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

$\%$ Bug $1$ Algorithm in MATLAB

clc; clear; close all;

$\%$ Start and goal positions

start $=[2,2]$; $\%$ Start point $($x$,$ y$)$

goal $=[15,15]$; $\%$ Goal point $($x$,$ y$)$

$\%$ Define obstacles as circles with center and radius

obstacles $=[5,5,2$; $10,8,3]$; $\%[$x$\_$center, y$\_$center, radius$]$

$\%$ Plot environment, start, and goal

figure; hold on; axis equal;

plot$($start$(1),$ start$(2),\text{'}$go$\text{'},$ 'MarkerSize', $10,$ 'DisplayName', 'Start'$)$;

plot$($goal$(1),$ goal$(2),\text{'}$ro$\text{'},$ 'MarkerSize', $10,$ 'DisplayName', 'Goal'$)$;

$\%$ Plot the obstacles

for i $=1$:size$($obstacles$,1)$

viscircles$($obstacles$($i$,1$:$2),$ obstacles$($i$,3),$ 'LineWidth', $1)$;

end

legend;

xlabel$(\text{'}$X$\text{'})$; ylabel$(\text{'}$Y$\text{'})$; title$(\text{'}$Bug $1$ Algorithm Path Planning'$)$;

$\%$ Initialize robot position at the start point

robot$\_$pos $=$ start;

path $=$ robot$\_$pos; $\%$ Store the robot's path

$\%$ Parameters

step$\_$size $=0\mathrm{.}2$; $\%$ Robot's step size

tolerance $=0\mathrm{.}1$; $\%$ Distance threshold for reaching the goal

while norm$($robot$\_$pos $-$ goal$)>$ tolerance

$\%$ Compute the straight$-$line direction to the goal

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

$\%$ Predict next step

next$\_$pos $=$ robot$\_$pos $+$ step$\_$size $*$ direction;

$\%$ Check for collisions with any obstacle

collision $=$ false;

for i $=1$:size$($obstacles$,1)$

obs$\_$center $=$ obstacles$($i$,1$:$2)$;

obs$\_$radius $=$ obstacles$($i$,3)$;

$\%$ Check if the next step is inside an obstacle

if norm$($next$\_$pos $-$ obs$\_$center obs$\_$radius

collision $=$ true;

break;

end

end

if collision

$\%$ Move around the obstacle $($following the edge$)$

fprintf$(\text{'}$Obstacle encountered at $(\%\mathrm{.}2$f$,\%\mathrm{.}2$f$)$

$\text{'},$ robot$\_$pos$(1),$ robot$\_$pos$(2))$;

$\%$ Follow the obstacle edge until free to move toward the goal again

while collision

theta $=$ linspace$(0,2*$ pi$,100)$; $\%$ Points along the obstacle's edge

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

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

$\%$ Move along the edge $($in small steps$)$

for k $=1$:length$($edge$\_$x$)$

robot$\_$pos $=[$edge$\_$x$($k$),$ edge$\_$y$($k$)]$;

path $=[$path; robot$\_$pos$]$; $\%$ Store the path

$\%$ Plot the robot's movement along the obstacle

plot$($robot$\_$pos$(1),$ robot$\_$pos$(2),\text{'}$b$.\text{'},$ 'MarkerSize', $5)$;

pause$(0\mathrm{.}01)$; $\%$ Slow down for visualization

$\%$ Check if free path toward the goal is possible again

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

test$\_$pos $=$ robot$\_$pos $+$ step$\_$size $*$ direction$\_$to$\_$goal;

if norm$($test$\_$pos $-$ obs$\_$center$)>$ obs$\_$radius

collision $=$ false; $\%$ Free to move toward the goal

break;

end

end

end

else

$\%$ No collision, move towards the goal

robot$\_$pos $=$ next$\_$pos;

path $=[$path; robot$\_$pos$]$; $\%$ Store the path

$\%$ Plot the robot's movement

plot$($robot$\_$pos$(1),$ robot$\_$pos$(2),\text{'}$b$.\text{'},$ 'MarkerSize', $5)$;

pause$(0\mathrm{.}01)$; $\%$ Slow down for visualization

end

end

fprintf$(\text{'}$Goal reached at $(\%\mathrm{.}2$f$,\%\mathrm{.}2$f$)$

$\text{'},$ robot$\_$pos$(1),$ robot$\_$pos$(2))$;

$\%$ Plot the final path

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

legend;

hold off;