movement. Then Robotic Rehabilitation device shares most of the joint activities (torque, angle, posture, impedance). As a result of the Robotic therapy of the lower limb, the brain is able to generate necessary EMG signal responsible for lower limb movement. This phenomenon is called plasticity. It is evident that for a successful plasticity from robotic rehabilitation therapy, prolonged span of therapy time and intensive rehabilitation are key issues of a stroke affected impaired patient. So far HALL

has implemented sEMG successfully at human-machine interaction in a very much bidirectional fashion. BLEEX, LOPES are other RRDs that are also used commercially for rehabilitation purposes without any consideration of dynamic set operating point extracted from sEMG muscle signal. One of the very key criteria to be addressed for a successful Wearable Robotic Rehabilitation suit is that users feel comfortable wearing exoskeleton and patient experiences minimum interaction force at the interaction point when the exoskeleton is in operational mode. The interaction force can be manipulated in two ways. In first case maximum or minimum interaction force is known due to prior knowledge of the interacting environment. In second case, manipulation of interacting force is very dynamic in nature because the environment is unknown and always changing. In such cases, Impedance controller act as spring, mass damper kind of knee joint. For the exoskeleton interaction force that is interacting with patient’s lower limb, patient has to be an active element rather than passive in the closed loop control system. The patients muscle and the sEMG from it provides Patient’s intention. The signal is then processed and executed by the actuator in advance as a control signal. By sEMG extraction one can control dynamic behaviour of exoskeleton knee joint properties when contacting with patient’s impaired limb, namely controlling the stiffness and the damping of the joint. The achievement of myoelectric control system (Control with sEMG signal) can be summarized into three distinct generations.

The 1st generation offers ON/OFF control schemes with a single speed or single rate of actuation

2nd generation includes a (i) state machine, (ii) Large scale threshold manipulator, (iii) signal amplification, (iv) the adjustment of muscle contraction rate, (v) proportional control.

3rd generation incorporates programmable microprocessors that allow an infinite range of adjustment of myoelectric characteristics. Advanced signal processing methods and artificial intelligence are employed by microprocessors in adjusting input characteristics.

sEMG signal lately is used to generate the above mentioned control signal by being an active element. sEMG is an electrical signal that has amplitude, frequency and phase feature that describes signal behaviour and contains lots of information of the patient’s intension that are across his mind. For example, sEMG peak amplitude describes how much maximum force a patient’s muscle can exert. Mean of sEMG that describes

sEMG signals strength and its endurance. Integrated sEMG describes how much energy produced during a certain period of time.

Root Mean Square of sEMG describes total activation timing of a muscle (Signal quality).

Some of the frequency domain feature of sEMG signal is Mean frequency MNF and Median frequency MDF, increase or decrease of which describes increase or decrease of muscle force or load.

Increase of MNF and MDF describes decrease of muscle length or joint angle.

Onset and offset time of sEMG signal describes the transient behaviour.

Onset and offset time of sEMG signal describes the transient behaviour.

Combination of both transient and steady state of EMG signal would increase utility and the robustness of the recognition of any particular type of patients intention in the robotic rehabilitation system for clinical applications . To boost the system accuracy, different approach like number of electrode per muscle, the electrode configuration, selection of good filters for noise reduction and various features (application dependent) are used so far. Time domain, frequency domain and combination of both are three different ways of preparing feature set data for various computational methods. For signal that are very static in nature, only time domain feature is enough. The signals that are very dynamic in nature and their composites are changing with respect of time, for such signal frequency domain features are very useful. For dynamic signal, features that contains ((dx(t))/dt) from x(t) yields higher accuracy than without ((dx(t))/dt). Root mean square (RMS), Integral of absolute value (IAV), Auto Regression Coefficients, Slope Sign Changes, Zero Crossing, Fourier Coefficients, Wavelets are most popular features used in research . The features data set is then mapped into desired target namely,

posture selection (flexion and extension, classification problem),

angle estimation of extension or flexion (Regression problem),

torque estimation (Regression or Classification,

sEMG signal can also be mapped into Stance, Swing, and Support phase of lower limb gait cycle(Sidek and Mohideen 2012).

sEMG signal can also be mapped to standing, sitting, climbing movements of lower limb gait cycle. The Muscle activity levels are different at different muscle at different phases of the gait. So looking at different intensity level of various muscles, one can identify standing, sitting or climbing phases of walking cycle. In standing position, estimated knee joint torque is observed to be decreasing and torque of hip is increasing. To lift upper body, a large hip torque is observed. Similarly, in sitting and climbing also such variations in sEMG signal intensity at various muscle involved in knee and hip are observed.

The relationship of angle, posture, torque and impedance to sEMG is very non-linear and is very difficult to model. So the computational methods are very handy to model such nonlinear behaviour of the muscle due to fatigue, cross-talk or rotating

joints. NN, SVM, SVR, ELM, FUZZY are various computational methods used to classify or estimate various parameters of knee joint kinematics and dynamics associated with gait cycle.

