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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL Crowd Simulations Sashi Kumar Penta Robotics – Class Presentation
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Crowd Simulations

Dec 30, 2015

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Crowd Simulations. Sashi Kumar Penta Robotics – Class Presentation. Overview. Motivation Background Behavior Planning for Character Animation , Kuffner et.al, Symposium on Computer Animation 2005 Continuum Crowds , Adrein et.al, SIGGRAPH 2006 Summary. Motivation. - PowerPoint PPT Presentation
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Page 1: Crowd Simulations

The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL

Crowd Simulations

Sashi Kumar Penta

Robotics – Class Presentation

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2The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL

Overview

• Motivation• Background• Behavior Planning for Character

Animation, Kuffner et.al, Symposium on Computer Animation 2005

• Continuum Crowds, Adrein et.al, SIGGRAPH 2006

• Summary

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Motivation

• Crowds are every where!! • Motivating video Clip• Movies

♦ The Chronicles of Nornia – The witch, The Lion and The ward robe

♦ The Lord of the ring♦ I, Robot, etc

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Applications

• Entertainment industry (animation production, computer games)

• Training of police & military (demonstrations, riots handling)

• Architecture (planning of buildings, towns, visualization)

• Safety science (evacuation of buildings, ships, airplanes)

• Sociology (crowd behavior)• Transportation research for urban

planning

Courtesy: Illknur

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Background

•Motion-graph approaches♦ [Gleicher et. al TOG 2003]♦ [Kuffner et. al SCA 2005]

•Static potential fields♦ [Kirchner 2002]

•Continuous density field♦ [Hughes 2003]♦ [Adrien et. al SIGGRAPH 2006]

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The UNIVERSITY of NORTH CAROLINA at CHAPEL HILL

Behavior Planning for Character Animation,

Kuffner et.al, SCA 2005

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Abstract

• Automatically generate realistic motions for animated characters

• Motion clips - FSM - movements of a virtual character

• Global search of the FSM – a sequence of behaviors for the character

From small amount of data

Scales to large motion DBs

Flexi

ble fr

amew

ork

Sta

tic/D

ynam

ic e

nvir

onm

ents

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Behavior Finite-State Machine

• Behavior FSM defines movement capabilities of the character

• Each state consists of a collection of motion clips that represent a high-level behavior

• Each directed edge represents a possible transition b/w two behaviors

• There can be multiple motion clips with in a state.

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Environment Abstraction

• Environment as a 2D height-field gridmap

• Gridmap also encodes ♦ Obstacles that the character should avoid♦ Free space where character can navigate♦ Information about special obstacles such as an

archway

• Height value is used so that we can represent terrains with slopes or hills.

• Virtual character is bounded by a cylinder with radius r & position is the center of the cylinder

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Data structures

• A tree with nodes that record explored states in the FSM♦ Each node in the tree stores the motion

clip, position, orientation, time and cost

• Priority queue of FSM states ordered by cost, which represent potential nodes to be expanding during the next search iteration

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A* - search

• Total cost = ( cost of the path up to that node) +

(expected cost to reach the goal)• Using A*-search, The planner

iteratively expands the lowest cost node in the queue until either the a solution is found or the queue is empty.

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ALGORITHM 1: BEHAVIOR PLANNER

Function F returns the set of actions A that the character is allowed to take from sbest

Function T takes the input state sin and an action a as parameters and returns the output state sout

Function G determines if we should expand Snext as a child of sbest in the tree.

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Motion Generation & Blending

• Search algorithm returns a sequence of behaviors

• Sequence is converted into an actual motion for the character

• Blending: to smooth out any slight discontinuities where the transitions b/w behaviors occur.

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Advantages

• Scalability• Memory Usage• Intuitive Structure• Generality• Optimality• Anytime

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Limitations

• This technique requires an existence of a behavior FSM

• This technique expects the data has been appropriately segmented & categorized

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Results

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What needs to be taken care …♦ Individual human motion♦ Environmental constraints♦ Intelligent path planning

Large group of people exhibit behavior of

enormous complexity and subtlety. ♦ Dynamic interactions between people

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Previous methods

• Agent based methods♦ Funge et al. [1999]♦ Shao and Terzopoulos [2005]♦ Massive Software [2006]

• Graph based techniques♦ Bayazit et al. [2002]♦ Kuffner et al. [2005]

• Static potential fields♦ Goldeinstein et al. [2001]

• Continuous density field♦ Hughes [2002]♦ Adrien et. al [2006]

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Agent based methods

• Pros♦ Operate with each individual making

independent decisions♦ Capture each person’s unique situation:

visibility, proximity of other pedestrians, etc♦ Different simulation parameter may be

defined for each crowd member

• Cons♦ Computationally expensive♦ Difficult to develop behavioral rules that

consistently produce realistic motion

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• Real-time crowd model based on continuum dynamics

