http://section.iaesonline.com/index.php/IJEEI/index Modeling and Fabrication of Smart Robotic Wheelchair Instructed by Head

Info 2021 The confronting problem faced by the handicapped, paralyzed, disabled, and quadriplegic people is their independent mobility. They need external assistance to perform their daily life activities. This paper aims to solve that problem by smart designing and deployment of the robotic wheelchair for those who cannot perform their voluntary activities and movements. The proposed automated wheelchair comprises two parts; the first part is the user's helmet that works as a master device, and the second part is a slave device, a smart wheelchair. The master device consists of an accelerometer, microcontroller, and wireless transmitter, in which the Accelerometer recognizes the movements of the user's head and transmits the signal according to the tiltation of the user's head. Besides this, the slave device consists of a wireless receiver, microcontroller, Gyroscope, power MOSFETs, and DC geared motors mounted on a smart wheelchair, which response as per the instructions of the master device. Furthermore, the paper also provides a brief construction of this mechatronic and amphibian system using static and dynamic


INTRODUCTION
Mobility and self-dependency are essential for a good quality of daily life. Loss of mobility due to an accident, injury, or illness is usually accompanied by a loss of a comfortable life and that person dependent on others. The paralyzed, handicapped, and disabled diseases usually include quadriplegic and paraplegic persons. People with quadriplegia are persons who cannot move their four limbs except the head, where paraplegics are persons who cannot move their two limbs.
The cause for such an increase in mobility impairment, as shown in Figure 1, can be different: arthritis, stroke, high blood pressure, degenerative diseases of joints & bones, cases of paralysis, and congenital disabilities. Also, quadriplegia appears because of accidents or age [2]. There have been several tests to overcome this problem, such as walking aid robots, muscle suit for nursing care, electric wheelchair, and electrical nursing robots. They commonly use an electric wheelchair because it can support older people who, by their hand-power, have trouble driving a wheelchair and typically don't need much support from care staff. Therefore, for a long time, the electric wheelchair was invented. There are, however, several issues with the electric wheelchair [3]. There are a variety of methods and techniques have been proposed in the world. For example, Shayban Nasif et al. [4] have used a Head gesture recognition acceleration sensor and RF module (radio frequency) for wireless control. Umar Mohammad et al. [5] proposed a MATLAB script, and the webcam performs retina capture. Recently, Brain-Computer Interface (BCI) techniques have also been widely used to assist human problems, more specifically to assist paralyzed people [6]. Various BCI techniques using eye blinks, EEG signals have been deployed to volunteer quadriplegic persons [7][8][9]. Eye motion is detected, and the motion tracking system begins to track the chair's movement through the webcam and ATmega1284P virtual serial communication. Steering control two-wheeled wheelchair designed has also been adopted, which has no caster and moves with only two wheels [10]. The gyro sensor measures the body's pitch angle, and the two in-wheel motors are used for moving the body. Rini Akmeliawati et al. [11] designed the wheelchair system, which regulates its movement by merely bending the fingers of a person. In order to control the wheelchair, a type of sensor known as 'flex-sensors' is incorporated into a hand glove. Nowadays, the tongue-controlled wheelchair has also become a famous technique [12], but this technique requires embedding sensors on the tongue, leading to serious problems if the sensor slips into the mouth or is ingested. Md Ashiqur Rahman Apu et al. [13] proposed a wheelchair that is used to detect intentional eye blinks by processing eyeball images of the subject. An algorithm is suggested to generate a command of wheelchair movement from consecutive intentional eye blinks. Image processing techniques are implemented using raspberry-pi to detect deliberate eye blinks from eyeball images. The authors' systems we discussed above are controlled by retina capture, steering control (caster-less), intentional eye blink, and finger bending techniques; moreover, the RF Modules is used for wireless communication. To addresses the problems found in the wheelchairs built above, a robotic wheelchair is developed based on MEMS technology; an accelerometer is used instead of the above techniques in which we can vary and set the particular range or angle of head tiltation as per the requirement when the head tilts and cross that particular range or angle, the wheelchair will start moving in the desired direction [14]. It is speechless the issues present in eye-controlled wheelchairs such as dim environment control, eyes strain, and very low precision & accuracy [15]. It also eliminates the un-stability & inefficiency in the steering control (caster-less) system and a very much costeffective & appropriate technique compared to the fingers bending method. Controlling any actuator or wheelchair with the help of an Accelerometer is more reliable and user-friendly way than the above authors' approach. Our proposed system is wireless; there is no wired connection between the head circuit and wheelchair circuit. In our wheelchair, Bluetooth in the master-slave combination is used for wireless communication between data, which has no high-power consumption, antenna, and interference issues, unlike the RF module [16]. Moreover, the gyroscope has been used in a developed system, which helps to maintain the speed and excellent stability of a wheelchair on concrete or rough surfaces and on an inclined plane. Furthermore, highly torque DC geared motors are used in a designed system for smooth performance and efficient power transmission.

