CS 387/680: GAME AI MOVEMENT

Transcription

1 CS 387/680: GAME AI MOVEMENT 4/5/2016 Instructor: Santiago Ontañón Class website:

2 Reminders Check Blackboard site for the course regularly Also:

3 Outline Movement Basics Aiming Jumping Basic Steering Behaviors Steering Behaviors on Vehicles Composite Steering Behaviors Project 1 (Chapter 3 of Millington and Funge s book)

4 Outline Movement Basics Aiming Jumping Basic Steering Behaviors Steering Behaviors on Vehicles Composite Steering Behaviors Project 1

5 Movement in 2D

6 Movement in 2D Controlling a character using AI involves at least 2 main processes:? - Decision Making - Control How would you implement an AI that can control Mario to reach any desired point in the map?

7 Movement in 2D Controlling a character using AI involves at least 2 main processes:? - Decision Making - Control How would you implement an AI that can control Mario to reach any desired point in the map? One solution is A*: Strengths? Weaknesses?

8 Game AI Architecture AI Strategy Decision Making World Interface (perception) Movement

9 Game AI Architecture AI Strategy Decision Making Recall, we said that strategy is typically only used in games where the AI controls groups of units World Interface (perception) Movement

10 Game AI Architecture AI Strategy Decision Making This World one decides the high-level Interface actions to (perception) perform Movement

11 Game AI Architecture AI Strategy Decision Making World Interface (perception) Movement This one executes those actions

12 Movement in 2D Decision Making in this case would determine that we can reach the goal with 3 jumps Decision Making Movement

13 Movement in 2D Decision Making Movement Movement is in charge of the low level control, determining when exactly to jump.

14 Movement in 2D Decision Making Or course Mario didn t have this kind of advanced AI!!! This is just an example. Movement You can think of it as: - Decision Making analyzes the situation and sets the goals. - Movement controls the character to achieve the desired goals.

15 Movement in Racing Games

16 Movement in Racing Games? Decision Making Movement

17 Movement in Racing Games In car racing games, Decision Making is typically hard coded. The game designers create a set of waypoints in the track (or in the track pieces), and cars go to them in order. Decision Making Movement

18 Movement in Racing Games Movement is in charge of driving the car to each of the waypoints, avoiding opponents, braking, accelerating, turning, etc. Decision Making Movement

19 Decision Making and Movement In the previous 2 examples (Mario and car racing): Using A* directly would work but: CPU intensive Too low level: might only be able to look a very few pixels ahead One solution could be to have a high-level representation of the map (navigation graph): Each platform in Mario would be a node in the graph Each road piece in the car racing game would be a node in the graph Connections exist between node A and B if we can directly move the character from A to B without passing through any other node. We can now use A* in this high-level map and an additional movement algorithm underneath. Today we will focus on this later part.

20 Basics of 2D Movement Game programming and movement AI involves a lot of (but simple) geometry, trigonometry and physics Even if most games look 3D, most AIs actually only perform 2D calculations (on the floor )

21 Coordinate Convention y In the rest of this class we will use the following convention: z x Y is up Horizontal games (e.g. Mario) use X and Y Top-view 2D games use X and Z

22 Outline Movement Basics Aiming Jumping Basic Steering Behaviors Steering Behaviors on Vehicles Composite Steering Behaviors Project 1

23 Aiming Two different problems: Prediction: determining where a projectile will land: Determining if a flying bullet is going to hit a character or not Determining where to run in a sports game to catch the ball Etc. Aiming: throw (shoot) a projectile to hit the desired spot

24 Projectile Prediction How would you build an AI that knows which direction to move when a projectile is incoming??

25 Projectile Prediction High-school Physics J Initial velocity p t = p 0 + us m t + gt2 2 p 0 gt u

26 Projectile Prediction High-school Physics J p t = p 0 + us m t + gt2 2 p 0 gt u Newton s equation tells us how it moves over time. But, where will it land?

