User:Positive/Optimal Velocity

To not clutter up the Talk:Robocode/Game Physics page:

I believe this is the correct getClosestReachableVelocityToVelocity function (feel free to comment):

double getClosestReachableVelocityToVelocity(double currentVelocity,double wantedVelocity)
{
 // this function assumes wantedVelocity<=Rules.MAXVELOCITY
 // with this function you can basically assume setAhead(Infinity) or setAhead(-Infinity)
 // was called, and you determine the next velocity based on the max velocity
 // set by the robot. For example, if the current velocity is 0 and the max velocity
 // set was 4.0, it would return 1.0. If the current velocity was 8.0, it would return 6.0.
 if(wantedVelocity<0)
  return -getClosestReachableVelocityToVelocity(-currentVelocity,-wantedVelocity);
 if(currentVelocity<0)
 {
  double nextVelocity;
  // we are travelling the wrong way, decelerate
  nextVelocity = currentVelocity + Rules.DECELERATION;
  if(nextVelocity>Rules.ACCELERATION)
   // make sure we can't jump from -0.1 to 1.9 or something
   nextVelocity = Rules.ACCELERATION;
  if(nextVelocity>wantedVelocity)
   // if the wanted velocity is for example 0.5, limit the velocity to that.
   return wantedVelocity;
  else
   // else return the highest possible
   return nextVelocity;
 }
 else
 {
  if(currentVelocity>wantedVelocity)
  {
   // both velocities are positive, but we need to decelerate
   double nextVelocity = currentVelocity - Rules.DECELERATION;
   if(nextVelocity<wantedVelocity)
    // if we can decelerate more than what's wanted, return what's wanted
    return wantedVelocity;
   else
    // else return the closest to it
    return nextVelocity;
  }
  else
  {
   // the wantedVelocity is higher than current
   double nextVelocity = currentVelocity + Rules.ACCELERATION;
   if(nextVelocity>wantedVelocity)
    // if we can accelerate more than what's wanted, return what's wanted
    return wantedVelocity;
   else
    // else return the closest to it
    return nextVelocity;
  }
 }
} 

getMaxVelocity function by Voidious:

    double getMaxVelocity(double distance)
    {
        if(distance>=20)  // temporary fix, works for maxVelocity==8.0 && maxDecel==2.0
          return Rules.MAX_VELOCITY;
        long decelTime = decelTime(distance);
        double decelDist = (decelTime / 2.0) * (decelTime-1) // sum of 0..(decelTime-1)
            * Rules.DECELERATION;
            
        return ((decelTime - 1) * Rules.DECELERATION) +
            ((distance - decelDist) / decelTime);
    }

    long decelTime(double distance) {
        long x = 1;
        do {
            // (square(x) + x) / 2) = 1, 3, 6, 10, 15...
            if (distance <= ((square(x) + x) / 2) * Rules.DECELERATION) {
                return x;
            }
            x++;
        } while (true);
    }

    long square(long i) {
        return i * i;
    }

The getNewVelocity function:

    double getNewVelocity(double velocity, double distance) {
    	 if(distance<0)
    	  return -getNewVelocity(-velocity,-distance);
    	  double highestVelocity = getMaxVelocity(distance); // highest velocity without overshooting
    	  double wantedVelocity = Math.min(highestVelocity,currentCommands.getMaxVelocity());
    	      // the actually wanted velocity by the robot is the highest possible,
    	      // limited by what the robot set by the setMaxVelocity command
    	  return getClosestReachableVelocityToVelocity(velocity, wantedVelocity);
    	      // return whatever is closest to that velocity
    }

Simulator:

    public void simulate()
    {
    	double currentVelocity = 8.0;
    	double distanceRemain = -2.0;
    	while(distanceRemain!=0.0 || currentVelocity!=0.0)
    	{
    		out.println("velocity = "+currentVelocity+"; distance="+distanceRemain);
    		currentVelocity = getNewVelocity(currentVelocity,distanceRemain);
    		distanceRemain -=currentVelocity;
    	}
    }

Results

StartVelocity = 0.0; StartDistance = 6.0;

velocity = 0.0; distance=6.0
velocity = 1.0; distance=5.0
velocity = 2.0; distance=3.0
velocity = 2.5; distance=0.5
velocity = 0.5; distance=0.0

StartVelocity = 0.0; StartDistance = 10;

velocity = 0.0; distance=10.0
velocity = 1.0; distance=9.0
velocity = 2.0; distance=7.0
velocity = 3.0; distance=4.0
velocity = 3.0; distance=1.0
velocity = 1.0; distance=0.0

StartVelocity = -1.9; StartDistance = 10;

velocity = -1.9; distance=10.0
velocity = 0.10000000000000009; distance=9.9
velocity = 1.1; distance=8.8
velocity = 2.1; distance=6.700000000000001
velocity = 3.1; distance=3.600000000000001
velocity = 2.8000000000000007; distance=0.8000000000000003
velocity = 0.8000000000000007; distance=-4.440892098500626E-16;
velocity = -4.440892098500626E-16; distance=0.0