MODEL AND DESIGN 2.1. Mathematical modeling of the system
The wheelchair's mathematical model is built on its mechanics and kinematic equations. The geometry of the wheelchair depends on the plane's physical construction see Figure 2, while its motion in space is defined by kinematic equations [17].   The Lagrange function is represented in the following form, taking into account the position of the wheelchair in the 3D space (xyz -coordinate system) indicated by = ( , , , ) with ( , , ) being the Cartesian coordinate of the wheelchair's center of gravity and being the angle of rotation of the wheelchair [18]. The Lagrange multiplier vector and . and respectively represent the left and right torque. While all are identical, in the opposite case, a rectilinear movement occurs, and rotational motion.
If lateral motions are not possible for wheelchair wheels without slipping, the matrix associated with the constraints is then written in equation form as = ( )̇= 0 perpendicular to the axis of the driving wheels. Considering ( ) ∈ ℝ × , we derive the kinetic equation as follows: a set of smooth and linearly independent vector fields spanning the null space of ( ) such that ( ) ( ) = 0. ̇= ( ) and simplifying it, we obtain a more fitting representation of the control system for the dynamic wheelchair model as follows.
As mentioned above, the model shows the wheelchair's reaction to a sloping flat surface. It can also be verified by the results found in [17], hence the need for a controller.

Stabilizing of the system
In order to control processes, several methods have been used. Two approaches to wheelchair regulation were applied by Dabo, and positive results were obtained for both methods. They are NCGPC and feedback linearization (Nonlinear Continuous-time Generalized Predictive Control). In this article, the latter, also implemented in [18], is used. The purpose is that the motion along the trajectory should conform to a given command.
The dynamic wheelchair model can be rewritten as a nonlinear square-MIMO structure in the following form [19].
where ∈ ℝ 2 , ∈ ℝ 2 and ∈ ℝ 2 which represents the state, control input, and output vectors, respectively. The tracking error is then expressed as a tracking error as the objective is to track the trajectory from a given pair of the linear reference velocity and angular location of the wheelchair .
It is then easy to rewrite Equation 3 as follows, since the number of the relative degrees ( 1 + 2 ) is equal to 3 more significant than the wheelchair method defined in Equation 5.
It is imperative to select the state feedback law as it compensates for the nonlinearity that happens in the wheelchair's input-output behavior. For its determinant not equal to zero for − 2 cos2 ≠ 0, the decoupling matrix (Equation 7) being invertible, the state feedback law linearizing wheelchair system is provided by

Torque calculations
The overall weight is distributed between all the four tires, that is, 34 kg each. Since the wheelchair is Rear Wheel Drive (RWD), the rear wheels are responsible for accelerating the forward tires as well. Now, the weight is distributed between two tires, that is 68 kg each.