II. ROBOTIC REHABILITATION CONTROL SCHEMATICS

In figure 1 different computational method have been used to generate whole set of set points for lower level PID controllers that are used to track a desired trajectory of lower limb. DC motor, hydraulic actuator, series elastic actuators are different actuators that execute the regulated control signal that are generated by different lower level controller like proportional, PD and PID controllers. SVM, ELM, GRNN, BPNN, NN are various machine learning methods are used in the high level controller to produce desired set points necessary to generate lower limb joint kinematics and dynamics. The inverse dynamics of the lower limb joints are as important as forward dynamics to the open loop control system. Interaction force at the interaction point and joint angle of knee, hip joint are input to Fuzzy Logic, Admittance, Impedance, Neuro Fuzzy controller to reset the set points (desired reference) of various lower level controllers (P,PD,PID) to keep track of a dynamic trajectory. Fuzzy Logic Controller is widely used to modulate the joint impedance parameters based on therapist experience using interaction force and joint angle as fuzzy input membership function. Usually trajectory of any joint consists of position, velocity and acceleration. So a controller is required that co-relate these joint kinematics to optimize an interaction force at the interaction force. In achieving an optimized interaction force, some parameters are penalized and some parameters are reward through multiplication of associated weights. So an automatic control system that tunes the parameters every few samples is required that serve our purpose.

Fig. 1. Bidirectional Robotic Rehabilitation Control Schematic

III. DATA ACQUISITION

In order to obtain the convincing experimental data, six able bodied subjects participated in leg extension exercise. The subjects were asked to do the leg extension exercise movement completed in 2s, 3s, 4s, and 5s. Two sets of muscles are involved for extension and flexion respectively. 1st set is called Quardriceps which consists of Rectus Femoris, Vastus medialis and vastus lateralis. This set is responsible for extension. The 2nd set of muscle is called Hamstrings and it consists of bicep femoris, semitendinosus and semimembranosus. This set is responsible for flexor movement.

Fig. 2. Flexion and Extension signal in Ch1 and Ch2

To extract information about information of flexor and extensor, one channel has been used for each posture. So Rectus Femoris is used for extensor and Bicep Femoris is used for flexor. The muscles are selected for posture selection based on their relatively better intensity over other muscle. Figure 2 shows the activity of Ch1 and Ch2 that are active alternately. For angle estimation, Rectus femoris and Vastus medialis are selected for extension angle estimation. Bicep femoris and semitendinosus are selected for flexion angle estimation. sEMG measuring device called flexiCom is used to record sEMG data of these muscles simultaneously. So each subject has been made to repeat a complete flexion and extension for six consecutive trials of EMG data. sEMG signal acquisition equipment used in the experiment named “FlexiCom” which is a product of Thought Technology Ltd, from Canada. The device can simultaneously capture 10 channels of sEMG data with sampling rate of 2048 Hz for each channel. The figure 3 shows the location of the electrodes respectively for flexion and extension.

Fig. 3. Flexion and Extension Muscles

The joint angle measurement device MPU6050, 6 axis gyroscope is used to measure knee joint angles. The MPU6050 is incorporated with Arduino nano microcontroller mounted the lower limb that is used to extend or flex about knee joint. The sensor MPU6050 communicate with Arduino through I2C protocol. Then collected angle data is then transferred to Matlab in PC from Arduino through serial port. Recording of EMG and recording of knee joint angle have been done simultaneously so that for each EMG data there is a corresponding angle data. The sampling rate of the joint angles is selected as 100 Hz.

Fig. 4. Feature of the EMG and Corresponding Joint Angle with Gyroscope

Shaving and cleaning of the skin surface is desired of all the muscles in order to reduce input resistance and the external disturbance. Ag/AgCl electrodes with glue solution were used for measuring the analog sEMG signal. Each of the electrodes in a pair was separated from each other by 2cm. The tissue underlying the sEMG electrodes on the skin filter the muscle action potentials. The filtering characteristics of this tissue depend on day to day variation in the position of sEMG electrodes, skin preparation, ambient temperature and electrical impedance. The tissue filtering characteristics are implicitly accounted for by the sEMG to activation filter .

IV. SIGNAL PROCESSING

It is very prominent that original sEMG signals are very contaminated during sig-nal acquisition. These noise signals may come from inherent noise in electronic equipment such as industrial frequency interference, DC bias and baseline noise. Motion artifact which is mainly caused by electrode interface and electrode cable will also cause irregularities in sEMG data. Firing rate of the motor units and the firing frequency region 0-20Hz also affect the sEMG signals. So the removal of the noise is very important. The power density spectra of the EMG contains most of its power in the frequency range of 5-500 Hz at the extremes, so the signal over the high cut off frequency 500 Hz should be eliminated. After the above discussion, a notch filter with 50 Hz and a band pass filter with low cut off frequency 500Hz should be applied to the raw sEMG signals to remove the noise signal. The sEMG data is high pass filtered between 20Hz to 450Hz with a forth order recursive Butterworth filter (30Hz) to remove the movement artefact. Then EMG is filtered again with Butterworth low-pass filter with a 6Hz low-pass cut-off frequency.

