A Study on Damping Profile for Prosthetic Knee

A Study on Damping Profile for Prosthetic KneeAnup Nandy, Soumik Mondal, Lokesh Rai, Pavan Chakraborty and G C Nandi

Robotics & AI Lab, Indian Institute of Information Technology – Allahabad

Telephone number: +91 532 2922120/2121

{ nandy.anup, mondal.soumik, erlokeshrai }@gmail.com, { pavan, gcnandi }@iiita.ac.in

ABSTRACTAn intelligent prosthetic leg for above knee amputee person has been developed by Indian Institute of Information Technology -Allahabad. The leg has been called as Adaptive Modular Active Leg (AMAL). The main aim of this paper was to generate suitable damping profiles required for above knee prosthetic patients for locomotion. A detailed analysis of human gait cycle is needed to provide damping profiles to the prosthetic knee. This information is obtained from the healthy leg. A simple potentiometer sensor is fitted beside the healthy knee to measure the knee angle and strain gauges mounted below the heel, in the shoe to measure gait strain. These signals from the knee and the heel are the input that describe the gait cycle of the patient. These two signal values are cleaned using Kalman filter to reduce the sensory noise for providing better performance to our system. Human gait cycle is divided into six different phases to evaluate damping profiles. In this paper, we formulate six different damping equations to produce damping profiles for prosthetic knee. The Artificial Neural Network has been used to classify different phase of walking cycle with suitable damping value.

Categories and Subject DescriptorsJ.3 [Computer Applications]: LIFE AND MEDICAL SCIENCES – Health, Medical Information Systems.

General TermsPerformance, Experimentation, Human Factors.

KeywordsKalman Filter; Damping Profile; MR Damper; Artificial Neural Network, Robotic Prosthetic Leg; Above Knee Amputee.

1. INTRODUCTIONWalking is indeed a very complex task which involves balancing,

stability and body movement. Human knee plays an important

role during walking. Prostheses are artificial replacement of body

parts lost due to injury or illness. For prosthetic knee, walking is

controlled by adjusting the damping of knee joint. The task of

making a disabled person’s walk requires a detailed analysis of his

gait. Human gait [1, 2 and 15] describes the walking behavior of

any particular person. Gait analysis gives us the required

parameters and their details which are used in artificial leg

implementation. The task is to replicate the normal walking using

artificial body parts. Different joint angle changes in different

manner during walking cycle. The moment of force at each joint

also varies. We have considered knee angle and knee moment/gait

strain variation over the time for implementation purposes. Proper

resistance is required at knee during walking. This is not constant

for a whole gait cycle. To provide the required resistance we use

Magneto Rheological (MR) damper [3]. We need to compute the

damping value to support comfortable walk. Since the damping

value [4, 5] varies over whole gait cycle, we need to find out the

periods where it follows some particular pattern and which can be

given by damping equations. To support this idea we divide the

whole gait cycle into six different phases and then we find out the

six different equations to get the damping value. Knee angle and

knee moment/gait strain values are captured using sensors.

Kalman filter is used to reduce the sensory noise. Kalman filter

estimates the true state of the system (leg) in presence of noise.

Then the system identifies the current phase of the gait in which

the walker is currently in. Then it selects one of the damping

equations to generate the damping coefficient value for that

identified phase of the gait. This provides the required necessary

resistance to knee to enable comfortable walk.

The paper is organized in the following manner. Human gait and

its division in different phases are described in section 2. Section

3 talks about the methodology. Section 4 tells about the Kalman

filter implementation in the noisy environment. Both linear

Kalman filter and unscented Kalman filter are discussed in this

section. Gait phase identification is done using feed forward back

propagation multilayer neural network. Its details are given under

section 5. The description of damping equations of different

phases is mentioned in section 6. Finally the results are given

under section 7 followed by conclusion and discussion.

2. HUMAN GAITHuman learns walking over a long period of time but a cuff or any

other animal child can start walking immediately after their birth.

