Improved Trajectory Planning of Mobile Robot Based on Pelican Optimization Algorithm

The mobile robot movement defined as a motion of a mobile wheeled robot beginning from the beginning point to the endpoint. The trajectory becomes more important as mobile robot application scenarios become more complicated and unpredictable [1]. One of the most common problems in mobile robots that have been addressed by several researchers over the past 20 years is obstacle avoidance. Trajectory with obstacle avoidance aimed to determine the best path for a mobile robot between two points [2]. For mobile robots, autonomous motion planning is a useful feature. It has been needed human intervention on their part. But it also involved a lot of work and issues to be resolved, such as Artificial Intelligence (AI) methods. The task at hand involved determining the optimal path to take a wheedled robot from its existing location to final one. For instance, both states could be the starting point and the objective, respectively [3]. Ibrahim et al. [4] employed a fuzzy logic intelligent technique to regulate and control mobile robot mobility in stationary obstacles. The software utilized for the robot's creation and simulation was Webot Pro and MATLAB. The mobile robot's objective was to move while avoiding immovable objects. Lyu et al. [5] enhanced the beetle swarm optimization (IBSO) technique which effectively resolved various trajectory issues in static environments. The IBSO method has demonstrated the mobile robot's ability to move in a stationary obstacle. Shao [6] investigated the Genetic Algorithm called (GA) which depended on the method of tracking a moving robot in a stationary setting. The researcher simulated the environment, and the robot trajectory using MATLAB.

Raheem et al. [7] presented the path of the robot using the Adaptive Neuro-Fuzzy Inference System which was summarized as (ANFIS) algorithm. It depended on training the positions of the robot to get better locations. Particle’s swarm method (PSO) was dependent on the swarm’s behavior such as bird flocks. For highly complicated and nonlinear models, the PSO helped resolve difficult issues [8-17]. Alam et al. [18] suggested a trajectory approach based on the PSO method to determine a good path which was avoided collision in static obstacles for a mobile robot. The suggested method simulated and randomly selected grid lines that were created between the beginning and end places of a robot. The Pelican Optimization Algorithm (POA) is among the most advanced optimization algorithms available today. In 2022, the POA was proposed. Based on how pelicans approach their chases and the tactics they were used. It was cunning adaption that allowed the birds to become expert searchers [19-21]. A clearer link between the above background information and the specific problem of this paper is being addressed in all researchers worked on mobile robot with AI algorithms but in this work, the mobile robot linked to WiFi camera based AI modern algorithm (POA) to detect the obstacles. It can be summarized the main contributions as:

• The BOE–Bot wheeled mobile robot with a WiFi camera can avoid two static obstacles.
• The accurate trajectory from beginning point to end-point is implemented by the proposed POA, and it avoids two static obstacles.
• A comparison between two proposed algorithms of PSO and POA implemented.

Comparative study between two proposed methods PSO and POA in terms of MSE measured. This article is structured into eight parts. The Section 2 offered the wheeled mobile robot mathematical model. The Mean Square Error (MSE) equation is illustrated in Section 3. The Section 4 explained the optimization trajectory of a mobile robot using PSO and POA. The proposed Flowchart existed in Section 5. Experimental work hardware connection is illustrated in Section six. The results are illustrated in Section seven. Lastly, conclusion of this work is represented in Section 8.

In this work, the two optimization algorithms are used for optimizing the mobile robot trajectory.

3.1 Particle swarm approach

PSO represented by way of a kind of intelligence swarm method that has benefits for simple program, less parameters. Every iteration found the optimal particle position, which is noted and given the name $pbest$. The optimal place identified by all particles is known as $gbest$ refers to the best place that all particles have discovered. The new position and velocity of each particle have been calculated using Eq. (14) and Eq. (15) taking into account$pbest$, $gbest$ [28]. The position of mobile robot trajectory ($x,y$) is described in Eq. (10) and orientation $\theta $ in Eq. (11). Within the optimization process, there are 2 measuring positions ($x_{i,j}^{k}$) and velocity ($v_{i,j}^{k}$). They were developed for the new variables $x_{i,j}^{k+1}$ and $v_{i,j}^{k+1}$ depending on the two formulas [28]:

