These slides are part of a course about interactive objects in games. The lectures cover some of the most widely used methodologies that allow smart objects and non-player characters (NPCs) to exhibit autonomy and flexible behavior through various forms of decision making, including techniques for pathfinding, reactive behavior through automata and processes, and goal-oriented action planning. More information can be found here: http://tinyurl.com/sv-intobj-2013

1. INTERACTIVE OBJECTS IN
GAMING APPLICATIONS
Basic principles and practical scenarios in Unity
June 2013Stavros Vassos Sapienza University of Rome, DIAG, Italy vassos@dis.uniroma1.it

2. Interactive objects in games
2
 Pathfinding
 Part 1: A* heuristic search on a grid
 Part 2: Examples in Unity
 Part 3: Beyond the basics
 Action-based decision making
 AI Architectures

3. Pathfinding: Beyond the basics
3
 Many neat tricks for efficient/nice pathfinding
 Alternative game-world representations
 Beyond A*
 Better heuristics

4. Pathfinding: Beyond the basics
4
 Many neat tricks for efficient/nice pathfinding
 Alternative game-world representations
 Beyond A*
 Better heuristics

5. Pathfinding: From grids to graphs
5
 A* works the same in a graph as in a grid
 Graphs nodes correspond to points in the 2D/3D space
 We can still use the same heuristics
 Manhattan, Chebyshev, Euclidean

6. Pathfinding: From grids to graphs
6
 A* works the same in a graph as in a grid
 Graphs nodes correspond to points in the 2D/3D space
 We can still use the same heuristics
 Manhattan, Chebyshev, Euclidean
But we need to
generate these
graphs in an
automated way!

7. Pathfinding: From grids to graphs
7
 Many types of graphs have been studied in video-
games as well as in robotics
 Waypoint graphs
 Circle-based waypoint graphs
 Visibility graphs
 Navigation mesh graphs
 Probabilistic road maps
 …

8. Pathfinding: From grids to graphs
8
 Many types of graphs have been studied in video-
games as well as in robotics
 Waypoint graphs
 Circle-based waypoint graphs
 Visibility graphs
 Navigation mesh graphs
 Probabilistic road maps
 …
 Nice description on Amit’s A* pages, next

9. Pathfinding: From grids to graphs
9
 Visibility graph
 Connected obstacle corners
 Navmesh graph
 Connected walkable areas

10. Pathfinding: From grids to graphs
10
 Visibility graph
 Connected obstacle corners
 Navmesh graph
 Connected walkable areas
Visibility graph:
Often contains too
many edges

11. Pathfinding: From grids to graphs
11
 Visibility graph
 Connected obstacle corners
 Navmesh graph
 Connected walkable areas
Navmesh graph:
Several ways to
map to a graph

12. Pathfinding: Navmesh graphs
12
 Navmesh graph
 Area decomposed in polygons
 One or more graph nodes per polygon
 Polygon center movement
 One node at the
center of each polygon
 Nodes connected if
they are in adjacent
polygons

13. Pathfinding: Navmesh graphs
13
 Navmesh graph
 Area decomposed in polygons
 One or more graph nodes per polygon
 Polygon edge movement
 One graph node at the
center of each edge
between adjacent
polygons
 Don’t have to go to the
center of a polygon

14. Pathfinding: Navmesh graphs
14
 Navmesh graph
 Area decomposed in polygons
 One or more graph nodes per polygon
 Polygon vertex movement
 Graph nodes and edges
at each as the polygons
 Helpful for moving
around an obstacle,
following its edges

15. Pathfinding: Navmesh graphs
15
 Navmesh graph
 Area decomposed in polygons
 One or more graph nodes per polygon
 Pick your own hybrid
combination!
 Here: graph nodes both
at nodes of polygons
and the middle
of edges of polygons

16. Pathfinding: Navmesh graphs
16
 Navmesh graph
 Widely used in video games!
 Supported natively in Unity Pro after version 4
 A lot of passionate supporters :)

17. Pathfinding: Navmesh graphs
17
 “Fixing pathfinding once and forall” by Paul Tozour
(2008) at www.ai-blog.net
 Pathfinding on waypoint graphs vs navmesh graphs
 1. Some graphs require too many waypoints

18. Pathfinding: Navmesh graphs
18
 “Fixing pathfinding once and forall” by Paul Tozour
(2008) at www.ai-blog.net
 Pathfinding on waypoint graphs vs navmesh graphs
 2. More difficult to make “smooth” realistic paths

19. Pathfinding: Navmesh graphs
19
 “Fixing pathfinding once and forall” by Paul Tozour
(2008) at www.ai-blog.net
 Pathfinding on waypoint graphs vs navmesh graphs
 3. More difficult to handle dynamic obstacle avoidance