StartVelocity = 8.0; StartDistance = -2.0;

velocity = 8.0; distance=-2.0
velocity = 6.0; distance=-8.0
velocity = 4.0; distance=-12.0
velocity = 2.0; distance=-14.0
velocity = -0.0; distance=-14.0
velocity = -1.0; distance=-13.0
velocity = -2.0; distance=-11.0
velocity = -3.0; distance=-8.0
velocity = -4.0; distance=-4.0
velocity = -3.0; distance=-1.0
velocity = -1.0; distance=0.0

StartVelocity = 5.0; StartDistance = 40.0;

velocity = 5.0; distance=40.0
velocity = 6.0; distance=34.0
velocity = 7.0; distance=27.0
velocity = 8.0; distance=19.0
velocity = 7.75; distance=11.25
velocity = 5.75; distance=5.5
velocity = 3.75; distance=1.75
velocity = 1.75; distance=0.0

Suggested updateMovement code

Original updateMovement code:

    private void updateMovement() {
        double distance = currentCommands.getDistanceRemaining();

        if (Double.isNaN(distance)) {
            distance = 0;
        }

        velocity = getNewVelocity(velocity, distance);

        double dx = velocity * sin(bodyHeading);
        double dy = velocity * cos(bodyHeading);

        x += dx;
        y += dy;

        if (dx != 0 || dy != 0) {
            updateBoundingBox();
        }

        if (distance != 0) {
            currentCommands.setDistanceRemaining(distance - velocity);
        }
    }

Now I'm thinking, if the distance remaining == 0.0, and the velocity is set from 6.0 to 4.0, shouldnt the distance remaining become -4.0? Also, the updateBoundingBox is called whenever velocity!=0, because the condition dx==0 && dy==0 is only when the velocity==0, so that can be easier to check. I suggest:

    private void updateMovement() {
        double distance = currentCommands.getDistanceRemaining();

        if (Double.isNaN(distance)) {
            distance = 0;
        }

        velocity = getNewVelocity(velocity, distance);

	if(velocity!=0)
	{
		x += velocity * sin(bodyHeading);
		y += velocity * cos(bodyHeading);
		updateBoundingBox();
	}

	currentCommands.setDistanceRemaining(distance - velocity);
    }

When I run your suggested version against the unit test for 1.6.1.4, I get an error. After some studying and experiments, I found out that the updateMovement() method used in 1.7.1.3 (the "original" on this page) and your suggested version are both buggy. The problem is that the remaining distance is incorrect. The bugfree version compared to 1.6.1.4 is this version:

	private void updateMovement() {
		double distance = currentCommands.getDistanceRemaining();

		if (Double.isNaN(distance)) {
			distance = 0;
		}

		velocity = getNewVelocity(velocity, distance);

		if (velocity == 0) {
			currentCommands.setDistanceRemaining(0);
		} else {
			currentCommands.setDistanceRemaining(distance - velocity);

			x += velocity * sin(bodyHeading);
			y += velocity * cos(bodyHeading);
			updateBoundingBox();
		}
	}

The problem was, that is the robot has a velocity of e.g. 8, and we call setAhead(0), the remaining distance would be set to 0. But this is not correct, as the robot needs to brake first, and will move at least 6 + 4 + 2 = 12 pixels more, meaining that it should end with a remaining distance of -12. My new version about take this into account and works in the 1.6.1.4 code. Unfortunately this also means that our Alpha versions are buggy, as I used this improved version for all of them. That might explain the "big" differences in score! I am affraid that we need to do new alphas and retest them all with this issue in mind. Argh! What to do? Should we make new alphas for Hijack 1 and 2 etc. and retest? We could do this + we gain benefits of all bugfixes that have been made since 1.7.1.3. --Fnl 22:04, 7 August 2009 (UTC)

Thankyou for taking the time to investigate this, could you please expand on why you added:

		if (velocity == 0) {
			currentCommands.setDistanceRemaining(0);
		} 

Say you are at -2 velocity, and set distance to travel=100. Wouldn't that code cause distance to travel to be incorrectly set to 0? --Positive 23:06, 7 August 2009 (UTC)

Fnl, what I think you are trying to do is prevent bots from reversing back to their original position if setAhead(0) is called? You shouldn't do that by checking if velocity == 0 but rather by checking if distance == 0 because velocity has nothing to do with what the bot passed as an arguments, distance is. So rather have the updateMovement() method as:

    private void updateMovement() {
	double distance = currentCommands.getDistanceRemaining();

        if (Double.isNaN(distance)) {
		distance = 0;
        }

        velocity = getNewVelocity(velocity, distance);

	if(velocity!=0)
	{
		x += velocity * sin(bodyHeading);
		y += velocity * cos(bodyHeading);
		updateBoundingBox();
	}
        if(distance != 0)
		currentCommands.setDistanceRemaining(distance - velocity);
    }

--Skilgannon 23:21, 7 August 2009 (UTC)