This is because of body structure. There is a continuous

refinement and learning process in our mind to stabilize or

balance our body during walk, run or in any other motion.

Keeping our body in balance, it sounds like such a simple task.

But even in the act of standing quickly, our balancing system

works a lot.

Walking is complex mechanism. It requires much balance and

coordination, yet we can do it without even thinking about it.

Human motion is analyzed in terms of gait. It is subject to

extensive research. Human gait [1, 2, 4 and 15] is extremely

complicated process. All limbs of the body move in concerted

fashion during gait. Their motion is controlled by the muscular

activity at each joint. The specific dynamic behavior exhibited by

each joint varies according to a large number of factors including

the walking speed, the surface being walked upon, load being

511

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. ICACCI’12, August 3-5, 2012, Chennai, T Nadu, India. Copyright 2012 ACM 978-1-4503-1196-0/12/08…$10.00.

carried out and the state of other limbs. Understanding the

function of a normal leg during walking is most important when

replacing it.

The most practical and only used way to understand and describe the walking is Gait Cycle. The duration between the two consecutive foot contacts of the same foot is called gait cycle. So it begins when one foot contacts the ground and ends when that foot contacts the ground again. Normally the gait cycle is symmetric and cyclic process. A single gait cycle can be divided in to two major phases of walking, Swing phase and Stance phase.Stance phase accounts for approximately 60 percent of a single gait cycle and swing phase accounts for 40 percent. Whole gaitcycle is shown in figure 2.1. For implementation purpose the gait cycle is divided into six phases. The division of gait cycle is based upon the nature of knee motion (flexion/extension) and the sign ofAngular velocity (positive/negative). Generally others [5] have

divided the gait cycle into 5 or 7 numbers of phases according to

their implementation. These six phases are named as follows.

Figure 2.1. Human gait cycle

Figure 2.2. Phases of gait cycle for knee angle

Figure 2.3. Phases of gait cycle for knee moment

Phase 1 is called Early Stance/Initial Contact/Stance Flexion.

Phase 2 is Mid Stance/Stance Extension. Phase 3 is Pre-Swing.

Phase 4 is Initial Swing. Phase 5 is Mid Swing. Phase 6 is

Terminal Swing. Figure 2.2 shows divided gait cycle phases for

knee angle. Figure 2.3 shows divided gait cycle phases for knee

moment/gait strain.

3. METHODOLOGYKnee angle and knee moment/gait strain are the two parameters

being used in our work. Knee angular velocity can be calculated

from knee angle data. These three variables are used in our work.

Here the data used, is downloaded from internet and is of one

person only. That data was originally published in Table 4.24b,

p.64 in Winter (1991) [14]. Work done under this project was a

part of the IIIT-Allahabad intelligent prosthetic knee project. Here

the overall approach will be discussed in detail which was used to

make the intelligent prosthetic leg work. The whole task is

divided into following fields. The entire system outline has been

demonstrated in figure 3.1

Reading Data from sensors.

Removal of Noise from Data.

Gait Phase Identification.

Generation of damping pattern for each phase.

Apply the actual damping to actuator (Damper).

Microcontroller is used here to implement the on-leg intelligence.

This Microcontroller reads the data from sensors. Then this sensed

data will be filtered out from noise and used to generate the

damping coefficient to make the leg work. Finally this damping

value is supplied to damper. We have developed a control

algorithm to make the leg intelligent enough so that it can adjust

the damping of leg efficiently during walk. Gait phase

classification is done with neural network. Supervised kind of

learning is used to make the network work. The walking data is

available for a particular person only. So the training pattern for

neural network learning can be easily created. Then this network

learns the pattern and adjusts its weights and biases accordingly.

Next time when test input is applied it will use those adjusted

weight and biases values and generate the corresponding output.

Now our main task is to identify the damping profile for normal

walk. Six equations are derived to generate damping coefficient.