20. Pathfinding: Navmesh graphs
20
 “Fixing pathfinding once and forall” by Paul Tozour
(2008) at www.ai-blog.net
 Pathfinding on waypoint graphs vs navmesh graphs
 Other interesting observations in the article

21. Pathfinding: Beyond the basics
21
 Many neat tricks for efficient/nice pathfinding
 Alternative game-world representations
 Beyond A*
 Better heuristics

22. Pathfinding: Beyond A*
22
 Incremental versions of A*
 Real-time/Any-time versions of A*
 Hierarchical versions of A*
 Any-angle pathfinding
 Diverse character pathfinding
 Cooperative pathfinding

23. Pathfinding: Beyond A*
23
 Incremental versions of A*
 Real-time/Any-time versions of A*
 Hierarchical versions of A*
 Any-angle pathfinding
 Diverse character pathfinding
 Cooperative pathfinding
 Nice article by Alex Nash at AiGameDev.com, next

24. Pathfinding: Beyond A*
24
 Any-angle pathfinding
 Theta*
 Combining visibility graphs and the power of A* on grids
 Simple extension based on A*
 Here: 8-connected nodes at the corners of each cell

25. Pathfinding: Beyond A*
25
 Finding better/nicer paths vs post-processing paths

26. Pathfinding: Beyond A*
26
 Finding better/nicer paths vs post-processing paths
Manhattan distance
heuristic
Chebyshev distance
heuristic

27. Pathfinding: Beyond A*
27
 Finding better/nicer paths vs post-processing paths
Manhattan distance
heuristic
Chebyshev distance
heuristic
Slower, but easier
to improve
Faster, but more
difficult to improve

28. Pathfinding: Beyond A*
28
 Any-angle pathfinding with Theta*
 Very similar to A*
 Search from the start node
 Open list of nodes to visit
 Closed list of visited nodes
 Expand a node by looking
into neighbors
 Compute and store f(s’) for each of the neighbors of
expanded node s: f(s’) = g(s’) + h(s’)

29. Pathfinding: Beyond A*
29
 Any-angle pathfinding with Theta*
 Very similar to A*
 Search from the start node
 Open list of nodes to visit
 Closed list of visited nodes
 Expand a node by looking
into neighbors
 Compute and store f(s’) for each of the neighbors of
expanded node s: f(s’) = g(s’) + h(s’)
 But, do a trick in computing g(s’) and the parent of s’!

30. Pathfinding: Beyond A*
30
 Any-angle pathfinding with Theta*
 Expand node s
 Look into neighbors of s, e.g., node s’
 Consider two cases when computing g(s’)

31. Pathfinding: Beyond A*
31
 Any-angle pathfinding with Theta*
 Expand node s
 Look into neighbors of s, e.g., node s’
 Consider two cases when computing g(s’)
Option 1: g(s’) = g(s) + c(s,s’)

32. Pathfinding: Beyond A*
32
 Any-angle pathfinding with Theta*
 Expand node s
 Look into neighbors of s, e.g., node s’
 Consider two cases when computing g(s’)
Option 1: g(s’) = g(s) + c(s,s’)
Option 2: g(s’) = g(p) + c(p,s’),
where p is the parent of s!

33. Pathfinding: Beyond A*
33
 Any-angle pathfinding with Theta*
 Expand node s
 Look into neighbors of s, e.g., node s’
 Consider two cases when computing g(s’)
Option 1: g(s’) = g(s) + c(s,s’)
Option 2: g(s’) = g(p) + c(p,s’),
where p is the parent of s!
If the Option 2 is better also
update the parent!

34. Pathfinding: Beyond A*
34
 Any-angle pathfinding with Theta*
 Essentially remove unnecessary grid-like steps, using
visibility information
 Simplifying and smoothing as you go!

35. Pathfinding: Beyond A*
35
 Any-angle pathfinding with Theta*
 Essentially remove unnecessary grid-like steps, using
visibility information
 Simplifying and smoothing as you go!

36. Pathfinding: Beyond A*
36
 Incremental versions of A*
 Real-time/Any-time versions of A*
 Hierarchical versions of A*
 Any-angle pathfinding
 Diverse character pathfinding
 Cooperative pathfinding
 Nice resources available!