Mechanical structure
The design of the mechanical structure is entirely developed on behalf of mathematical modeling, see Equation 8, calculations and considering the effects of physical quantities. The material we have used in the mechanical structure is mild steel and a complete wheelchair structure of proper dimensions made with the help of welding and lathe machines. We have attached 2 caster wheels below the front part of the wheelchair, due to which the wheelchair can move in every direction smoothly, and the 2 rear wheels are the driving wheels, which are attached with the motor shaft with the help of a chain and sprocket. We have set the sprocket ratio 1:1 to drive the rear wheels, and this is done to reduce the mechanical load on the motor's shaft. We have used bearing in the bushes of the spindle shaft, which ensures the fluent movement of the wheelchair on every surface. The square-shaped slots are designed for mounting the motors and batteries. The structure utilizes Allen key bolts and grip screws for any joint or attachment instead of using ordinary nuts or bolts. Analysis of battery sizing is used to choose the most suitable battery bank, check the full capacity of the current batteries, and easily simulate a wide range of backup, power, and other scenarios. For a given duty cycle, the Battery Sizing module specifies the number of strings, number of cells, and cell size of a battery and also compensates for real-life factors such as temperatures, aging, and initial power that relate to critical electrical systems of this kind. In order to meet the maximum system voltage during the battery charging period and the minimum system voltage during the battery discharging period, the number of cells is determined. As revealed in Figure 5, the number of strings and cell size are calculated to provide adequate load power, taking into account the minimum device voltage and the minimum operating current.

Battery selection
The power of the battery is measured in milliamps x hours (mAH). For example, if a battery has a capacity of 250 mAH and provides a load with an average current of 2 mA, the battery would theoretically last 125 hours. Nevertheless, in fact, the way the battery is discharged has an effect on the actual battery life. Typically, discharging a battery at the manufacturer-recommended rate allows the battery to deliver near its nominal power. But it is not possible to actually extrapolate the result linearly to other discharge profiles. In Table 1, we considered significant parameters for the selection of an appropriate battery. Based on consuming current, I(Amp) by the motors and desired operating timing of the system, we can select the suitable battery for our wheelchair by just calculating the battery AH capacity and voltages V(Volts).