Then one of the damping equations has to be selected to generate

damping coefficient for damper according to the identified phase

of the leg.

Figure 3.1. System outline

4. KALMAN FILTER IMPLEMENTATIONIn IP Knee two types of sensors are mounted on it. First is

potentiometer which measures the knee angle made by the leg and

other sensor, strain gauges, reads the moment of force at the knee

while walking. But there is a possibility that these sensors

readings might be affected by noise. The whole system (leg) will

512 International Conference on Advances in Computing, Communications and Informatics (ICACCI-2012)

work accurately and will give correct output of gait phase and

damping if we provide the required information without having

the effect of noise. So the first task is to remove noise from the

sensor readings. The Linear Kalman Filter needs a model of the

system and measurements [6, 7, 8] in order to predict and correct

the system’s state. The system model describes how the true state

of the system evolves over time. The state equations and output

equations of the linear system are given by

Xk = A Xk-1 +B uk-1 + wk-1 (4.1)Zk = H Xk + vk (4.2)

In the above equations A, B and H are matrices; k is the time index; X is called the state of the system; Z is the measured output; and w and v are the noise. The variable w is called theprocess noise and v is called the measurement noise. In our system two quantities are going to be measured, Knee angle and knee moment at knee. So the state consists of knee angle Xknee and knee moment Xmoment. So the state is represented by

X = Xknee

(4.3)Xmoment

Let’s analyze the behavior of leg. As the leg moves the state of the system changes continuously with respect to time. This movement of both knee angle and knee moment is given by

X k = A * Xknee, k-1 + B * DeltaT (4.4) Xmoment, k-1

The knee angle variation during motion can be explained by figure 4.1

At Time t At Time t + DeltaT

Figure 4.1. Knee angle variations

Suppose that the angle made by the knee at time t is 1 and after duration of DetlaT the knee angel is 2 at time t+DeltaT. TheKnee is moving with the angular velocity of . So the relationship can be expressed as

2 = 1 + ( * DeltaT ) (4.5)

The knee angular velocity is defined as rate of change of knee angle and can be calculated as

= d / d t (4.6)

Hence the relationship of current knee angle with previous knee angle is obtained. This will help us in defining the system model for knee angle. In the very similar way the same sort of relationship for knee moment is also required to be found out. To find out the relationship the difference between successive knee

moment readings is calculated first and then based on the observation of knee moment variation, so the relationship can be formulated as,

M2 = M1 + {Sqrt ( ) * DeltaT} / 10 (4.7)

Where M1 is the value of knee moment at time t and M2 is the value of knee moment at time t+DeltaT. is the knee angular velocity and is the knee angle.

A = 1 0 (4.8)

0 1

It is a unit matrix because there is no multiplicative term used here with previous state value. In a similar way matrix B will be

B = (4.9)

{Sqrt ( * )} / 10

And DeltaT will be acting as control input. Matrix H will be

H = 1 0 (4.10)

0 1

Now our linear equations can be written, using the matrix A, B

and H of equations (4.8), (4.9) and (4.10), as follows

Xk = 1 0 Xk-1 + DeltaT + PNoise (4.11)

0 1 { Sqrt ( * ) } / 10

Zk = 1 0 Xk-1 + Measurement Noise. (4.12)

0 1

The noise covariance matrices are defined as

Process Noise covariance

R = E ( w wT )

Measurement Noise covariance

Q = E ( v vT )

For nonlinear system Unscented Kalman Filter [9, 10] is being used. Its implementation is as follows:-

In our case, the system model that we are looking for describes how the state of the leg changes due to the motion. The need is for a system model that given the last state and a relative measurement, determines the new state. In order to derive this model, let us formalize a state and a relative measurement more precisely.

As already mentioned that state of the leg at current situation k

can be defined as in equation (4.3).

