Founda'ons of Game AI

Transcription

1 Founda'ons of Game AI Level 3 Basic Movement Prof Alexiei Dingli

2 2D Movement

3 2D Movement

4 2D Movement

5 2D Movement

6 2D Movement

7 Movement Character considered as a point 3 Axis (x,y,z) Y (Up) Z X

8 Character Movement

9 2D vs. 3D 3D calcula'ons can be complex Go for 2½ D which is much simpler Similar to 3D The 3 rd dimension is constrained (because of gravity which is found in most games) Orienta'on is considered as a single value (like 2D) Thus offering 4 degrees of freedom

10 Kinema'cs Character moving in one direc'on cannot change it instantly Algorithms have to consider velocity Change velocity slightly to get smooth mo'on Sir Isaac Newton

11 Facing the right direc'on Characters must face the direc'on they re moving But this has to happen gradually

12 Basic Chase Algorithm if (predatorx > preyx) predatorx- - ; else if (predatorx < preyx) predatorx++; if (predatory > preyy) predatory- - ; else if (predatory < preyy) predatory++;

13 Basic Evade Algorithm if (preyx > predatorx) preyx++; else if (preyx < predatorx) preyx- - ; if (preyy > predatory) preyy++; else if (preyy < predatory) preyy- - ;

14 Basic Chase & Evade Algorithm

15 Straight Line Chasing Predators should move directly towards prey But if prey is moving, path needs not be a straight line Path chosen is obviously more natural

16 Bresenham Line Algorithm Determines a close approxima'on to a straight line between two given points It uses only integer addi'on, subtrac'on and bit shi`ing thus being very cheap

17 Bresenham Line Algorithm func0on line(x0, x1, y0, y1) int deltax := x1 - x0 int deltay := y1 - y0 real error := 0 real deltaerr := abs (deltay / deltax) // Assume deltax!= 0 (line is not ver'cal), int y := y0 for x from x0 to x1 plot(x,y) error := error + deltaerr if error 0.5 then y := y + 1 error := error - 1.0

18 Bresenham Line Algorithm Walkthrough deltax = 2 10 = - 8 deltay = 2 6 = - 4 deltaerr := abs (- 4 / - 8) = 0.5 for x from x0 to x1 plot(2,2) error := error if then y := y + 1 error := error - 1.0

19 Straight Line Chasing in Con'nuous Environments Steering force Thrust force Steering force

20 Straight Line Chasing in Con'nuous Environments Prey Path Predator Path

21 If the speed of the predator is set too fast? Predator Path Prey Path

22 Fleeing Since we now understand chasing, Fleeing is just doing everything the reverse Update movement in opposite direc'on Looking at rota'on should steer to opposite face

23 Seeking Vs. Arriving

24 Seek and Flee

25 Further improvements? Accelera'on (and decelera'on) for thrust force and steering force? Any way to improve intelligence of chasing movement?

26 Intercep'on NPC will always head in a straight line towards the player What happens if the target is moving?

27 Intercep'on Movement can be more intelligent, if it knows how to intercept the player somewhere along the player s trajectory How do we work this out? What informa'on do we need?

28 Intercep'on Predict some future posi'on of the player and move towards that posi'on, so that it reaches the same 'me as player

29 Intercep'on Future can be safely predicted linearly Important to consider rela've veloci0es (direc'on and magnitude) and distance instead of just their current posi'ons

30 Intercep'on There are scenarios where intercep'ng may not be possible or unrealis'c NPC moving at much slower velocity NPC ends up chasing from behind a player moving in straight line NPC gets ahead of player and moving at a faster speed

31 Nature inspired Movements

32 Nature inspired Movements

33 Nature inspired Movements

34 Nature inspired Movements

35 Swarm Intelligence Any asempt to design algorithms or distributed problem- solving devices inspired by the collec've behaviour of social insect colonies and other animal socie'es

36 Boids Created in 1987 Simulates a flock of birds Each boid is Independent Navigates on its own percep'on of the environment

