About 10–20% of every country’s population is disable. There are at least 650 million people with a kind of disability worldwide. Assistance and support are perquisites for many handicap people for participating in society. Electric powered wheelchairs provide efficient mobility to motor impaired persons. In this paper a smart controller of a wheel chair mobile robot using Particle Swarm Optimization Proportional controller (

In Saudi Arabia, about 800,000 of the population suffer from moving disability. 100,000 of those are with extreme disability conditions [

The effort of improving electric wheelchairs and carts control is continually developed by researchers. In Emam et al. [

Although the classical controllers have gained widespread usage across technological industries, it must also be pointed out that the unnecessary mathematical rigorosity, preciseness and accuracy involved with the design of controllers have been a major drawback. Designing and tuning a conventional controller appears to be conceptually intuitive, but can be hard in practice, if multiple objectives are to be achieved [

In this paper,

The purpose of the research is to achieve a good control trajectory performance in terms of the system error and robustness for the system uncertainties. In this article, the dynamic model of the wheelchair will be introduced in Section 2. Then A

The wheel chair as shown in _{R}_{R}) and reference frame (_{I}_{I}). Also

To perform the controlled movement of the wheel chair, the dynamic model of the system should be known. The Lagrange dynamic approach is showed systematically derives the equations of system motion [

Lagrange is a popular formulating approach for the governing equations of wheel chair motion. The general Lagrange equation is introduced by

where:

The generalized coordinates

The kinetic energy is formulated as:

where

_{wR}: The right axis kinematic.

_{wL}: The left axis kinematic.

_{c}: The mass of the chair only.

_{w}: The wheel and motor mass.

_{c}: The chair moment of inertia.

_{w}: The wheel and motor moment of inertia around the wheel axis.

_{m}: The wheel and motor moment of inertia around the wheel diameter.

The axes velocities are formulated as:

The coordinates of wheels can be presented as:

From

The wheeled chair moves on a horizontal level which is described by the position of the mobile chair and the angular difference [

The rotation matrix of the chair position is formulated as:

This rotation matrix describes the motion reference frame {_{I}_{I}} to local frame {_{R}_{R}}. The velocity of each driving wheel in the system can be the average of the left and right wheel velocities.

Also the system angular velocities:

Gathering the previous formulas, a kinematic model for the wheel chair can formulated as:

It is supposed

The traditional method for finding the optimum tuning of control system parameters is to optimize the system model for each parameter and decide the characteristics of the system which give local optimum solution. This method may lead to solutions far away from the optimum as the method strongly depends on the peculiarities of the system and the intuition of the modeler. Thus, different approaches to optimize the control system to find global optimum solution are needed.

Aly [

Compared with

In this study, the control design has two steps. The first step is finding the P controller gains using PSO algorithm which is search algorithms. The second step is applying the designed _{d}), angular velocity (_{d}) according to the required position of the trajectory. The desired velocities (_{d}), and _{d}) will be the input to wheel chair dynamics which will use those values to produce the final velocities (

Developmental computational strategy is dependent on the development and insight of multitudes searching for the most fertile feeding location. A “swarm” is an obviously disrupted assortment (populace) of moving individual that will in general bunch together while every individual is by all accounts moving an irregular way. It utilizes various specialists (particles) that establish a swarm moving around in the quest space searching for the best arrangement [

The

The speed is restricted to the scope of _{max}, _{max}

In _{p1} of the first control axis while in _{p2}.

_{p1} of the first control axis and _{p2}. It ought to be noticed that the estimations of an element in the particle may surpass its sensible range. This calculation is continued until most extreme cycle is attainable as illustrated in

PSO look through the entirety of the forerunner and resulting parameters in 50 dimensional spaces. The order of a particle is illustrated as:

where the _{ij} and _{ij} represent the center and deviation parameters of the MFs. The underlying estimations of particles are haphazardly created in the first generation.

The important step in implementing

where _{1}_{2}

The population size is chosen to be _{f}

To illustrate the system behavior under the proposed controller several standard test commands such as fixed point, line, and circle inputs are applied to the system. The responses of _{p1}, and _{p2}, are found by

For testing the controller performance, different three dynamic loads are used from references of [

In the simulation, the mobile chair reaches fixed point from its original position, while another test is starting from its original position and moving to be closed with reference line and final test that the robot should follow a circular trajectory of reference.

^{2} while max rotation velocity of 1.9 rad/s. The obtained results for fixed point of (1.0 m, 1.0 m) has settling time about of (54 s for payload of 10 and 55 kg) while for the dynamic load of 125 kg the settling time increased. The steady state error changed from about zero second to be 0.066 m when the dynamics parameters of payload of 125 kg was implemented as presented in

The circular trajectory with radius

This article presented a tuning method based on the

It has the advantages of rapid respond, tracking accuracy and good anti-interference, so the

The future work for this study is verifying experimentally the proposed control algorithm to assure its performance with non-predicted dynamic parameters.

_{ij} center parameters of the MFs

^{th} particle

_{1}^{st} joint error

_{2}^{nd} joint error

_{c} chair moment of inertia.

^{th} particle sample

_{m} wheel and motor moment of inertia around the wheel diameter.

_{w} wheel and motor moment of inertia around the wheel axis.

_{p1} control gain of axis1

_{p2} control gain of axis2

_{c} mass the chair only.

_{w} wheel and motor mass.

_{i} ^{th} particle position

_{f} final time

_{wL} left axis kinematic.

_{wR} right axis kinematic.

_{i} ^{th} particle velocity

_{L} left wheel velocity

_{R} right wheel velocity

(_{I} _{I}) motion reference frame

(_{R}_{R}) wheel chair frame

_{1} speed of axis1

_{2} speed of axis2

ω system angular velocity

_{ij} deviation parameters of the MFs