The Perfect AI

Ok, I'm struggling a little bit, as you can tell from my game. Basically, right now I am trying to make the AI perfect so it hits the ball with almost every shot. This is the code I am using

Code:

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TurretAI = function () {
        var turret = _root.turret2;
        var ball = _root.ball;
        var unsolved = true;
        var counter = 1;
        var turret_x = turret.x;
        var turret_y = turret.y;
        var turret_xSpeed = turret.xSpeed;
        var ball_x = ball.x;
        var ball_y = ball.y;
        var ball_xSpeed = ball.xSpeed;
        var ball_ySpeed = ball.ySpeed;
        //bullet_speed = 15*15;
        var bullet_speed = 15;
        while(unsolved) {
                counter++;
                turret_x += turret_xSpeed;
                if(turret_xSpeed > 0) {
                        if(turret_x > 500) {
                                turret_xSpeed *= -1;
                        }
                } else {
                        if(turret_x < 50) {
                                turret_xSpeed *= -1;
                        }
                }
                ball_x += ball_xSpeed;
                ball_y += ball_ySpeed;
                if(ball_x > 540) {
                        ball_x = 540;
                        ball_xSpeed *= -1;
                } else if(ball_x < 10) {
                        ball_x = 10;
                        ball_xSpeed *= -1;
                }
                var bullet_distance = (bullet_speed*counter)*(bullet_speed*counter);
                var xDist = turret_x-ball_x;
                var yDist = turret_y-ball_y;
                var dist = (xDist*xDist) + (yDist*yDist);
                if(dist < bullet_distance) {
                        //Find the correct rotation and how long it will take to rotate there
                        var rot = Math.atan2(yDist, xDist);
                        var rotation = rot*57.2957795130823;
                        rotation -= 90;
                        if(rotation < 0) {
                                rotation += 360;
                        } else if(rotation > 360) {
                                rotation -= 360;
                        }
                        var rotation_time = Math.ceil((rotation-turret.rotation)/turret.rotation_speed);
                        if(rotation_time > counter) {
                                counter = rotation_time;
                        }
                        turret.needed_rotation = rotation;
                        turret.counter = counter;
                        unsolved = false;
                }
        }
}

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Does anyone know where I am going wrong, or know of a different method to achieve the perfect AI? Thanks for any help, it is greatly appreciated.

double...

Seems like it could be a pretty fun game. Nice idea ...

Hmm ... can you explain exactly how the code works? Do you already try to predict the position of the ball and where to shoot at then?

It seems like the AI is just shooting at the current position of the ball - but the code seems to do a lot more than just that.

Well what I was trying to do was this. Check to see where the cannon and the ball will be in one frame. See if the distance the ball would have traveled is great enough. If it is too great, check for two frames. Keep this up until the balls will meet up, find the angle and shoot.

So you find the shortest amount of time in the future where you would be able to hit the ball - if you fired the canon now.

Then you have the future position of the ball, the future position of the canon - and calculate how to rotate the canon to point at that future location. But doesn't that mean you first fire the canon at exactly the point where the ball is? So this would work perfectly if you were firing laser beams. But not for a slow moving bullet

Okay, I think I'm starting to realize my mistake. So basically I need to choose a point when I will shoot, say in 10 frames. Make not of the turrets position at that point. Then run my testing from that point to see how far the ball is from the turret and how far my ball would be traveling. Repeat until ball moving distance is greater than ball turret distance. Find the angle, and shoot?

You could probably make it work but you would have the 10 frame lag.

My suggestion would be to calculate if the ball would hit if you fired now - simply make lines, check for intersections and calculate if the balls are both at the intersection at that point.
If they don't hit the try and see if you get closer or further to hitting if you rotate one way. Otherwise try rotating the other direction. The repeat until you either calculate a hit or you run out of CPU (some fixed amount of max tries) :)

It could probably be calculated perfectly by some formula, but I'm not that big on math unfortunately.

okay, I am sooo close ... This is my updated code

Code:

---

TurretAI = function () {
        var turret = _root.turret2;
        var ball = _root.ball;
        var unsolved = true;
        var counter = 10;
        var turret_x = turret.x;
        var turret_y = turret.y;
        var turret_xSpeed = turret.xSpeed;
        var ball_x = ball.x;
        var ball_y = ball.y;
        var ball_xSpeed = ball.xSpeed;
        var ball_ySpeed = ball.ySpeed;
        //bullet_speed = 15*15;
        var bullet_speed = 15;
        for(var n = 1; n < counter; n++) {
                turret_x += turret_xSpeed;
                if(turret_xSpeed > 0) {
                        if(turret_x > 500) {
                                turret_xSpeed *= -1;
                        }
                } else {
                        if(turret_x < 50) {
                                turret_xSpeed *= -1;
                        }
                }
                ball_x += ball_xSpeed;
                ball_y += ball_ySpeed;
                if(ball_x > 540) {
                        ball_x = 540;
                        ball_xSpeed *= -1;
                } else if(ball_x < 10) {
                        ball_x = 10;
                        ball_xSpeed *= -1;
                }
        }
        while(unsolved) {
                ball_x += ball_xSpeed;
                ball_y += ball_ySpeed;
                if(ball_x > 540) {
                        ball_x = 540;
                        ball_xSpeed *= -1;
                } else if(ball_x < 10) {
                        ball_x = 10;
                        ball_xSpeed *= -1;
                }
                var bullet_distance = (bullet_speed*counter)*(bullet_speed*counter);
                var xDist = turret_x-ball_x;
                var yDist = turret_y-ball_y;
                var dist = (xDist*xDist) + (yDist*yDist);
                if(dist < bullet_distance) {
                        //Find the correct rotation and how long it will take to rotate there
                        var rot = Math.atan2(yDist, xDist);
                        var rotation = rot*57.2957795130823;
                        rotation -= 90;
                        if(rotation < 0) {
                                rotation += 360;
                        } else if(rotation > 360) {
                                rotation -= 360;
                        }
                        var rotation_time = Math.ceil((rotation-turret.rotation)/turret.rotation_speed);
                        if(rotation_time > counter) {
                                counter = rotation_time;
                        }
                        turret.needed_rotation = rotation;
                        turret.counter = 10;
                        unsolved = false;
                }
                counter++;
        }
}

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You need to jump a few more frames into the future.

Looks like this is going to be a very fun game!
First offtopic critic: Make the main-ball different colour than the cannonballs.

Quote:

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First offtopic critic: Make the main-ball different colour than the cannonballs.

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I was thinking the same thing ;)

I will say this... I don't know the proper answer but there IS a mathematical way to calculate the exact solution to the problem. Jobe tried to explain it to me once but my math skills arn't up to the challenge. I'll see if I can get him to post in here talking about it.

Yes, the maths needed to do this is pretty complex, I'm not going to try and work it out now :p. The problem is that there are two unknowns, where the ball will be when it collides with the bullet, and when they will collide.
You could always cheat, and change the speed of the opponent’s bullets so that it always takes the same amount of time for them to go from the turret to the centre line. That way you are removing the unknown "when" because it will always collide 'N' frames after the bullet was fired. Then you just have to work out where the ball will be that much time in the future, find the distance between that position and the turret, and fire the bullet at that position giving it a speed of distance/time. It might be too obvious that the computer is cheating, but if not then you are getting the result you want with 10x less complexity.

Ali

Looks like you got it working pretty well if you actually want to know the correct math well here it is. It is actually quite simple. What you have is a triangle with a known angle and two sides which have a know ratio of lengths. You can simple use the law of sines to calculate the desired secondary angle: the law of sines states that A / sin(a) = B / sin(b) and angle a is know as is A/B so b = asin(A / B sin(a))

there are a couple things to notice here: first A / B sin(a) may not be a valid entry for asin (AKA no angle can produce it) this would mean that no shot will hit the ball (this is not quite true since you have walls so it is possible that the ball will bounce off the wall and then hit your shot) Also note this can only be the case if the ball is traveling faster than your shot.

Another thing to not if the ball is about to hit the wall and bounce back. Your shot will still hit the ball it will just hit the wall first. Since if there is no wall the ball would just keep going and your shot would hit the ball past where the wall was.

Third instead of using the center of the ball I would use the highest point of the ball (if the computer is above like in your game). This will help in two ways. First it will hit the ball so that it is pushed further away from itself and if the other player hits the ball the shot has a better chance of hitting the ball.