SOFTWARE FORMATION
The flowchart of the wheelchair acknowledged in Figure 6 revealed the software deployment of the system. We used some special libraries and functions in the software to make the hardware compatible with the software. In the programming of the master device, we also have defined and set the particular range or angle of head tiltation by using user-defined commands when the head tilts and crosses that particular range or angle, some specific alphabets generated according to the head's movement on which the operating directions of the wheelchair depend. The generated alphabets are transmitted wirelessly to the slave device. In the slave device, we used the negative axis of pitch coordinate to monitor the wheelchair's orientation continuously. Therefore, the slave device checked the angle of pitch coordinate of the wheelchair, and if the pitch angle is less than -5, this means the wheelchair is on the inclined plane, or rough surface, so different duty cycles are generated based on angles which slow down the speed of the system so that the wheelchair can move smoothly and firmly on the inclined plane. If the pitch coordinate angle is more significant than -5, this means the wheelchair is on the regular or flat surface so that the duty cycle remains 100% and no pulse width modulation generated, and the wheelchair remains at its full speed. If the head tilts on the front side, the alphabet 'f' is generated, and the wheelchair moves in the forward direction. When the head tilts on the backside, the alphabet 'b' is generated, and the wheelchair moves in the backward direction. The alphabet 'r' is generated, and the wheelchair moves in the right direction when the head tilts on the right side, and the head tilts on the left side, alphabet 'l' is generated, and the wheelchair moves in the left direction. Moreover, the wheelchair remains in a steady state when the head does not tilt on any side and remains in the center in its normal position. Figure 6. Flowchart of the proposed system This system is an automated head tilt-movement controlled wheelchair that can work using head movements in any direction, i.e., Forward, backward, right, and left. When the person does not tilt his head in either direction, it stops. In the proposed system shown in Fig. 7, an accelerometer of 3-axis with high resolution (13-bit) measurement at up to ±16 g is interfaced with a microcontroller. The purpose of this Accelerometer is to measures the static acceleration of gravity in tilt-sensing applications, as well as dynamic acceleration resulting from motion or shock. Whenever the patient tilts its head, this movement is detected by the Accelerometer. In this work, we used an accelerometer (ADXL 335) with an ATmega328 controller. The controller has builtin10-bit ADC (analog to digital converter). A 10-bit ADC has 210 =1,024 possible output codes. Hence, the resolution is 5V/1,024 or 4.88mV; this is called the reference value. But, the values of possible outputs of ADCs come at various speeds and provide differing degrees of accuracy. In our case, the ADC values vary from 0 to 1023. If the accelerometer value of the pitch (y-axis rotation) lies between 500 to 814, the master controller sends the command 'F" to the slave controller, and the wheelchair moves toward the forward direction. Similarly, if the accelerometer value of the pitch (y-axis rotation) reaches between 200 to 401, the master controller sends the command 'B" to the slave controller, and the wheelchair moves toward the backward direction. Likewise, to obtain left and right motion, we have set the accelerometer values of roll (xaxis rotation) between 100 to 300 (for left) and 700 to 100 (for right). The command 'L' and 'R' send by the master controller to the slave when the set roll values arise. It is worth mentioning that the values of ADC are selected after several trials by considering the involuntary movements of the head. High performance, low power Atmel AVR 8-bit microcontroller reads the signals which are generated as a result of head movement and transmits some specific alphabetic data in the form of characters to the slave microcontroller wirelessly through the two-way (full-duplex) Bluetooth modules. As soon as data begins to arrive at the slave controller, the MPU6050 3-axis gyroscope inside, interfaced with the slave microcontroller, starts measuring the orientation angles (pitch) of the wheelchair, as shown in Figure 6. The logic on which the DC geared motors rotate or the polarities of the voltages are totally based on the received alphabetic data characters. The slave microcontroller reads the signals which are generated as a result of the orientation angles of the wheelchair, thus induces pulse width modulation to the H-bridge, which is an electronic circuit used to switch the polarity of a voltage applied to a load. In our system, we could also use the relays instead of using H-bridge, but one of the main objectives of our system is to control or vary the speed of the wheelchair, so this feature is not possible with the relays. On the basis of originated logic and induced duty cycles, the motor will start rotating, which operates the wheelchair in a particular direction at a specific speed.

METHODOLOGY
The system utilizes two DC geared motors, a helmet circuit, and a wheelchair circuit. The deployed DC geared motors selection is purely based on mathematical calculation. The helmet circuit is comprised of an accelerometer sensor, ATmega328 microcontroller, and Bluetooth module. Wheelchair circuit comprised of Bluetooth module, ATmega328 microcontroller, gyroscope, and power MOSFET. The low-power Bluetooth modules are configured in a master-slave combination to transmit the signal wirelessly. The tiltation of the head is sensed by the Accelerometer, and the microcontroller reads the data from the coordinates of the Accelerometer. On behalf of reading data, the microcontroller generates the signal, which is transmitted by the master Bluetooth module wirelessly from the head circuit to the wheelchair circuit. Through the slave Bluetooth module, the microcontroller receives the signal and controls the directions of the wheelchair as per the head movements of the user with the help of power MOSFETs and DC geared motor. The variation in the speed of the wheelchair on the normal or inclined surface is controlled with the help of a gyroscope that is also deployed in the wheelchair circuit, and its responsibility is to give continuous feedback of the wheelchair's orientation angles to the microcontroller. Table 2 shows the motor's rotation and wheelchair operating direction. The forward motion achieves when the slave controller gives two positive signals to the motor driver; as a result, both motors rotate clockwise. Similarly, the backward motion achieves when the slave controller gives two negative inputs to the motor driver; as a result, both motors rotate anti-clockwise. Likewise, left and right movements are achieved, IJEEI ISSN: 2089-3272  and one motor rotates clockwise, and one motor rotates anti-clockwise when one positive and one negative signal are received by the slave controller. We have also tested our wheelchair while taking a right and left turns by stopping one motor instead of anti-clockwise, but in that case, the wheelchair requires too much space to take turns, and this also increases the load on one motor. In our method, the wheelchair takes turns on its center of axis without consuming the unnecessary space and makes a smooth turn without any resistance or load. Table 2. The motors rotation and wheelchair direction Table 3 reveals the gyroscope orientation angles of a wheelchair on an inclined plane or rough surface and duty cycles of PWM generated by the microcontroller. If the pitch angle is greater than -5° and the roll angle is between -10° to 10°, then the duty cycle would be 100%; as a result, the wheelchair moves at full speed. When the pitch angle is between -5° and -15°, and roll angle is between -10° and 10°, then the controller generates an 80% duty cycle; as a result, the wheelchair starts to decrease its speed. The wheelchair further decreases its speed when the pitch angle is between -15° and -35° and the roll angle is between -10° to 10°. The wheelchair stops, and the duty cycle becomes zero when the pitch angle becomes less than -35°, and the roll angle lies between -10° to 10°. These duty cycles totally depend on the pitch angle of the gyroscope mounted on the wheelchair to monitor its orientation and provide continuous feedback to the microcontroller. The duty cycles decrease with the increase in the inclined plane or sloped surface. Table 3. Orientation angles of wheelchair and duty cycle of PWM

