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Adaptive Neuro-fuzzy Inference System (ANFIS) controller was designed to control knee joint during sit to stand movement through electrical stimuli to quadriceps muscles. The developed ANFIS works as an inverse model to the system (functional electrical stimulation (FES)-induced quadriceps-lower leg system), while there is a proportional-integral-derivative (PID) controller in the feedback control. They were designated as ANFIS-PID controller. To evaluate the ANFIS-PID controller, two controllers were developed: open loop and feedback controllers. The results showed that ANFIS-PID controller not only succeeded in controlling knee joint motion during sit to stand movement, but also reduced the deviations between desired trajectory and actual knee movement to ±5°. Promising simulation results provide the potential for feasible clinical application in the future.

Sit to stand movement is necessary for many activities in human life. However, paraplegics have particular difficulty with this movement due to their lower limb paralysis caused by spinal cord injury (SCI) [

In addition to arm support, paraplegics can use functional electrical stimulation (FES). It is a promising technology that can facilitate sit to stand in paraplegia [

Achieving desired movement requires suitable electrical stimulation currents to the muscles [

The solution of FES control problems requires intelligent systems that emulate the way how human brain controls the muscles. Researchers used artificial neural network [

To overcome the drawbacks of neural networks and fuzzy logic, Adaptive Neuro-Fuzzy Inference System (ANFIS) was successfully applied to robotic motion and controlling free leg swing during electrical stimuli to quadriceps muscles. The present study aims to develop an adaptive intelligent controller which calculates the required stimulus activation of quadricep muscles to assess the paraplegic sit to stand. It depends on ANFIS which is combining the adaptive learning capability of artificial neural network with the intuitive fuzzy logic of human reasoning formulated.

Paraplegic model is essential for design FES controllers. A model for a patient height 1.80 m and weight 75.35 Kg was built. The model contains: body segments, muscles, and passive joint properties as is illustrated in

The body segments model was developed using Visual Nastran which is a powerful CAD tool used for 3-D modeling [

Quadriceps muscles group (which consists of four muscles: Rectus Femoris, Vastusmedialis, Vastus medium, and Vastuslateralis) was modeled in Virtual Muscle 4.0.1 by using muscles parameters from [

In the body-segmental dynamics, total joint moment is the sum of active, passive elastic and passive viscous joint moments. The latter has been modeled as a linear relation between the angular joint velocity and the damping coefficient [

The Adaptive Neuro-Fuzzy Inference System (ANFIS) technique was originally presented by Jang in 1993 [

ANFIS architecture consists of five layers with the output of the nodes layered architecture [

The first layer generates the membership grades.

The second generates the firing strengths by multiplying the incoming signals and outputs the t-norm operator results.

The third layers normalize the firing strengths.

The fourth layer calculates the first-order Takagi-Sugeno rules for each fuzzy rule based on the consequent parameters.

The fifth layer—the output layer, calculates the weighted global output of the system as the summation of incoming signals [

ANFIS uses back propagation learning to determine premise parameters and least mean squares estimation to determine the consequent parameters [

• In the first or forward pass, the input patterns are propagated, and the optimal on consequent parameters are estimated by an iterative least mean square procedure, while the premise parameters are assumed to be fixed for the current cycle through the training set.

• In the second or backward pass the patterns are propagated again, and in this epoch, back propagation is used to modify the premise parameters, while the consequent parameters remain fixed. This procedure is then iterated until the error criterion is satisfied [

ANFIS model has two inputs: knee joint angle and angular velocity, and the activation pattern as output. The implemented is based on:

• First-order Sugeno fuzzy model so the consequent part of fuzzy if-then rules is a linear equation.

• T-norms operator that performs fuzzy AND is algebraic product.

• The type of membership functions (MF) of the inputs are Gaussian functions.

• Each input has three membership functions which are chosen by trial and error, so the number of fuzzy rules is nine.

The ANFIS training off-line methodology using ANFIS GUI in Matlab Fuzzy Logic Toolbox is summarized in

thod. If this error is larger than the threshold value, then the premise parameters are updated using the gradient decent method (back propagation). The process is terminated when the error becomes less than the threshold value. The checking data set is then used to compare the model with the actual system [

Proportional-integral-derivative (PID) controller may be the most widely used controller because of its simplicity and efficiency. The PID controller transfer function, F(s), is:

where:

K_{P} is the proportional gain of the Controller.

K_{P}/τ_{i} is the integral gain of the controller.

K_{p}τ_{d} is the differential gain of the controller.

The parameters of the PID controller were tuned using the Ziegler–Nichols’ method based on the step response of the open-loop system [

Building FES controller-ANFIS-PID controller-as a tracking controller requires two steps:

1) Determine reference trajectory-the controller input-which represents the desired joint angles during sit to stand movement. This paper defined it based on [

2) Determine the control system configuration that makes the plant follows the desired trajectory. ANFIS-PID structure is used in this paper (

Then the study uses different control system configurations-ANFIS open loop controller, and a PID controller and compares their control performances during sit to stand movement to the ANFIS-PID controller

The simplest approach for controller design is a completely open-loop control strategy, in which the controller is the inverse of the process.

Failing to control knee joint position during sit to stand causes a disaster accident to the body [

The moments given by controllers are varying between 0 - 104 N∙m (

Simulation results confirm that ANFIS-PID improves sit to stand performance comparing with conventional control methods like open loop and PID controllers. The success of the ANFIS-PID control system in this evaluation indicates that it may provide significant improvements to existing FES control system. In comparison with other studies which use intelligent techniques such as Fuzzy logic [

According to simulation the paralysis subject model was leaning further forward at the hips and trunk during the movement to control knee angular velocity, which caused an increase in knee joint moment. If the model’s knee angular velocity can be reduced and better controlled by either stimulating hip extensors beside to quadriceps muscle group during the rising motion or damping knee flexion with an appropriately tuned Orthosis, then it should be possible to reduce the knee moment and reach smoother movement.

However, since this study is in its preliminary stages, these theoretical results are encouraging and supporting the feasibility of FES for controlling sit to stand movement, a major obstacle to the development of a practical system that achieves this level of performance is that the reference trajectory is limited to sit to stand without upper body support which is not enough to generalize the control system result, in addition more studies are essential for investigating the controller performance during various sit to stand conditions like changing the initial position, using upper body effort, and stimulation more muscles group.

Computer simulation results indicate that ANFIS-PID control of sit to stand via using FES of the knee extensors in individuals with paralysis from SCI is feasible and may lead to improved movement stability. The use of computer simulations has provided a platform for iterative design and for this initial evaluation. While the results are encouraging, experimental evaluation on human subjects is required in order to thoroughly evaluate this technique. Since using ANFIS for controlling sit to stand is not studied thoroughly in previous studies, this study highlights the need to use such techniques to improve paraplegic’s daily activities like walking, standing, climbing stairs etc. So this study suggests using such intelligent modeling methods to improve FES control systems.