Path-Finding with Motion Constraints Amongst Obstacles in Real Time Strategies

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Path-Finding with Motion Constraints Amongst
Obstacles in Real Time Strategies

• By Jeremiah J. Shepherd
• Committee
• Jijun Tang
• Roger Dougal
• Jason OKane

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Introduction

• Most video games have some form of path-finding
• Methods for finding paths are primitive
• Motion Constraints not easily implemented
• Agent movement is not realistic
• Some games fabricate path realism

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Introduction

• Real Time Strategies (RTS) are notorious for
  simple path-finding
• In an RTS, as in other wargames, the
  participants position and maneuver units (agents)
  and structures under their control to secure
  areas of the map and/or destroy their opponents'
  assets. (Gervk)

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Introduction

• Path-finding in RTSs generally involves these
  steps
• A unit and destination for the unit is selected
• An obstacle free path is the calculated by using
  an algorithm like A
• The path is followed by a move-rotate-move
  method

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Introduction

• These paths can be created in this fashion
  because of the structure of the environment
• The environment is generally a grid
• The size an number of cells are known
• Obstacles exist in the environment and are known
• Each grid cell has an occupancy flag

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Introduction
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Old Game Path-finding Example

• Command and Conquer

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New game path-finding example

• Halo Wars

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Introduction

• A problem emerges when adding motion constraints
  to these paths
• Paths found may not reach the destination
• Paths are no longer guaranteed to be obstacle free

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Introduction
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Introduction

• The method I propose uses an algorithm found in
  motion planning and path-finding for robotics
• Combines plans and paths found with the algorithm
  with carefully crafted data structures
• Paths with motion constraints could be calculated
  in real-time

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Related Work

• Rapidly Exploring Random Trees (RRT) is an
  algorithm that can find a path and a motion plan
  that adheres to motion constraints

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Related Work

• Goal biased RRTs work by
• Choose the point nearest to the goal state in the
  tree and attempt to connect the two
• If it succeeds in connecting then a path and a
  plan is found
• Else choose a random point in the configuration
  space
• Find the point in the tree nearest to the random
  point
• Choose actions that will incrementally move
  toward the new point, creating new points in the
  tree
• Repeat until goal is reached or it is determined
  that the goal is unreachable

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Related Work
SUCCESS
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Related Work

• Why not use RRTs?
• They are inconsistent in regards to speed
• In previous tests, the range of time it took to
  find a path and motion plan was from six seconds
  to two minutes

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Related Work

• Previous Attempts (Trail of Tears)
• Tube Guided RRT
• Preprocessing with Motion Planning Matrix and
  Environment Matrix (MPMEM)

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Related Work

• Tube Guided RRT
• Use a tube to constrict sampling
• The less samples the faster it will find a path
• Algorithm
• Draw a Probablistic Road Map (PRM)
• Find the shortest path on the PRM
• Construct a tube with the width the size of the
  turning radius around the path
• Run the RRT, only sampling points in the tube

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Related Work
SUCCESS
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Related Work

• Tube Guided RRT Problems
• It ran on par with a regular RRT
• Some cases it took much longer than a regular RRT
• More inconsistent than a regular RRT

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Related Work

• MPMEM
• The broad idea is to piece together small paths
  and motion plans to create a large motion plan
  and path
• There are two stages to this algorithm
• Offline Stage
• Online Stage

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Related Work

• The Smallest Turning Radius Square (STRS) is
  important to both stages
• Contains a full turn to the left and right

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Related Work

• Offline Stage
• Create the environment matrix (EM)
• Create an initial motion plan matrix (MPM)
• Add references in the environment matrix (EM) and
  the calculate the final (MPM)
• Online Stage
• Traverse the EM from the starting state to the
  goal state
• Follow the motion plans stored in the MPM as
  referenced by the information in the EM cells

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Related Work
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Related Work

• Create an initial motion plan matrix (MPM)
• 3D data structure based on the x, y and q in the
  configuration space
• Contains potential motion plans that can be used
  when the STRS is obstacle free
• A special environment is used for this step
• All paths are contained inside of the STRS

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Related Work
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Related Work
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The Algorithm Offline Stage
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Related Work

• Create the EM continued
• For all the points in the EM and for all the
  points in the STRS at that EM find and store a
  motion plan and path
• If a motion plan is collision free in the MPM
  then a reference to that plan is stored in the EM
• Else calculate a new motion plan store that in
  the MPM and store a reference to that in the EM

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Related Work
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Related Work
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Related Work

• From the starting point calculate a path using A
• The points that lay on the outer edge of the STRS
  are given higher priority
• Traverse the EM using the path
• Create a full motion plan with the references in
  the EM to the MPM

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Related Work
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Related Work

• Problems with MPMEM
• Uses too much memory
• Paths can look very unnatural

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New Algorithm

• Principles
• Similar idea of piecing together smaller paths
• FORGET RRTs!
• Use Dubins curves to find paths

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New Algorithm

• Dubins Car
• It finds the shortest path for a nonholonomic
  model in an obstacle free environment
• The car that only moves forward
• The car can only steer all the way right, all the
  way left, or not at all
• Paths and plans are very small

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New Algorithm

• Dubins Cars 6 motion primitives

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New Algorithm

• Algorithm Overview
• Create an album of motion-plans and paths (AMAP)
• Create a collision set (CS) containing colliding
  edges

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New Algorithm

• AMAP Construction
• Create paths for all cells to the right of the
  center STRS using Dubins Curves
• We can do this because the left side will mirror
  the right
• Cuts the memory consumption in half

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Related Work
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Related Work
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New Algorithm

• CS Construction
• For every cell in the environment check to see if
  an edge collides
• If so add it to the CS

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New Algorithm

• Online Portion
• Use a slightly modified version of A to traverse
  AMAP
• Includes a short circuit

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New Algorithm
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New Algorithm
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Results
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Results
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Conclusion

• It is consistently gooder

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Questions?