Now the relative displacement is the displacement made by the leg over a certain time interval. This relative displacement will include both knee angle relative displacement and knee moment relative measurement. So the relative displacement can be defined as

Uk = U (4.13)

U

1 2

International Conference on Advances in Computing, Communications and Informatics (ICACCI-2012) 513

calculate these relative changes is already described earlier in this section itself. Equation (4.5) and (4.7) gives us the values of relative measurement for knee angle and knee moment respectively.

Now given the relative information Uk-1 and given the last state of the leg Xk-1 we can express the current state of the leg using the following function f

Xk = f (Xk-1 , Uk-1) = f A (Xk-1 , Uk-1) (4.14)

f M (Xk-1 , Uk-1)

In the same way the noisy system model can be represented by

Xk = f (Xk-1 , Uk-1) + wk-1

= f A(Xk-1 , Uk-1) + wA,k-1 (4.15)

f M(Xk-1 , Uk-1) wM,k-1

The perfect measurement Zk of all the variables of a state Xk issimply a vector containing for each state variable, a variable that takes on the value of the corresponding state variable. Thus, in our leg case, the measurement Zk is

Zk = ZA,k (4.16)

ZM,k

The measurement model is implemented in such a way that given the state of a leg Xk it returns the measurement of the full state sensor, as

Zk = h ( Xk )

Where h (.) function is the measurement function relating a state to a measurement, and which in this case simply is

h ( Xk ) = h A ( Xk ) = XA,k (4.17)

h M ( Xk ) XM,k

Noise can be incorporated in measurement model as

Zk = h ( Xk ) + vk (4.18)

5. GAIT PHASE IDENTIFICATIONTo apply the damping we are required to find out the current phase of the leg out of six defined phases in previous section. Based on this classified phase the control algorithm will select the damping equation to generate damping coefficient. This phase identification is most important because the required damping is not constant over whole gait cycle. During the natural walk the knee resistance varies over whole gait cycle.Here neural network [11, 12, 13] is used to classify among six phase. Knee angle, Knee moment/gait strain and knee angular velocity are taken as input to the classifier. The output is one of the six phases of the gait cycle. Knee angle and knee moment are taken from sensor (after applying filtering) and knee angular velocity is calculated as mentioned in section 4.2, equation 4.6.Feed-forward back propagation type of neural network is used for classification purpose. This classification is done through a

supervised learning method. It is mainly divided into two parts. First is the training of neural network and next is classification.Around forty-two samples (Table 1) from all the six phases are used to train the neural network. After training, our network is able to understand the data pattern and set its weight accordingly. Then test data is provided for classification to check the correctness of classifier.This network has three layers. First layer is input layer which takes the input and supplies it to the neurons of second layer. Second layer has five neurons with logsig transfer function and the third layer has six neurons with purelin as a transfer function. Selection of number of layers and number of neurons in each layer is a difficult task. There is no proper method to select these numbers.The formulas for transfer functions are

logsig(n) = 1 / (1 + e-n).

purelin(n) = n.

Increasing the number of layer will only increase the amount of computation in this particular application. There has to be six neurons in output layer (second layer) because there are six phases of gait cycle in which we have to classify. But the selection of number of neurons in first layer is dependent on the output of classifier.MATLAB is used to design the classifier. It gave a detailed look on the use of MATLAB for neural network [12]. Design of this feed-forward network is shown in figure 5.1. It describes all the connection between the neurons and the transfer function in each layer. Training function used is ‘trainlm’, Adaptation learning function is ‘learngdm’ and performance function is ‘MSE’.