$v_{i,j}^{k+1}=v_{i,j}^{k}+{{c}_{1}}{{r}_{1}}(pbest_{i,j}^{k+1}-x_{i,j}^{k})+{{c}_{2}}{{r}_{2}}(gbest_{j}^{k+1}-x_{i,j}^{k}$    (14)

   $x_{i,j}^{k+1}=x_{i,j}^{k}+v_{i,j}^{k+1}$  (15)

There are two components of joints (i and j) which are represented as i^th and j^th. The ${{r}_{1}},{{r}_{2}}$ were two random parameters varied from 0 to 1. The two symbols ${{c}_{1}},{{c}_{2}}$ were illustrated as the cognition and social coefficients which they were varied from 0 to 2, correspondingly. $k$ was an iteration number. The next stage in this algorithm depends on the particle individual which was the best ($pbes{{t}_{i,j}}$) and also global particle which was the best ($gbes{{t}_{j}}$). This technique enhanced the performance by minimizing the problem of the MSE objective function as in Eq. (14). In this work, the PSO algorithm enhanced the performance of mobile robot trajectory by suggesting the following cost function:

$Cost~function~=min\left( MSE \right)$  (16)

In this work, the data of ($x,y,~\theta $) are generated from Eq. (10), Eq. (11), Eq. (12) and from a case study of linear velocities where ${{\nu }_{r}}$ > ${{\nu }_{l}}$. A block diagram for an enhanced PSO algorithm was shown as in Figure 2. It contains 3 blocks. The 1^st block is the inputs $\left( x,y,\theta  \right)$ which are generated from a mobile robot model represented mathematically as mentioned in section 2. In addition, the right and left linear velocities (${{\nu }_{r}}$ , ${{\nu }_{l}}$) are initialized. PSO algorithm has received these 3 inputs for optimization as in the 2^nd block. The optimal mobile robot’s trajectory output is based on optimal values of $\left( x,y,\theta  \right)$ calculated as in 3^rd one. Due to an Eq. (16), PSO worked in order to diminish a cost formula depending on $MSE$ of a mobile robot. The PSO parameters are illustrated in Table 2.

2.png

Figure 2. The block diagram for enhanced PSO algorithm

Table 2. PSO parameters

3.2 Pelican optimization algorithm (POA)

Pelican Pelicans introduced the population, which serves as the basis for the POA. Any community of pelicans can be a probable solution in populace depends on algorithms. Due to their positions in searching operation of a planetary, every member’s population supplied the values for the variables in the optimization problem. Eq. (17) is used to obtain the lower and upper boundaries for a task, and the population members are started at random. Before discussing the POA procedures, the population is set up. Since pelicans typically seek within a specific radius for prey, the starting locations of each member of the population may be indicative of the group as a whole [19-21].

${{x}_{i,j}}=l{{b}_{i,j}}+random\left( u{{b}_{j}}-l{{b}_{j}} \right)$ (17)

where, $i$ was ranged (1…n), $j$ was ranged (1…$m$), ${{x}_{i,j}}~$represented as the first site’s pelican. A symbol $n$ presented as number of populace, the symbol $m$ is denoted variables number, $random$ has been varied from 0 & 1. The $ub$ and $lb$ are the minor and higher boundary of $m$ respectively [19-21]. The pelican population matrix $X$ can be expressed as Eq. (2) and ${{X}_{i}}$= i^th pelican [19-21].

$X=\left[\begin{array}{c}X_1 \\ \vdots \\ X_i \\ \vdots \\ X_{n, 1}\end{array}\right]=\left[\begin{array}{ccccc}x_{1,1} & \cdots & x_{1, j} & \cdots & x_{1, m} \\ \vdots & \ddots & \vdots & \cdots & \vdots \\ x_{i, 1} & \cdots & x_{i, j} & \cdots & x_{i, m} \\ \vdots & \cdots & \cdots & \ddots & \vdots \\ x_{n, 1} & \cdots & x_{n, j} & \cdots & x_{n, m}\end{array}\right]$    (18)

The fitness function matrix is as below [20]:

$f=\left[\begin{array}{c}f_1 \\ \vdots \\ f_i \\ \vdots \\ f_n\end{array}\right]=\left[\begin{array}{c}f_1\left(x_1\right) \\ \vdots \\ f_1\left(x_i\right) \\ \vdots \\ f_1\left(x_n\right)\end{array}\right]$   (19)

The inspiration behind the POA algorithm and how it related to the pelican's hunting behavior can be explained briefly. The POA has been inspired by the collaborative, effective, and adjustable hunting behaviors for pelicans. These natural strategies were mimicked and the POA accomplished the robust performance for solving compound optimization problems. Agents cooperated and adjusted the two phases: exploration and exploitation.

