1.
Path finding in partially
explored environments
John Stamford
De Montfort University
Centre for Computational Intelligence

2.
Introduction
• Aims and Objectives
• The Problem
• The Proposed Solution
• Occupancy Grids
• Representation of the Occupancy Grid
• Path Finding Algorithm
• Final Performance

3.
The Problem
• Path Finding in Games
• Generally know the environment
• Predefined node based systems
• Works well on tiled based gamesBourg (2004 p.128)
Node Based Example - Chin (2012) Tile Based Example – Bourg (2004)

4.
How can we emulate real
world path finding in game
AI systems?

5.
The System
• Unity 3D Games Engine
• Physics / Collision Boxes
• Simulates Sonar/LIDAR
• Builds a path based on what it
knows about the environment
• Updates the path as it learns
more about the environment

6.
The System
• Does not need to know the
environment
• Can adapt in Real Time
with dynamically changing
environments

7.
The System
• Does not need to know the
environment
• Can adapt in Real Time
with dynamically changing
environments

8.
How is ‘knowledge’ store?
Probably
Occupied
Probably
Empty
Unknown
1.00.0 0.5
Occupancy Grids
- 100 x 100
- Multidimensional Array (Doubles)
Storage
- 10,000
- 8 bit per double
- 9.8 KB (or 0.01 MB)
Representation
- Create a dynamic Mesh
- UV Texture every update

9.
Sensor Readings

10.
Updating the Grids values
Zone 1Zone 2 Zone 3
Sub Section
𝑷 𝑯 𝒔 𝒏 =
𝑷 𝒔 𝒏 𝑯 𝑷 𝑯 𝒔 𝒏−𝟏
𝑷 𝒔 𝒏 𝑯 𝑷 𝑯 𝒔 𝒏−𝟏 + 𝑷 𝒔 𝒏 ¬𝑯 𝑷 ¬𝑯 𝒔 𝒏−𝟏
Grids values are updated using a Bayesian approach as discussed by Murphy (?????)
𝐖𝐡𝐞𝐫𝐞 𝑷 𝑯 𝒔 𝒏 𝐫𝐞𝐩𝐫𝐞𝐬𝐞𝐧𝐭𝐬 𝐭𝐡𝐞 𝐥𝐚𝐭𝐞𝐬𝐭 𝐎𝐜𝐜𝐮𝐩𝐚𝐧𝐜𝐲 𝐆𝐫𝐢𝐝 𝐯𝐚𝐥𝐮𝐥𝐞𝐬 𝐚𝐧𝐝
𝑷 𝒔 𝒏 𝑯 𝐫𝐞𝐩𝐫𝐞𝐬𝐞𝐧𝐭𝐬 𝐭𝐡𝐞 𝐜𝐮𝐫𝐫𝐞𝐧𝐭 𝐒𝐨𝐧𝐚𝐫 𝐕𝐚𝐥𝐮𝐞.
𝑷 𝑶𝒄𝒄𝒖𝒑𝒊𝒆𝒅 =
𝑹 − 𝒓
𝑹
+
𝜷 − 𝜶
𝜷
𝟐
× 𝑴𝒂𝒙𝑶𝒄𝒄𝒖𝒑𝒂𝒏𝒄𝒚
𝑷 𝑬𝒎𝒑𝒕𝒚 = 𝟏 − 𝑷(𝑬𝒎𝒑𝒕𝒚)
𝑷 𝑬𝒎𝒑𝒕𝒚 =
𝑹 − 𝒓
𝑹
+
𝜷 − 𝜶
𝜷
𝟐
𝑷 𝑶𝒄𝒄𝒖𝒑𝒊𝒆𝒅 = 𝟏 − 𝑷(𝑬𝒎𝒑𝒕𝒚)
𝑷 𝑶𝒄𝒄𝒖𝒑𝒊𝒆𝒅 = 𝟎. 𝟓
𝑷 𝑬𝒎𝒑𝒕𝒚 = 𝟏 − 𝑷(𝑬𝒎𝒑𝒕𝒚)
Zone1Zone2Zone3

11.
Video 1 – Occupancy Grid
https://www.youtube.com/watch?v=pwfPg2diKOY

12.
Path Finding Methods
• Alternative methods
• A* Algorithm
• Dijlstra’s Algorithm
• Anytime D*
• Final Choice – A*
• Bourg (2004 p.126) highlights that A*is the most widely used and fastest
method
• Millington (2009 p.275) discuss performance issues with path finding and
states that the A* can minimise this by the ability for it to be stopped and
started
𝒇 = 𝒈 + 𝒉

13.
G Cost
• Movement Cost
14 10 14
10 10
14 10 14
10
10 10
10

14.
H Cost
5 4 3 2 1 2
4 3 2 1 0 1
5 4 3 2 1 2
6 5 4 3 2 3
7 6 5 4 3 4
8 7 6 5 4 5
Heuristic
Manhattan
dx + dy
Pre-calculated
Experimental
dx + dy + On
Where On is a value based
on the squares Occupancy
Grid value

15.
Path Finding Process
14
4 + 10
13
13 + 10
12
3 + 10
14
4 + 10
13
13 + 10
12
3+ 10
11
1 + 10
16
5 + 10
14
4 + 10
13
13 + 10
12
3 + 10
18
4 + 10
15
5 + 10
14
4 + 10
18
5 + 10
15
5 +10
17
7 + 10

16.
Path Finding - Obstacle

17.
Path Finding - Obstacle

18.
Video 2 – Route Planning
The robot knows...
• The target position
• Its own position
Everything else is automated
https://www.youtube.com/watch?v=ZoWj5-bWGV0

19.
Video 3 – More complex
The robot knows...
• The target position
• Its own position
Everything else is automated
https://www.youtube.com/watch?v=3JRBRpuOxcE

20.
Summary
• Overall Performance is good
• Uses sonar based models
• Could be omitted to reduce complexity
• Unique combination of Occupancy Grids
and the A* Algorithm
• Fine tuning of tolerances and resolution
can be performed for different scenarios
• Low computational costs, however could be
better optimised

21.
References
Bourg, DM. (2004) AI for Game Developers. 1st Edition. O'Reilly Media.
Chin, R. (2012) “Beginning iOS 3D Unreal Games Development” 1st
Edition. Apress.
Millington, I. (2009) Artificial Intelligence for Games. 2 Edition. CRC
Press.
Murphy, R. (2000) “An Introduction to AI Robotics (Intelligent Robotics
and Autonomous Agents)” 1st Edition. A Bradford Book.