Figure 5.1. Design of gait phase classifier network

6. DAMPING PROFILE GENERATIONAfter identifying the phase in which the walker is in, the next task is to apply appropriate damping for efficient walking. This control algorithm takes information from the filtered data coming from sensors. Now based on the phase of the gait and the sensor input, the algorithm determines the required damping for the knee for the duration of that phase only. Since the whole gait cycle is divided into six phases. Therefore, six different damping patterns have been identified for each phase. Each phase has its own damping pattern which can be defined by separate damping equations. These equations are as follows:


D1 (t) = [ abs ( M ( t ) ) * A ( t ) / abs ( V( t ) ) ] (1)

D2 ( t ) = [ abs ( M ( t ) ) * A ( t ) / abs ( V ( t ) ) ] (2)

D3 ( t ) = [ abs ( M ( t ) ) / ( abs ( V ( t ) ) * A ( t ) ) ] (3)

D4 ( t ) = [ A ( t ) / abs ( V ( t ) ) ] (4)

D5 ( t ) = [ 1 / abs ( V ( t ) ) ] (5)

D6 ( t ) = [ A ( t ) / abs ( V ( t ) ) ] (6)

Where D1 to D6 denotes the damping coefficient for phase 1 to

phase 6. M (t) is the Knee Moment at time t. A (t) is the Knee

angle at time t. V (t) is the Knee angular Velocity at time t. abs (.) is a function which returns absolute value of its argument.

7. RESULTS AND DISCUSSIONSThe results for Kalman Filter are shown here using system and measurement model with noise. In practice, the process noise covariance and measurement noise covariance matrices might change with each time step or measurement, however here we assume they are constant. We are assuming here that there will be variance of 4 degree and 0.2 N-m/kg for knee angle and knee moment measurement respectively. Since the modeling of process noise is very difficult so the process noise covariance is kept unity.

Figure 7.1. Knee Angle (True, Measured and Estimated)

This graph shown in the figure 7.1 tells about the Kalman filter behavior. Curve plotted by red line shows the knee angle value calculated by process model. Curve plotted by green line shows the value obtained from sensor reading. Curve plotted by blue lineshows the estimated value of knee angle and is final outcome.Now let’s have a look at the error between actual value and measured value and estimated value. Figure 7.2 shows this error plot. It can be seen from figure 7.2 the red curve tells the measurement error (difference between actual value and the value from the sensor). The blue curve shows the estimation error (difference between actual value and estimated value). So it is clear from the figure that the estimated value is much closer to the actual value instead of measured reading from sensor. In the same way the Kalman filter output for knee moment can also be analyzed. Figure 7.3 gives the Knee moment estimated value and figure 7.4 tells about the errors in measurement and estimation.Let’s have a look at the graph of figure 7.3 then we will find out that for stance phase it is producing nearly smooth result but for swing phase it is showing a little variation. This is because of the process model used for knee moment. Since this model is based on data observation it is giving good result as compared to knee angle estimation results.

Figure 7.2. Error Plot for Knee Angle

Figure 7.3. Knee Moments (True, Measured and Estimated)

Figure 7.4. Error Plot for Knee Moment

Now let’s analyze the behavior of Unscented Kalman Filter applied for nonlinear system. Here all the four graphs figure 7.5 to figure 7.8 are plotted as they were plotted for linear system.

Figure 7.5. Knee Angle (True, Measured and estimated) using

UKF

Figure 7.6. Error Plot for Knee angle using UKF


Figure 7.7. Knee Moment (True, Measured and estimated)