• Global navigation with moving obstacles such as other people

• Motion of large crowds without need for explicit collision avoidance

Key points

Dynamic potential field

Interactive rates

Smooth flow

Emergent phenomena

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The Governing Equations

• Hypothesis 1:♦ Each person is trying to reach a geographic

goal G R2

• Hypothesis 2:♦ People move at the maximum speed possible.♦ Maximum speed field f

♦ Where

• Hypothesis 3:♦ There exist a discomfort field g so that,

people would prefer to be a point x rather than x’ if

g(x’) > g(x)

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Tying together – Hypothesis 4• People choose paths so as to

minimize a linear combination of ♦ The length of the path♦ The amount of time to the destination♦ The discomfort felt, per unit time, along the

path

• Hypothesis 4:♦ A path P that minimizes

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Optimal path Computation

• Suppose, Cost function every where equal to the cost of the optimal path to the goal.

• Optimal strategy: to move the opposite the gradient of this function.

• Potential function ( ) : by following set of all optimal paths outwards from the goal. ♦ In the goal = 0♦ Every where,

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Speed field

• Speed is a density-dependent variable • Crowd density field

• Low density (< min): depends on slope

• High density (> max): depends vel of crowd

• Medium density (> min ; < max)

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Models of the future

• Predictive discomfort♦ Future path planning through a

constantly updated static view of environment.

• Expected periodic changes♦ When the field deterministically

changes over time

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Algorithm

•For each time step:♦ Convert the crowd to a density field.♦ For each group:

•Construct the unit cost field C.•Construct the potential and it’s

gradient•Update the people’s locations

♦ Enforce the minimum distance between people

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Implementation details

• Physical fields as 2D arrays of floating point numbers.♦ Scalar fields : defined at the center of each grid cell

• Its true for average velocity ( ), stored as pair of floats

♦ Anisotropic fields : those depend on both position and

direction• Stored with four floats per cell corresponding to = {0o, 90o, 180o, 270o} , i.e. EAST, NORTH, WEST and SOUTH faces of each cell

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• “Splat” the crowd particles onto a density grid, to compute speed field which are dependent on density

• Requirements of density function1. Must be continuous w.r.t location of the people

♦ to avoid sharp discontinuities in density and subsequently to the speed

2. Each person should contribute no less than to their own grid cell, but no more than to any neighboring grid cell♦ to ensure each individual is not affected by its own

contribution to the density field

Density Conversion

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Density Conversion ctd..

• For each person, we find the closest cell center whose coordinates are both less than that of the person

• Relative coordinates of that person w.r.t the cell center

• Person’s density then added to the grid as

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• Compute speed field f

• Then calculate cost field C using

• f and C are anisotropic ♦ We would evaluate the speed

and discomfort at the cell into

which the person would be moving if they choose that direction

Unit cost field

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Dynamic Potential Field

• Constructing is the dynamic potential is the most complex and time consuming step of the algorithm

• Implicit eikonal equation – Solution♦ Assign the potential field inside the goal to 0; include these

cells in KNOWN cells; all other to UNKNOWN ;♦ UNKNOWN cells adjacent to KNOWN cells are included in the

CANDIDATE cells and we approximate at these locations by solving a finite difference approximation to

♦ The CANDIDATE cell with the lowest potential is then included in the KNOWN cells and its neighbors are introduced into the CANDIDATE set by re-approximating the potentials at these cells

♦ This process is repeated, propagating the KNOWN cells outwards from the goal until all cells are defined.

♦ HEAP DATA STRUCTURE : O(N log N)

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• First find the less costly adjacent grid cell along the both x- and y-axis

• Solve the equation for

• Once we have computed , we take its difference with the neighboring grid cells in the upwind direction gives us • Renormalize the gradient, multiply by the

speed in the appropriate directions to compute the velocity field at that point

Finite difference approximation

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Crowd Advection

• Once velocity field is knownEach person’s position is displaced by

their velocity, which is effectively computing an Euler integration to

• Min displacement Enforcement♦ All pairs within a threshold distance,

symmetrically pushed apart so that min distances are preserved

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General Algorithm OverviewGrids

Potential Fields New positionsDensity

Goal

Boundary

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Results

Video

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Contributions

• Integrates both global navigation & local collision avoidance into one framework

• Velocity dependent term: which induces lane formation

• Distance based term: which stabilizes the flow

• Complexity depend on the number of grid cells

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Limitations

• Complex heterogeneous motion• Individual path planning• Depends on the number of groups• Depends on the resolution• Approximations

♦ Dynamic potential field♦ Minimum distance enforcement to remove

visual unpleasant artifacts

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What remains challenging • Individual behavior planning in

crowds• Inertia – walking & running

♦ 4D eikonal equation (Position and Velocity)

• Potential function across nonuniform grids for speed up♦ Sparse data points in areas with few people♦ Finer discretizations in areas of congestion

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Summary

• Behavior planning approach to automatically generate realistic motions for animated characters

• Crowd simulation framework based on a continuum perspective

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Questions?

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Thank you!!