37 Main Program ini'alise_posi'ons() LOOP draw_boids() move_all_boids_to_new_posi'ons() END LOOP

38 move_all_boids_to_new_posi'ons() PROCEDURE move_all_boids_to_new_posi'ons() Vector3d v1, v2, v3 Boid b FOR EACH BOID b v1 = rule1(b) v2 = rule2(b) v3 = rule3(b) END b.velocity = b.velocity + v1 + v2 + v3 b.posi'on = b.posi'on + b.velocity END PROCEDURE

39 Rules of Boids Based on simple vector opera'ons Each boid rule works independently Calculate how much the boid will get moved by each of the rules, giving different velocity vectors Add those vectors to the boid's current velocity to work out its new velocity.

40 Rules of Boids 1. Centre 2. Avoidance 3. Alignment or Copy

41 Steer to move towards the average posi'on of flockmates Centre Rule

42 Centre Rule PROCEDURE rule1(boid b J ) Vector3d pc J FOR EACH BOID b IF b!= b J THEN pc J = pc J + b.posi'on END IF END pc J = pc J / N- 1 RETURN (pc J - b J.posi'on) / 100 END PROCEDURE

43 Avoidance Rule Avoids collisions Acquire the unfilled space

44 Avoidance Rule PROCEDURE rule2(boid b J ) Vector3d c = 0; FOR EACH BOID b IF b!= b J THEN IF b.posi'on - b J.posi'on < 100 THEN c = c - (b.posi'on - b J.posi'on) END IF END IF END RETURN c END PROCEDURE

45 Alignment Rule Copy movements of neighbours by steering towards the average Match velocity

46 Alignment Rule PROCEDURE rule3(boid b J ) Vector3d pv J FOR EACH BOID b IF b!= b J THEN pv J = pv J + b.velocity END IF END pv J = pv J / N- 1 RETURN (pv J - b J.velocity) / 8 END PROCEDURE

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48 Principles of Flocking Homogeneity Every bird has the same behaviour model Locality Mo'on is only influenced by its nearest flock mate Collision avoidance Velocity matching Flock Cantering Stay close to nearby flock mates

49 Exercise Can you implement flocking in Space Invaders?

50 Addi'onal Func'ons: Wind PROCEDURE strong_wind(boid b) Vector3d wind RETURN wind END PROCEDURE

51 Addi'onal Func'ons: Move to place PROCEDURE tend_to_place(boid b) Vector3d place RETURN (place - b.posi'on) / 100 END PROCEDURE

52 Addi'onal Func'on: Dispersing the flock v1 = - rule1(b)

53 S0gmergy the mechanism of indirect coordina'on between agents

54 Ants Agents S'gmergy can be opera'onal Coordina'on by indirect interac'on is more appealing than direct communica'on S'gmergy reduces (or eliminates) communica'ons between agents

55 Ant Behavior

56 Interrupt The Flow

57 The Path Thickens!

58 The New Shortest Path

59 Adap0ng to Environment Changes

60 Adap0ng to Environment Changes

61 Algorithm Condi0on Food Pheromone Trail Loca'on Ac0on Walk random, Lay pheromone Follow pheromone, Lay pheromone Home Turn around, follow pheromone Food Pickup food, follow pheromone opposite Follow pheromone, Lay pheromone Home Deposit food, Turn around, follow pheromone

62 Travelling Salesperson Problem Ini'alize Loop /* at this level each loop is called an itera0on */ Each ant is posi'oned on a star'ng node Loop /* at this level each loop is called a step */ Each ant applies a state transi'on rule to incrementally build a solu'on and a local pheromone upda'ng rule Un0l all ants have built a complete solu'on A global pheromone upda'ng rule is applied Un0l End_condi'on M. Dorigo, L. M. Gambardella : `p://iridia.ulb.ac.be/pub/mdorigo/journals/ij.16- TEC97.US.pdf Ant Colony System: A Cooperative Learning Approach to the Traveling Salesman Problem

63 Traveling Sales Ants

64 Ques'ons?

65 Homework Implement boids in Space Invaders and present them next 'me