27 Landing Spot Prediction Estimate the time at which it will reach a certain altitude (the ground level: p yi ) s t p t = p 0 + us m t + gt2 2 Considering only the y dimension t i = u y s m ± u 2 y s2 m 2g y(p y0 p yt ) g y

28 Landing Spot Prediction Now substituting time in the original equation we get the landing spot: p i = [ px0 + u x s m t i g xt 2 i p yi p z0 + u z s m t i g zt 2 i ]

29 Landing Spot Prediction Now substituting time in the original equation we get the landing spot: p i = [ px0 + u x s m t i g xt 2 i p yi p z0 + u z s m t i g zt 2 i ] Rocket blast radius

30 Landing Spot Prediction Now substituting time in the original equation we get the landing spot: p i = [ px0 + u x s m t i g xti 2 p yi p z0 + u z s m t i g zt 2 ] If the distance i we have to travel to get out of the blast radius is too long for our moving speed, then there is no point (although the AI should try, to make it look realistic) Rocket blast radius

31 Prediction with Complex Physics What if there is Drag? (water, wind) Magnetic effects? Rotation and lift effects? (e.g. baseball) Movement equations get complex: Impossible or very difficult to solve directly Solution: Simulation

32 Prediction with Complex Physics Offer the physics engine simulation capability to the AI The AI can (through the Physics engine API), internally simulate the effect of different actions For example: Simulate the trajectory of a projectile until it lands This can tell the AI the landing spot without equation solving Simple and can handle arbitrarily complex physics, but CPU consuming (needs to run multiple simulations)

33 Aiming How can the AI aim to hit a target? How would you build an AI that knows which direction to fire a parabolic projectile in order to hit a target? p t = p 0 + us m t + gt2 2?

34 Aiming Given a target position E zzl p t = p 0 + us m t + gt2 2 E x = S x + u x s m t i g xt 2 i E y = S y + u y s m t i g yt 2 i E z = S z + u z s m t i g zt 2 i, = + +

35 Aiming Given a target position E zzl p t = p 0 + us m t + gt2 2 E x = S x + u x s m t i g xt 2 i E y = S y + u y s m t i g yt 2 i 4 unknowns and only 3 equations! We need an additional constraint E z = S z + u z s m t i g zt 2 i, = + +

36 Aiming Given a target position E zzl p t = p 0 + us m t + gt2 2 Let s assume we cannot control the strength of the rocket launcher, thus, we are only interested in the direction E x = S x + u x s m t i g xt 2 i E y = S y + u y s m t i g yt 2 i E z = S z + u z s m t i g zt 2 i, 1 = u 2 x + u2 y + u2 z.

37 Aiming Resolving the previous equation system, we obtain: g 2 ti 4 4 ( g. + sm 2 ( ) ) t 2 i = 0 where: = E S. And thus: g. + sm 2 t i =+2 ± ( g. + sm 2 )2 g 2 2, 2 g 2

38 Aiming Substituting time, we obtain (recall that launching speed): u = 2 gti 2. 2s m t i s m is the u

39 What does that mean code-wise? ( ) Ok, so we know that if we want to determine which direction to shoot the projectile to hit the player we have to do this: 1) 2) = E S. g. + sm 2 t i =+2 ± ( g. + sm 2 )2 g 2 2, 2 g 2 3) u = 2 gti 2. 2s m t i But how would the source code look like?

40 ( ) What does that mean code-wise? Vector g = new Vector3(0,-9.8,0); Vector S = getgunposition(); Vector E = gettargetposition(); Vector Delta = E S; Double s_m = PROJECTILE_SPEED; Ok, so we know that if we want to determine which direction to shoot the projectile to g. + s t i =+2hit the m 2 player ± we have to do this: // Solve for t : double g_delta = dotproduct(d,delta); double s_m2 = s_m * s_m; double tmp1 = g_delta + s_m; double tmp2 = g.norm()*g.norm() * Delta.norm()*Delta.norm(); 1) double tmp3 = sqrt(tmp1*tmp1 tmp2); double tmp4_a = (g_delta + s_m2 + tmp3)/(2 * g.norm()*g.norm()); double tmp4_b = (g_delta + s_m2 + tmp3)/(2 * g.norm()*g.norm()); double t = 0; if (tmp4_a>0) t = 2*sqrt(tmp4_a); 2) if (tmp4_b>0) { double t_tmp= 2*sqrt(tmp_b); if (t_tmp< t) t = t_tmp; = E S. // Find direction u and fire! if (t > 0) 3) { Vector u = (2 * Delta g * t * t)/(2 * s_m * t); shootprojectile(u); } u = 2 gt 2 i 2s m t i. ( g. + sm 2 )2 g 2 2, 2 g 2 But how would the source code look like?

