here is a code for bug $2$algorithm in matlab. the output of this code is shown in the $2$nd image which is not desired. the output graph should look like the $1$st image. so rewrite the code make the changes so that the output looks like the $1$st image:

$\%$ BUG$2$ Algorithm Implementation in MATLAB

clear;

clc;

$\%$ Define initial and goal positions

init$\_$pos $=[0,0]$; $\%$ Initial position

goal$\_$pos $=[10,10]$; $\%$ Goal position

$\%$ Define obstacle as a boundary $($for simplicity, a circular obstacle$)$

obstacle$\_$center $=[5,5]$; $\%$ Center of the circular obstacle

obstacle$\_$radius $=2$; $\%$ Radius of the circular obstacle

$\%$ Create figure

figure;

hold on;

$\%$ Plot obstacle

theta $=$ linspace$(0,2*$pi$,100)$;

x$\_$obstacle $=$ obstacle$\_$center$(1)+$ obstacle$\_$radius $*$ cos$($theta$)$;

y$\_$obstacle $=$ obstacle$\_$center$(2)+$ obstacle$\_$radius $*$ sin$($theta$)$;

plot$($x$\_$obstacle, y$\_$obstacle, $\text{'}$r$\text{'},$ 'LineWidth', $2)$; $\%$ Red boundary for obstacle

$\%$ Plot initial and goal points

plot$($init$\_$pos$(1),$ init$\_$pos$(2),\text{'}$go$\text{'},$ 'MarkerSize', $10,$ 'MarkerFaceColor', $\text{'}$g$\text{'})$;

plot$($goal$\_$pos$(1),$ goal$\_$pos$(2),\text{'}$bo$\text{'},$ 'MarkerSize', $10,$ 'MarkerFaceColor', $\text{'}$b$\text{'})$;

$\%$ Set axis limits

axis equal;

xlim$([-1,11])$;

ylim$([-1,11])$;

$\%$ Start moving towards goal

current$\_$pos $=$ init$\_$pos;

plot$\_$path $=[]$; $\%$ To store the path of the robot

while norm$($current$\_$pos $-$ goal$\_$pos$)>0\mathrm{.}1\%$ Continue until the goal is reached

$\%$ Check if line of sight is clear $($no obstacle intersection$)$

if ~is$\_$in$\_$obstacle$($current$\_$pos, goal$\_$pos, obstacle$\_$center, obstacle$\_$radius$)$

$\%$ Move straight towards the goal

current$\_$pos $=$ move$\_$towards$($current$\_$pos, goal$\_$pos$)$;

else

$\%$ Encounter obstacle, follow boundary

current$\_$pos $=$ follow$\_$obstacle$($current$\_$pos, goal$\_$pos, obstacle$\_$center, obstacle$\_$radius$)$;

end

$\%$ Plot the robot's path

plot$\_$path $=[$plot$\_$path; current$\_$pos$]$; $\%$#ok

plot$($plot$\_$path$($:$,1),$ plot$\_$path$($:$,2),\text{'}$k$\text{'},$ 'LineWidth', $2)$;

pause$(0\mathrm{.}1)$; $\%$ Slow down the plotting for visualization

end

$\%$ Function to check if a path is within an obstacle

function is$\_$obst $=$ is$\_$in$\_$obstacle$($pos$1,$ pos$2,$ center, radius$)$

$\%$ Check if the line between pos$1$ and pos$2$ intersects with the circular obstacle

$\%$ For simplicity, use distance to the obstacle center

midpoint $=($pos$1+$ pos$2)/2$;

distance$\_$to$\_$center $=$ norm$($midpoint $-$ center$)$;

if distance$\_$to$\_$center $$ radius

is$\_$obst $=$ true;

else

is$\_$obst $=$ false;

end

end

$\%$ Function to move the robot towards the goal

function new$\_$pos $=$ move$\_$towards$($current$\_$pos, goal$\_$pos$)$

step$\_$size $=0\mathrm{.}5$; $\%$ Define the step size

direction $=($goal$\_$pos $-$ current$\_$pos$)/$ norm$($goal$\_$pos $-$ current$\_$pos$)$;

new$\_$pos $=$ current$\_$pos $+$ step$\_$size $*$ direction;

end

$\%$ Function to follow the obstacle boundary

function new$\_$pos $=$ follow$\_$obstacle$($current$\_$pos, goal$\_$pos, center, radius$)$

$\%$ For simplicity, move around the obstacle in a circular fashion

step$\_$angle $=0\mathrm{.}1$; $\%$ Step size around the obstacle

direction$\_$vector $=$ current$\_$pos $-$ center;

current$\_$angle $=$ atan$2($direction$\_$vector$(2),$ direction$\_$vector$(1))$;

new$\_$angle $=$ current$\_$angle $+$ step$\_$angle; $\%$ Move along the boundary

new$\_$pos $=$ center $+$ radius $*[$cos$($new$\_$angle$),$ sin$($new$\_$angle$)]$;

end