V. METHODOLOGY APPLIED

After raw sEMG data acquisition and filtering the unnecessary frequencies (noise), the data is resampled to new dimension and then rectified. The rectified data is then used to get various features. To get the final data set desired to train the GRNN and NN, the featured data is filtered with a second order digital filter to increase the robustness of the angle estimation system. The RMS (Root Mean Squire) featured EMG signal data set has been used to SVM to classify flexion and extension posture. There is no ambiguity into the EMG data of two channels as it is very prominent from figure 5. The Muscle activity of Ch1 and Ch2 for flexion and extension respectively is pretty much in on/off fashion. Already existing SVM classifier tools in Matlab has been used to serve our interest. The testing data has been tested on the trained model with 100% accuracy.

Fig. 5. RMS feature of sEMG data for classification with SVM

Fig. 6. Simulation Result of Classified EMG data with SVM

Due to non-linear nature of relationship between EMG and joint angle, different computational methods has been tried to model the above mentioned input-output relations. In this paper NN (Neural Network), GRNN (Generalized Regression Neural Network) have been tested to angles estimation about knee joint. NN has been used with 50 neurons and with neuron activation function “tansig” or “logsig”. Non-linear activation function estimates the joint angle best. Generalized regression neural networks (GRNN) is a kind of radial basis network that is often used for function approximation. GRNN has two layers in the network. The first layer has “Radbas” neurons and second layer has “Purelin” neurons. For angle estimation, RMS, MAV, IAV, Wave Length, Wavelet coefficients are various features that are selected for NN and GRNN. Transient of sEMG signal that is proportional to joint angle variation. The above mentioned features are used along with knee joint angles that are measured with gyroscope MPU6050 as target data. The average of 10 trials is used as target data set. Too much variation in input vector cause the NN and GRNN estimate joint angle that is very abruptly changing and it is not desired as it may cause vibration in exoskeleton. To avoid instability from control point of view, the featured data has been filtered using a second order digital filter. The performance of the GRNN and NN improved after the features are filtered significantly. A recursive filter has been used which is a second order discrete linear mode to model muscle excitation from the rectified and the low-pass filtered EMG data. The filter used is as follows ,

u_j (t) = αe_j (t-d)- β_1 u_j (t-1)-β_2 u_j (t-2) (1)

Where e_j (t) is the feature data, full wave is rectified and low-pas filtered EMG of muscle j at time t, u_j (t) the post-processed EMG of muscle j at time t, α the gain coefficient for muscle j, β_1,β_2 the recursive coefficients for muscle j, d is the electromechanical delay. To achieve a positive stable solution of Eq. (1), a set of constraints are employed, i.e.

β_1=C1+C2,

β_2=C1.C2,

Where,

|C1|<1 and |C2|<1.

In addition to the above constraints, the unit gain of this filter has been maintained by ensuring,

α – β_1 – β_2 = 1.0

In figure from 7 to 11 are feature and filter data of 26 trials of knee joint extension angle of two muscles.

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Fig. 7. RMS of sEMG signal before filtering

Fig. 8. RMS of sEMG signal after filtering

Fig. 9. H-jorth feature of sEMG before filtering

Fig. 10. H-jorth feature of sEMG signal after filtering

Fig. 11. Wavelet feature of sEMG signal before filtering

Fig. 12. Wavelet feature of sEMG signal after filtering

VI. DATA ANALYSIS

For classification of flexion and extension, SVM of LIBSVM is also used with Radial Basis Activation Function, C=200 and γ =64. We have received mean square error (MSE) = 0.25 and root mean square error (RMSE) =0.999. For estimation of flexion and extension angle, sEMG data is used with or without filter. Without filter, GRNN ensures an accuracy of 17.6094 and NN ensures an accuracy of 17.5511. But when GRNN and NN are used after raw sEMG data is filtered with second order digital filter provided into Eq. (1), both of them exhibit significantly very impressive accuracy. The improvement of GRNN and NN are very prominent from the table-1 which shows the relative accuracy of features and methods.

TABLE I. ACCURACY OF GRNN AND NN

Different Method

Accuracy of Angle Estimation

RMS LOG MAV IAV HJORTH

WL MSWT

GRNN 6.7387 6.8273 6.8022 9.7974 7.7671 9.7974 1.5704

NN 7.0787 17.1321 6.8440 6.8648 2.7337 8.2862 2.9498

Fig.13. GRNN angle estimation performance

Of all the features, the wavelet features ensures the best accuracy of 1.5705 and it serves our interest best. Fig-13 shows the simulation of GRNN with wavelet features that is filtered with second order digital filter. The green line is the estimated angle and it closely follows the desired target which is shown in red colour.

VII. CONCLUSION

The methodology described here is able to classify the desired postures and estimate joint angle with desired accuracy. Other parameters of joint dynamics are joint torque and impedance is also possible to be estimated in a similar fashion.

ACKNOWLEDGMENT

I would like to acknowledge the Khairul Anam, Amara Masud for their cooperation in assisting me with simulation.

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