41 Aiming with Complex Physics Equations quickly become unsolvable for physics that are more complex than the simple Newtonian equations described here For complex physics, there is only one solution: Iterative targeting Use Newtonian physics (what we just described) to have an initial guess Use the Physics engine to try different trajectories, adjusting each time until the target is hit

42 Example of Predictive and Non-predictive Aiming

43 Physics in Games You don t need to remember the equations themselves But you must remember which problems can be solved, and remember that there was an equation for it (so that you can quickly go look it up) It is very important that you understand the principles behind the equations, so that can code solutions to these problems, and modify the equations according to the needs of your game

44 Physics in Games You don t need to remember the equations themselves But you must remember which problems can be solved, and remember that there was an equation for it (so that you can quickly go look it up) It is very important that you understand the principles behind the equations, so that can code solutions to these problems, and modify the equations according to the needs of your game 1) If physics is simple: use equations In summary, 2 approaches for AI that involves physics: 2) If physics is complex: use simulations

45 Outline Movement Basics Aiming Jumping Basic Steering Behaviors Steering Behaviors on Vehicles Composite Steering Behaviors Project 1

46 Jumping Why it is important: v=lw9g-8gl5o0&feature=player_embedded (from second 45) Enemies are typically very bad at jumping in games: Jumping is a hard problem! Specially in complex 3D geometries

47 Jumping: Jump Points Jumping is hard. In Game AI, when something is hard, the solution is always hardcoding! Jump points provide an easy way to hardcoding jumping A Jump point: Location in the map specially marked by the game designer Location from where it makes sense to attempt a jump It is marked with constraints in the minimum / maximum speed required for the jump

48 Jump Points Minimum jump velocity Jump point Defined at map creation time Each jump point defined as: Area Direction of jump Minimum velocity Jump point If a character is in the area and its velocity along the direction of jump is higher than the minimum, the jump will be successful

49 Jump Points Minimum jump velocity Jump point Defined at map creation time Each jump point defined as: Area Direction of jump Minimum velocity Jump point If a character is in the area and its velocity along the direction of jump is higher than the minimum, the jump Do you see any problems with this? will be successful

50 Jump Points Jump point Jump point Jump point Easy to implement Need to encode more information if jump is hard (maximum and minimum velocities in different directions) Bug-prone and hard to debug

51 Jumping: Jump Points/Landing Pads Jump points are hard to debug in complex maps (each of them has to be defined by hand) Better approach for complex maps: landing pads Idea: Annotate the map with jump point and landing pads (they might be different objects or not) Only allow jumps from the marked jump points but: Let the AI do the calculations of the minimum/maximum speeds required for each jump

52 Jumping: Jump Points/Landing Pads Defined at map creation time Jump Point/ Landing Pad Jump Point/ Landing Pad Each jump point/landing pad only defined by an area The rest of parameters will be figured out by the AI Given a map with lots of jump points/landing pads, the AI analyzes it and for the pairs that are close enough, figures out the minimum/maximum speeds, and other restrictions for successful jumping

53 Speed of Jump E zzl S. at Jump Point/ Landing Pad Jump Point/ Landing Pad Given a starting and ending position, and a given initial jump speed (the vertical speed at the beginning of the jump) E x = S x + v x t, E y = S y + v y t g yt 2, E z = S z + v z t.

54 Speed of Jump E zzl S. at Jump Point/ Landing Pad Jump Point/ Landing Pad Given a starting and ending position, and a given initial jump speed (the vertical speed at the beginning of the jump) E x = S x + v x t, E y = S y + v y t g yt 2, E z = S z + v z t.

55 Speed of Jump We first compute the time it will take to complete the jump (based on the y positions of start and end): v y ± 2g(E y S y ) + v 2 y t = g And then substitute to obtain the speed in x and z: v x = E x S x t v z = E z S z t

56 Jumping: Jump Points/Landing Pads E zzl (vx,vy) S. at Jump Point/ Landing Pad Jump Point/ Landing Pad Once computed, the speeds are added to the jump points/landing pads During game play, if the AI wants to jump from one to the other, it will know exactly at which speed it needs to move to perform the jump This approach is much more robust, since we don t need to debug each jump point separately

57 Jumping: Beyond Jump Points What happens in games where users can create maps? Do they have to define the jump pads? Have you ever seen a game where players create maps AND the enemies do jumps AND enemies don t fall down cliffs? In principle, a map could be preprocessed and jumping points/landing pads automatically detected: Time consuming Game AI: if there is an easy way to make the character look intelligent, do it! No need to have real AI (in this case, no need to let the AI really figure out it can or not jump)