Velocity adjustment calculation

Question

I'm developing an Android 2D "space fighters" game, and I am now developing the AI.

The AI (enemy) is moving at a certain velocity V1 (V1x, V1y), and it wants to adjust this velocity so that it matches the intercept vector at max speed.

I know that the intercept velocity is achievable as:

V_intercept = (player.x - enemy.x, player.y - enemy.y)
normalize(V_intercept)
V_intercept.x *= MAX_SPEED
V_intercept.y *= MAX_SPEED

What I'm looking for is a way to find a single velocity v_correction, which, when applied for t time, will put the enemy in the correct velocity towards the player.

I suppose I'm looking for 2 functions:

getCorrectionVelocity(current_velocity, desired_velocity, acceleration) // not sure if acceleration is even needed here

getTimeToReachVelocity(current_velocity, desired_velocity, acceleration)

Note:

Mass & steering time are not relevant. Imagine all mass = 1, and time to turn to a certain direction = 0

Also, I will need these methods in other parts of the AI (for instance, to calculate how much time it will take for the enemy to match its velocity with the player's velocity), and so I need them to be generic, meaning be able to calculate the correction & time to any velocity I give them.

Thanks in advance!

Answer 1

I do it differently. Forget about computing exact correction impulse per time instead just control steer

So compute dot_product(AI_velocity,delta) and according to sign of it steer left or right (direction depends on your coordinate system). So for intercepting apply continuously main thrust and also some minor steer thrust.

But you have to implement Newtonian D'Alembert physics something like this.

If you want to apply frictions also look here