using UKF

Figure 7.8. Error Plot for Knee Moment using UKF

Table 1. Training Dataset

Knee AngleGait

strain

Knee Angular

velocityPhase

8.833 -0.23 83.3462 1

9.833 -0.27 89.7308 1

11.166 -0.18 96.1538 1

21.5 0.61 32.0385 1

21.666 0.62 12.8077 1

21.833 0.63 6.4231 1

15.333 0.17 115.3846 1

16.833 0.26 102.5769 1

21.833 0.58 -6.4231 2

21.666 0.55 -19.2308 2

21.333 0.51 -32.0385 2

17.333 0.15 -64.0769 2

16.5 0.11 -51.2692 2

16 0.06 -51.3077 2

9.833 -0.2 -19.2308 2

9.5 -0.22 -19.2308 2

9.333 -0.23 -6.4231 2

9.333 -0.25 6.4231 2

9.5 -0.25 12.8077 3

9.666 -0.27 25.6154 3

10.166 -0.27 32.0769 3

37 0.16 217.6923 3

39.66 0.17 230.7692 3

43 0.17 237.4231 3

20.666 0.01 134.6154 3

22.5 0.03 179.5 3

45.833 0.14 250 4

49.5 0.11 217.9615 4

64.5 0.045 38.4615 4

64.5 0.045 0 4

64.5 0.04 19.2308 4

59.5 0.07 166.9231 4

64 0.03 -45 5

63.33 0.02 -83.3462 5

42.5 -0.05 -250 5

39.5 -0.06 -243.6154 5

54.333 -0.02 -192.3077 5

36.166 -0.07 -288.4615 6

32 -0.09 -352.5385 6

27 -0.1 -269.2308 6

6.833 -0.26 -76.9231 6

Calculation of damping values for different phases has already been discussed. If equations for their corresponding phases are applied then the damping profile will be like figure 7.9. From this figure one can easily infer that this damping profile fulfills our requirement for normal walking. For phase 1, stance flexion, damping starts increasing to support body weight and to restrict the body from being fallen down. During phase 2 to support stance extension the damping decreases. But at the end of stance flexion there is a slight increase in damping so that the effect of sudden straightening can be avoided. Otherwise this sudden straightening effect deviates from normal gait. Preswing, phase 3, is the phase prior to swing phase. During this phase the knee damping should be as low as possible to allow flexion of knee. So that it can achieve enough velocity to propel the body forward.During phase 4, swing flexion, knee reaches its maximum flexion. So at that point the damping has to be such that to avoid flexion beyond a limit. Then for the rest of the two phases the damping is low to allow easy extension prosthetic knee. But at the end there is a slight increment in damping to reduce the velocity.

Figure 7.9. Damping Profile for Prosthetic Knee


Figure 7.10. Classified Gait Phases

Now let’s analyze the results of gait phase neural network classifier. Training data set of 42 samples from whole gait cycle was provided for learning. Table 1 lists all the training samples. Then we have used some test data to check the output of classifier. We have checked this classifier at boundary conditions i.e. at the boundary of two subsequent phases and it is classifying them correctly. The network is designed with different combinations of neurons and number of layers. First we tried with two layer network with three neurons in first layer. Number of neurons in output layer are kept fix i.e. six. But this shows only 50% classifier accuracy. Next network made was not able to correctly classify between phase 1 and phase 3. It also has two layers with four neurons in first layer. Then another network with the same two layers and four neurons in first layer was designed. This time logsig as transfer function was used instead of transig.This works fine but fails at phase boundaries. Finally we tried with five neurons in first layer having logsig as transfer function.After training the network is set with its wait and bias values. The MSE was 0.013. When we applied test data we got the results as figure 7.10.

8. CONCLUSIONS AND FUTURE WORKResults of Kalman filter for both knee angle and knee moment/gait strain are displayed in figure 7.1 to figure 7.8. The error plots definitely show that the filtered output is close to the actual values. The plotted graph of filtered values follows nearly the same curve as actual values. The only problem with the Kalman filter is that the knee moment could not be modeled perfectly. Since the system model generated the required oscillations for knee moment is based on observed data. Error in actual and estimated values could not be optimized as per our expectations. But when we compare the graphs of knee moment error for the linear system and the nonlinear system we find that nonlinear implementation gives better results. Error is very well minimized in UKF instead of linear one. To obtain the more accurate results it is necessary to model the knee moment accurately. The fact that only local mechanical sensors were employed in the electronic knee in this investigation led to dramatic limitations in the system ability to assess user intent. Such prosthesis cannot determine whether a patient’s wishes to turn to the right or to the left, or whether an obstacle could be negotiated by the amputee. However the healthy leg and the thigh stub, on which the prosthetic leg is fitted, can follow the patient’s wishes to turn to the right or to the left, or to avoid obstacles. This will compensate the above drawback. During this work only one set of knee angle and knee moment data were used for testing and result generation. More systematic data sets are required to be captured and calculated since human walking pattern changes slightly every time. It will also help Neural Network in learning the slight variation during walk.

