Artificial Intelligence ( for games ) Chapter 3: Movement

1. ArtificialIntelligence (forgames)Chapter 3: Movement Universität zu Köln Historisch Kulturwissenschaftliche Informationsverarbeitung WS 12/13 Übung: Visuelle Programmierung I – Simulation und 3D Programmierung Prof. Dr. Manfred Thaller Referent: Jan Moritz Kohl

2. Die Basics • Kinematisch • Input: position (character + target) + orientation • output: direction + velocity • Dynamisch „Steeringbehaviors“ • input:velocity + position, • outpout:forces + accelerations • flocking

4. Mathematik

5. Independent Facing # update position and orientation # and the velocity and rotation position += velocity * time velocity += steering.linear * time orientation += rotation * time rotation += steering.angular * time

6. Kräfte und Antrieb • Kraft führt zu Änderung der kinetischen Energie • Beschleunigung abhängig von Trägheit • steering algorithmen haben Beschleunigung als output -> post-processing: actuation (Antrieb)

7. Kinematische Bewegung (Seek) voidKinematicSeek::getSteering(SteeringOutput* output) const { // First work out thedirection output->linear = *target; output->linear -= character->position; // Ifthereisnodirection, do nothing if(output->linear.squareMagnitude() > 0) { output->linear.normalise(); output->linear *= maxSpeed; } }

8. Kinematische Bewegung (Flee) voidKinematicSeek::getSteering(SteeringOutput* output) const { // First work out the direction output->linear = character->position; output->linear -= *target; // If there is no direction, do nothing if (output->linear.squareMagnitude() > 0) { output->linear.normalise(); output->linear *= maxSpeed; } }

9. Kinematische Bewegung (Arriving) voidKinematicArrive::getSteering(SteeringOutput* output) const { // First work out thedirection output->linear = *target; output->linear -= character->position; // Ifthereisnodirection, do nothing if(output->linear.squareMagnitude() < radius*radius) { output->linear.clear(); } else { // We'dliketoarrive in timeToTargetseconds output->linear *= ((real)1.0 / timeToTarget); // Ifthatistoo fast, thenclipthespeed if (output->linear.squareMagnitude() > maxSpeed*maxSpeed) { output->linear.normalise(); output->linear *= maxSpeed; } } }

10. Kinematische Bewegung (Wandering) • Bewegung erfolgt sukzessiv (schlendern) • randomBinomial() funktion liefert Wert zwischen -1 und 1 Werte um 0 sind wahrscheinlicher

11. Steering Behaviors • Speed ist jetzt acceleration • Problem: Orbit • Lösung: target Radius slow Radius

12. Steering (Align) radian(-,)

13. DelegatedBehaviors: PursueandEvade Face Lookingwhereyou‘regoing Wander Path Following Separation Collision

14. Pursue and Evade ifspeed <= distance /maxPrediction: prediction:maxPrediction

15. Face / Looking where you‘re going • Delegation der Alignmethode • Character schaut nicht zwingend in die Richtung des target #Check for a zerodirection, andmakenochangeif so ifcharacter.velocity.length() == 0: return #Otherwisesetthetargetbased on thevelocity target.orientation = atan2(-character.velocity.x, character.velocity.z) #2. Delegatetoalign returnAlign.getSteering()

16. Wander • Zielloses umherwandern • delegated face behavior

17. Path Following • „Chase the rabbit“

19. Limit the getParam algorithm: kohärenz

20. Separation • Linear separation: strength = maxAcceleration * (threshold – distance) / threshold • Inverse squarelaw(Abstandsgesetz): strenght = min(k / (distance * distance), maxAcceleration) „repulsionsteering“

21. Collision Avoidance

25. Obstacle and Wall Avoidance

28. The Corner Trap

29. Source Code und Demo unter: www.ai4g.com Millington, Ian/Funge, John: Artificial Intelligence. For Games.Burlington, Massachusetts 2009.