Here is some code that makes B2 aim at where B1 will be

Code:

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B1.vel = .125;
B2.vel = .25;
B1.ang = 1/4 * Math.PI;

dif_ang_1 = Math.atan2(B2._y - B1._y, B2._x - B1._x);
if (dif_ang_1 < 0)
        dif_ang_1 += 2*Math.PI;
dif_ang_2 = Math.atan2(B1._y - B2._y, B1._x - B2._x);
if (dif_ang_2 < 0)
        dif_ang_2 += 2*Math.PI;

if (Math.abs(B1.vel/B2.vel * Math.sin(B1.ang - dif_ang_1)) > 1.0)
        trace("couldn't shoot");
else
        B2.ang = dif_ang_2 + Math.asin(B1.vel/B2.vel * Math.sin(dif_ang_1 - B1.ang));

function onEnterFrame():Void
{
        B1._x += B1.vel*Math.cos(B1.ang);
        B1._y += B1.vel*Math.sin(B1.ang);
        B2._x += B2.vel*Math.cos(B2.ang);
        B2._y += B2.vel*Math.sin(B2.ang);
}

---

Hope this helps.
Remember just because this will give the correct solution doesn't mean you always want to use it. Often it works better if the computer doesn't act perfectly it makes him unpredictable and some times (due to other errors such as round off error) it can work better.

I haven’t had much time to look at your method, I’ve got to go in a second, but I'm not too clear on how that works. You say you know an angle, but I can't see how you do, in your code you seem to be using 45 degrees as a angle, where did that come from? Anyway I will have a better look when I get back.

Ali

I specified the angle and both velocities for examples, but normally this would already be set. The angle is where the ball is heading so it is know, if the ball is not moving then the angle is meaningless, since it will just be the asin of zero or zero so the shot will be fired directly at the ball. If you input my code and make two objects B1 and B2 you will see that if you change the starting positions of them and the initial angle of B1 and the speeds: B2 will fire and hit B1, unless of cource it is impossible in which case it does nothing. Note at great distances it may easilly miss due to imprecise sin and asin measurements.

shavlor's method works. I did this in a game recently, the important thing about this method is that the distance to the ball is unimportant, only the angle the target is traveling relative to the angle it is from the shooter.

here's a little demo: http://www.evilbastard.org/slight/leadtarget.html

In the demo, click OK and use arrows/ space to get shot by a little spaceship thingy.

Ignore all the mumbo jumbo around the diagram, that was from me trying to work it out without using any trig, the only important thing is A = asin((a/c)*sin(C))

Code:

---

cantarget = (targetSpeed / bulletSpeed)*Math.sin((targetDir - angleToTarget) * DEG2RAD);

if (cantarget<1 && cantarget>-1) {
        angleToShoot = 180 + angleToTarget - Math.asin(cantarget) * RAD2DEG;
}else{
//can't target
}

---

Hopefully someone posts a way to do it using vectors without trig though, that would be faster.

Thanks everyone. Shavlor, I tried your method but I couldn't get it to work. Does it matter that both the turret and the ball are moving every frame? Also does it calculate in if the ball changes directions because it hits a corner? Slight that looked pretty cool. Do you guys think my TurretAI is good enough as is? I'll probably post an actual game thread for this, but any other critiques?

I like the latest version of your game with the power ups (speed and radius should cost more in my opinion)

anyway to answer your question:
You only calculate the angle of firing once, so you just use the initial conditions in my example both of the objects are moving every frame. If the ball hits another ball the shot will miss (unless it changes the path so that it will hit at a different location...) If it hits the wall (I am assuming you just switch the x_velocity) the shot will still hit the target since the shot is going to hit the wall to and bounce back and it the target.

FYI: the game got into an infinite loop on me right as I was blasting away with lots of fast moving bullets. I do like the power ups though :)

On level 12, I had a speed of 8 I think, first goal, crashed the game on what appeared to be the frame just before a goal is scored on your opponent.

Hm... that's no good. I will check things out, maybe it has something to do with the speed. Anything I can improve on? How many levels should I have, and what should be on the final level? Graphically, what needs improvement? Is the game hard enough?

shavlor - thanks, that makes a little more senes. I will at least try and get it to work. I'm not sure if I will keep it, as it might be too intensive.