Till now our efforts have been to find out the damping for normal walking sequence only. A strategy for fast walking leading to running can be made by studying the period of oscillation of the knee and the heel strike. The damping profile computed by ANN will be shrunk or expended to match the period of oscillation. This will enable a speed variance which will allow the patient to walk at different speeds. Stair climbing will be a daunting task it will be a difficult for the patient to achieve it without support. A systematic study of the prosthetic limb has to be carried out in different categories of patients. The patient will be categorized as first by sex (male/female), height, weight and age and the duration that the patient has been amputated. The duration is important because the patient tends to forget his natural gait pattern. Healthy subjects who have both legs should also be investigated by externally fitting our sensors on them. The data on healthy subject categorized by sex, height, weight and age will help us to determine the natural damping profile. It has to be seen if the natural damping profile can be fitted on a patient with a similar category (sex, height, weight and age).

9. ACKNOWLEDGMENTSWe would like to thank to Dr. M.D. Tiwari, Director of IIIT-Allahabad to bring this project from Department of Science of Technology (DST), Govt. of India.

10. REFERENCES

[1] Glassman, E. 1982. Design and fabrication of an electronically controllable, variably damped above knee prosthesis. M.Sc. Thesis M.I.T. (October 1982).[2] Darling, D. T. 1978. Automatic damping profile optimization for computer controlled above knee prosthesis. M.Sc. Thesis M.I.T. (May 1978).[3] Lord MR Damper: http://www.lord.com/products-and-solutions/magneto-rheological-%28mr%29.xml. [4] Wilkenfed, A. J. 2000. Biologically inspired auto adaptive control of knee prosthesis. PhD. Thesis M.I.T. (July 2000).[5] Herr, H. and Wilkenfeld, A. 2003. User-adaptive control of a magnetorheological prosthetic knee. Industrial Robot: An InternationalJournal, Vol. 30 (Number 2003).[6] Kalman, R. 1960. A new approach to linear filtering and prediction problems. Transactions ASME Journal of Basic Engineering, Vol. 82 (1960).[7] Maybeck, P. S. 1979. Stochastic models, estimation and control.Academic Press, Inc., New York, USA (1979).[8] Welch, G. and Bishop, G. 2001. An Introduction to the Kalman Filter. Chapel Hill (2001). SIGGRAPH 2001.[9] Julier, S. J. and Uhlmann, J. K. 1997. A New Extension of the Kalman Filter to Nonlinear Systems. Proc. SPIE Vol. 3068, pp. 182-193, Signal Processing, Sensor Fusion, and Target Recognition VI, Ivan Kadar; Ed (1997).[10] Tak, S. and ko, H. S. 2005. A Physically-Based Motion Retargeting Filter. ACM Transactions on Graphics, Vol. 24, No. 1, (January 2005).[11] Kumar, Satish. 2004. Neural Network: A Classroom Approach. Tata McGraw-Hill Publication (Jun 2004).[12] Hagan, M. T. Demuth, H. B. Beale, M. H. 1996. Neural Network Design. Thomson Learning publication (1996).[13] Haykin, S. S. 1999. Neural Network, A comprehensive Foundation. Second edition, Pearson Prentice Hall publication (1999).[14] Winter, D.A. 1991. The Biomechanics and Motor Control of Human Gait. University of Waterloo Press (1991).[15] Mondal, S. Nandy, A. Chakrabarti, A. Chakraborty, P. Nandi, G.C.2010. A framework for synthesis of human gait oscillation using intelligent gait oscillation detector (IGOD). Springer, LNCS-CCIS, vol. 94, pp. 340–349 (2010).


A Study on Damping Profile for Prosthetic Knee

Documents