EXPERIMENTAL RESULTS
After the research, design, and implementation of our proposed smart robotic wheelchair, we have tested and analyzed its response for different situations such as normal, rough, and inclined surfaces; the wheelchair is operating entirely and efficiently for all the conditions. Results are indeed the same as desired, and almost 99% accuracy has been achieved. Moreover, the tiny circuit mounted inside the cap with Accelerometer and the circuit mounted on the wheelchair with a gyroscope work precisely and effectively on account of the head's gestures. Using head commands, we can easily and smoothly drive the wheelchair in the forward direction, backward, left, and right direction, furthermore, on the inclined plane and stop the wheelchair when the user wishes.   Figure 9 shows the testing of the wheelchair on the inclined plane or slope. In these figures, the wheelchair smoothly moves downward and upward on the inclined plane without any type of slip or free movement.  The simulation tests the validity of the proposed approach compared with previously proposed models and parameter adjustments. These results are obtained via employing the Kalman filter on our sensor results. Figures 10(a) and (b) are the graphs between the time (x-axis) and the pitch angle (y-axis). Here, the blue signals correspond to the actual results of pitch up and pitch down angles of an accelerometer with respect to time that refers to the upward and downward motions of the developed wheelchair; however, the red signals correspond to the filtered and smooth output. Similarly, in Figure 10 (c) and (d), the graphs show the actual accelerometer sensor and filtered output with respect to time. The green signals correspond to the actual sensor results, and red signals refer to the filtered results which are plotted between roll angles(y-axis) and time (xaxis). Likewise, Figures (e) and (f) exhibits the gyroscope yaw angles (y-axis) actual and filtered results with respect to time, which correspond to the inclined plane movement of the wheelchair. The simulation concentrated on the scenes where the user goes straight up and down on an inclined plane and turns on the head's instructions. From these filtered results, we proved that the proposed method could eliminate the moving distance and increase lateral force without losing the pitch angle stability. It can also be said that through this simulation, the validity of the proposal has been validated.

CONCLUSION AND PERSPECTIVES
Our proposed system is not the only novel in designing, but also it has conquered all the drawbacks and issues found in previously designed wheelchairs. With the finalization and execution of our system, we have concluded that our proposed system is ideal for the handicapped, paralyzed, disabled, quadriplegic, and for those people who are suffering from spinal cord injuries. Furthermore, it is a very efficient, user-friendly, and cost-effective system in comparison with the previously proposed systems.