I. Movement to rapacious phase

Pelicans find their quarry and fly to its direction in the chief step. It has enhanced the POA's ability to precisely assess a problem-solving domain. The pelican's method of achieving its goal and the ideas that were previously covered are mathematically reproduced in Eq. (20).

$x_{i, j}^{p_1}=\left\{\begin{array}{c}x_{i, j}+\operatorname{random}\left(p_j-I . x_{i, j}\right), \text { if } f_1<f_{\mathrm{i}} \\ x_{i, j}+\operatorname{random}\left(x_{i, j}-p_j\right), \quad \text { else }\end{array}\right.$     (20)

where, $x_{i,j}^{{{p}_{1}}}$= modernized pelican’s position of this phase. ${{p}_{j}}$ = quarry spot,$~I$ is randomly adjusted between one or two. It was changed in every repetition. When, it was reached to 2; the supporter has more transposition; it should be yield them into next regions for the interplanetary. Thus, a constraint $I$ determines the extent to which a POA can investigate the space search. A pelican may relocate as long as it enhances its fitness function. It is referred to as operative apprising. This process is simulated using Eq. (22).

$X_i=\left\{\begin{array}{cc}X_i^{p_1}, & \text { if } f_1<f_{\mathrm{i}} \\ X_i, & \text { else }\end{array}\right.$   (21)

where, $X_{i}^{{{p}_{1}}}~$is the updated position of i^th pelican in the exploration phase and $f_{i}^{{{p}_{1}}}$ is the fitness function value of an exploration phase.

Ⅱ. Exploitation phase

In their second phase, pelicans forced fish upward by expanding their wings and ensnaring them in their neck pouches, which allowed them to rise to the water's surface. Using this strategy, pelicans can capture many fish in the attacked area. The pelicans converged to gain better sites within the hunting zone. This procedure improved the POA's local search and exploitation capabilities. To get the algorithm to converge to an optimal solution, the areas surrounding the pelican site must be mathematically explored. The pelican's hunting habit is mathematically modeled by Eq. (22).

$x_{i, j}^{p_2}=x_{i, j}+R \cdot\left(1-\frac{t}{T}\right)(2 \cdot$ random -1$) x_{i, j}$   (22)

where, $x_{i}^{{{p}_{2}}}$is an updated position pelican of the exploitation phase and $f_{i}^{{{p}_{1}}}$ presented as the cost function of the exploitation phase. A factor R = 0.2. The coefficient $R.~\left( 1-\frac{t}{T} \right)$ is a pelican of populace for neighborhood’s radius$~~{{x}_{i,j}}$; $t$ which is represented as a counter of iteration, The symbol $T$ expressed by maximum iteration. To find the optimal overall solution, the POA's exploitation power technique is aided by the R.(1-t/T) coefficient. In the beginning iterations, it has been given the high value of this coefficient, a greater area around each member is considered. The approach diminishes with more replications, bringing each neighborhood member's radii down. toward this reason, POA may adapt toward almost globally optimum—that is, nearly absolutely global optimal—solutions, contingent upon the utilization strategy. As a result, it is feasible to scan the region around every person in the population in fewer, more precise steps. The pelican position is now updated and takes on the following form:

$X_i=\left\{\begin{array}{cc}X_i^{p_2}, & \text { if } f_i^{p_2}<f_{\mathrm{i}} \\ X_i, & \text { else }\end{array}\right.$   (23)

where, $X_{i}^{{{p}_{2}}}$ denoted as an updated position pelican of the exploitation phase and $f_{i}^{{{p}_{2}}}$ represented as an objective function of the exploitation phase [19-21]. The POA algorithm improved a robot’s trajectory performance in our research, by putting forth the following cost function minimization issue, which is described as:

$Cost~function~=min\left( MSE \right)$    (24)

Figure 3 shows the enhanced POA algorithm block diagram. It contains of three blocks. The 1^st block is the inputs $\left( x,y,\theta  \right)$ which are generated from a mathematical expression of a wheeled robot as mentioned in section 2. In addition, the right and left linear velocities (${{\nu }_{r}}$, ${{\nu }_{l}}$) are initialized. POA has received these 3 inputs for optimization as in 2^nd block. The optimal mobile robot’s trajectory output is based on optimal values of $\left( x,y,\theta  \right)$ calculated as in 3^rd block. Due to Eq. (16), the POA method worked to minimize cost function depending on $MSE$ of the mobile robot. The POA parameters seen in Table 3.

For the case study of linear velocities if ${{\nu }_{r}}$ > ${{\nu }_{l}}$ then the wheeled robot moved from beginning to endpoint within static obstacles. In this paper, the $k$ equals 2 while the final time of trajectory equals 4 seconds. In real time response of mobile robot Obstacle Avoidance using WiFi camera, the two algorithms POA and PSO are getting a best solution for a given problem. A modern algorithm called POA is capable to detect obstacle and avoid it faster than PSO. POA is also faster convergence as compared to PSO.

3.png

Figure 3. The block diagram for enhanced POA algorithm

Table 3. POA parameters

The experimental BOE–Bot wheeled mobile robot platform has been manufactured by (Parallax) as shown in Fig. 5. BOE–Bot wheeled mobile consists of the following hardware components:

• Black rotation crystal
• Wireless WiFi camera monitoring webcam type MD81 mini Wi-Fi P2P sends the Wi-Fi signal to the iPhone and all specifications of this camera are explained in the study [29]. Figure 5 shows the connection between the WiFi camera and iPhone as follows:

1. (A) After fully charging the WiFi camera, Open it on.
2. (B) Install the p2pCamVewier application on an iPhone and then open it.
3. (C) From Wifi iPhone, search for the name of the Wifi camera then choose it.
4. (D) The image has been shown in the figure below:

5.png

Figure 5. Connection steps between WiFi camera and WiFi iPhone

Figure 6 shows the wheeled mobile robot parts are explained as below:

1. The mobile robot chassis is made from aluminum material.
2. Wifi-camera.
3. Aluminum structure of BOE–Bot wheeled mobile robot.
4. Two motor wires, each wire connected between servo motor and mobile robot.
5. Switch on/off button.
6. BASIC Stamp microcontroller used for programming the code.
7. Left robot wheel.
8. Right robot wheel.
9. Left motor type parallax continuous servo rotating with 360 degrees.
10.  Right motor type parallax continuous servo rotating with 360 degrees.
11.  Battery holder attached with 6 volts.

6.png

Figure 6. Two views of an experimental BOE-Bot wheeled mobile robot

Figure 11 shows an experiment mobile wheeled robot trajectory moving from start to goal point based on the proposed POA algorithm. At time zero, the mobile robot stands and the WiFi camera detects the object. A center mobile robot (x,y,θ) point computed from the camera and proposed POA algorithm. Then, at the time of one second the mobile robot faced the first obstacle. At two seconds, A wheeled BOE–Bot robot is moved to the left side and avoids the first obstacle. At three seconds, A wheeled BOE–Bot robot detected the second obstacle. At four seconds, the mobile robot rotated the left side avoiding obstacle 2 then moved to the end point. A wheeled mobile robot can bypass the obstacles without contact collision and move according to the goal point successfully as compared with the simulated results in Figure 9.

11.png

Figure 11. The experiment mobile robot of the optimal trajectory of the proposed POA algorithm avoiding 2 static obstacles

To cover this work’s study to future works. One suggestion is to use modern artificial intelligence techniques to improve the path planning [30-44]. In order to make real path planning, the dynamic of mobile robot may be considered and hence a recent control schemes are required [45-54]. Finally, one may use other optimization techniques to replace and compare the proposed method [55-58].