How Do Rocket League AI Bots Calculate Mid-Air Interceptions?

Chasing a ball's current position in a physics game produces 'dog-curve' paths that constantly overshoot or trail the target. This paper reframes the aerial hit as a predictive interception problem — finding the exact future time at which the car and ball positions coincide — and solves it with Newtonian kinematics and the bisection method.

• Models the ball as a Newtonian projectile under constant gravity, and the car's reachable radius as a simple max-speed × time bound.
• Defines the intercept objective function f(t) = ||ball position(t) − car position|| − (max speed · t), whose root is the exact intercept time.
• Coarse-searches for a bracket where f(t) crosses zero, then refines it with a 100-iteration bisection search for floating-point precision.
• Verifies the result numerically: the Python implementation proves an absolute positioning error of 0.000000000000 units at the computed intercept time.