Path Planning for Coherent Groups using Clearance

1
Path Planning for Coherent Groups using Clearance

• Authored by
• Arno Kamphuis Mark Overmars
• Presented by Tim Toxopeus

2
Introduction

• Path planning for groups of units
• Need to stop thinking individually.
• Stay together, rather than break apart.
• Currently games compute path for 1 unit.
• Stay together by local computation.
• Unnatural behaviour, group breaks apart.

3
Table of contents

• Previous work
• Problem setting and Global solution
• Phase 1 (The backbone path)
• Phase 2 (Group movement)
• Corridors
• Dispersion (Lateral and Longitudinal)
• Social Forces
• Results and Conclusions

4
Previous work

• Flocking
• A adaptations
• Social potential fields
• Deformable rectangle
• PRM ( Flocking)
• Helbings Crowd Model

5
Problem setting and Global Solution

• Units must move as a group from same start
  position to same goal position.
• Avoid collisions with environment and each other.
• Two phase approach
• Compute backbone path.
• Plan group movement.

6
Phase 1 (The backbone path)

• Create a backbone path that leads from start to
  goal.
• Many algorithms exist for this, does not matter
  much which you use.
• Important Path must have sufficient clearance to
  allow for flexible movement.
• All units use it, so they get similar paths
  backbone path homotopic.

7
Phase 2 (Group movement)

• Follows backbone path
• Requirements of group movement
• Group not too wide. (Lateral dispersion)
• Group not too long. (Longitudal dispersion)

8
Corridors

• Is created by the union of circles based on
  minimum of maximum clearance circles and a
  constant.
• Why the constant?
• To prevent the path from becoming too wide.
  (Lateral dispersion)

9
Dispersion (Lateral)

• Lateral Dispersion is the maximum distance of any
  unit to its closest point on the backbone path.
• Prevents groups from becoming very wide.
• Limited by previously chosen constant. (Unit
  would exit corridor if it would go further away.)
• This means lateral dispersion must always be less
  than or equal to c.

10
Dispersion (Longitudinal)

• Longitudinal Dispersion is the distance between
  the minimum and maximum group attraction points.
• Compute two attraction points, one for the front
  end of the group and one for the back end of the
  group.

11
Dispersion (Longitudinal)

• Minimum group attraction point is the minimum of
  maximum attraction points.
• The attraction point furthest along the path for
  the unit that is the furthest in the back.
• Maximum group attraction point is the maximum of
  the minimum attraction points, but never less
  than the minimum group attraction point.
• The attraction point furthest back along the path
  for the unit that is the furthest in the front.
• Because its never less than the minimum group
  attraction point, guarantees units have
  attraction point between them.

12
Dispersion (Longitudinal)

• To prevent long single file formations a limit is
  necessary.
• Group regions
• Size is the union of circles between minimum
  group attraction point and maximum group
  attraction point.
• By limiting this we can limit the length of the
  group!

13
Social Forces

• Generates the path inside the corridor.
• CMM uses forces to navigate
• Collision avoidance force
• Only if you can see the other unit!
• Corridor force and driving force
• Both handled by the minimum and maximum group
  attraction points.

14
Results and Conclusions

• Performance relies on group size.
• Quadratic!
• Because of Collision Avoidance Force.
• Only two parameters to adjust group coherence.
• Corridor width constant.
• Group region size.
• High performance.
• 2.4 processor load with large group of 100
  units.
• In games groups are only this big in the Total
  War series. ?

15
Future research

• Allow for small obstacles inside the path.
• Right now a small obstacle like a pillar would
  cause for a different homotopic path. This
  solution would thus never split a group evenly
  across both sides.
• Joining and splitting of groups.
• What about formations?

16
Thoughts and questions

• Some thoughts
• Situation can exist where group gets stuck due to
  Group Region size constraints.
• Small obstacles such as a pillar causes weird
  group movement behaviour.