37. Pathfinding: beyond A*
37
 AAAI 2008 tutorial on path planning
 Part 1: Advances in Path Planning by Sven Koenig
 http://webdocs.cs.ualberta.ca/~nathanst/aaai_tut1.pdf
 Any-angle pathfinding
 Field D*, Theta*
 Incremental versions of A*
 FSA*, AA*, LPA*, MTAA*, D*Lite
 Real-time versions of A*
 LRTA*, RTAA*

38. Pathfinding: beyond A*
38
 AAAI 2008 tutorial on path planning
 Part 2: Abstraction in Pathfinding by Nathan Sturtevant
 http://webdocs.cs.ualberta.ca/~nathanst/aaai_tut2.pdf
 http://webdocs.cs.ualberta.ca/~nathanst/pathfinding.html
 Abstraction for minimizing memory
 Used in BioWare’s Dragon Age
 Generalized Cooperative pathfinding
 CA*, WHCA*, PRA*, CPRA*

39. Pathfinding: beyond A*
39
 Beyond A*: Speeding up pathfinding through
hierarchical abstraction by Daniel Harabor
 http://harablog.files.wordpress.com/2009/06/beyonda
star.pdf
 Hierarchical pathfinding
 HPA*
 Dealing with diversity
 HAA*
 Beyond grids
 Probabilistic
Road Maps

40. Pathfinding: beyond A*
40
 AAAI 2008 tutorial on path planning
 Part 3: Map Representations & Geometric Path Planning
by Michael Buro
 http://webdocs.cs.ualberta.ca/
~nathanst/aaai_tut3.pdf
 Polygon-based
 Free space decompositions
 TA*: Triangulation A*
 TRA*: Triangulation reductions A*

41. Pathfinding: Beyond the basics
41
 Many neat tricks for efficient/nice pathfinding
 Alternative game-world representations
 Beyond A*
 Better heuristics

42. Pathfinding: Better heuristics
42
 True distance memory based heuristics (TDHs)
 Main idea based on precomputing useful information
 Store true distance between selected pairs of nodes
 Use these to calculate admissible estimates for any pair
 Different variations
 How to chose the initial pairs to pre-compute
 How to calculate heuristic values from pre-computed
pairs
 Recent IJCAI-09 paper and SOCS-10 paper

43. Pathfinding: Better heuristics
43
 Differential heuristic
 Pick a set of “canonical” nodes
 Compute true distance between every node and the
canonical nodes
 For dist(a,b) look into all canonical nodes c and take as
estimate the max value of |dist(a,c)-dist(b,c)|

44. Pathfinding: Better heuristics
44
 Differential heuristic
 Pick a set of “canonical” nodes
 Compute true distance between every node and the
canonical nodes
 For dist(a,b) look into all canonical nodes c and take as
estimate the max value of |dist(a,c)-dist(b,c)|
 Admissible!
 Intuition: think of just one canonical state c
 dist(a,b)+dist(b,c) has to be greater or equal than dist(a,c)
otherwise this would have been stored as a shorter route
 The max out of many canonical states is a better lowerbound
a b
c

45. Pathfinding: Better heuristics
45
 Canonical heuristic
 Pick a set of “canonical” nodes
 Compute true distance between the canonical nodes
 Compute true distance between every node and the m
closest canonical nodes
 For dist(a,b) look into all pairs of m canonical nodes c1
close to a and m canonical nodes c2 close to b, and
take as estimate the max value of
|dist(c1,c2) - dist(a,c1) - dist(b,c2)|

46. Pathfinding: Better heuristics
46
 Border heuristic and portal-based heuristic
 Domain is partitioned in regions
 Borders between regions
 Portals connect regions
 Store true distance
between pairs of portals
 Portal-based search
that breaks pathfinding
into sub-problems

47. Pathfinding: Compress Path Databases
47
 Another neat idea in a recent AIIDE-11 paper
 Ultra-Fast Optimal Pathfinding without Runtime Search

48. Pathfinding: Compress Path Databases
48
 Another neat idea in a recent AIIDE-11 paper
 Ultra-Fast Optimal Pathfinding without Runtime Search
 Pre-computing and store all paths!
 Compress Path Databases that bring the data to
manageable size
 Compared to A* runtime speedup reaches two orders
of magnitude
 It has been tested over maps of Baldur’s Gate

49. Pathfinding: Compress Path Databases
49
 “Path coherence”
 The shortest paths from a current node to any target in
a remote area share a common first move
 Think of going from Rome to a destination in any city in
western Europe
 Most probably all shortest paths from a specific
starting point to any of these destinations have to pass
through some fixed landmarks, e.g., a major intersection
 CPDs store this information for every node in the graph

50. Pathfinding: Compress Path Databases
50
 CPDs compress this information for every node in
the graph using boxes of destinations that can be
“directed” in the same way
1. Starting from here
2. Going to here

51. Pathfinding: Compress Path Databases
51
 CPDs compress this information for every node in
the graph using boxes of destinations that can be
“directed” in the same way
1. Starting from here
2. Going to here
3. You need to go NE!

52. Pathfinding: Compress Path Databases
52
 CPDs compress this information for every node in
the graph using boxes of destinations that can be
“directed” in the same way
 One starting node
 For all possible destinations
 Compute the next move that you
needs to be performed
 Make this map
 Store it by compressing
regions