LOCAL NAVIGATION 2 FORCE-BASED BOOKKEEPING Social force models The - - PowerPoint PPT Presentation

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LOCAL NAVIGATION 2 FORCE-BASED BOOKKEEPING Social force models The - - PowerPoint PPT Presentation

May 29, 2023 31 likes •432 views

LOCAL NAVIGATION 2 FORCE-BASED BOOKKEEPING Social force models The forces are first-class abstractions Agents are considered to be mass particles Other models use forces as bookkeeping It is merely a way to combine multiple

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SLIDE 1

LOCAL NAVIGATION 2

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SLIDE 2

FORCE-BASED BOOKKEEPING

2

  • Social force models
  • The forces are first-class abstractions
  • Agents are considered to be mass particles
  • Other models use forces as bookkeeping
  • It is merely a way to combine multiple influences
  • n an agent

University of North Carolina at Chapel Hill

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SLIDE 3

OPENSTEER

3

  • Based on Boids (Reynold’s 1987)
  • Flocking model based on three rules
  • Separation
  • Alignment
  • Cohesion
  • http://www.youtube.com/watch?v=GUkjC-69vaw
  • http://www.red3d.com/cwr/boids/

University of North Carolina at Chapel Hill

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SLIDE 4

OPENSTEER

4

  • Based on Boids (Reynold’s 1987)
  • The rules are typically implemented as forces
  • Arbitrary weights define behavior
  • Linear extrapolation detects possible collisions
  • Normal forces applied to change heading
  • Poor at collision avoidance
  • http://www.youtube.com/watch?v=dKW-psERFGA
  • http://www.youtube.com/watch?v=3CRjPwb5qoI

University of North Carolina at Chapel Hill

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SLIDE 5

HiDAC - Pelechano et al. 2007

5

  • Incorporates high-order behaviors into the model
  • Applies various forces
  • Attractor force
  • Wall force, Obstacle force
  • Agent force
  • Inertial force
  • Collision force
  • Fallen-agent avoidance force
  • http://www.youtube.com/watch?v=KsbChtHmwfA

University of North Carolina at Chapel Hill

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SLIDE 6

HIDAC

6

  • Application of forces is based on rules
  • Examples
  • When in collision, only collision force is

considered

  • When “stopping” or “waiting” repulsive forces are

ignored

University of North Carolina at Chapel Hill

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SLIDE 7

HIDAC

7

  • Force formulation
  • “Nearby” defined by a “rectangle of influence”
  • Obstacle force
  • Wall force

University of North Carolina at Chapel Hill

From paper

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SLIDE 8

HIDAC

8

  • Apply extra rules
  • In low-speed, high-dense scenarios jittering
  • ccurs
  • The authors apply a “stopping rule”
  • Prevents responses when the forces are too

strong against desired direction of travel

  • Stopping lasts for a random period of time
  • Waiting for queues (also disables responses)

University of North Carolina at Chapel Hill

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SLIDE 9

AUTONOMOUS PEDESTRIANS

9

  • Shao & Terzopolous, 2005
  • Agent behavior based on six rules – evaluated

sequentially

  • Static obstacle avoidance
  • Static obstacle avoidance with turn
  • Maintain separation
  • Avoid oncoming pedestrians
  • Avoid “dangerously” close pedestrians
  • Validate against obstacles
  • http://www.youtube.com/watch?v=cqG7ADSvQ5o

University of North Carolina at Chapel Hill

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SLIDE 10

AUTONOMOUS PEDESTRIANS

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  • Static obstacle avoidance
  • Turns preferred velocity based on nearby
  • bstacles
  • If a great deal of turning is required, the

magnitude of the preferred velocity is reduced

University of North Carolina at Chapel Hill

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SLIDE 11

AUTONOMOUS PEDESTRIANS

11

  • Static obstacle avoidance with turn
  • Turning requires more than a single step (gait

step, not time step)

  • Curves of increasing curvature are tested in both

directions

University of North Carolina at Chapel Hill

From paper

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SLIDE 12

AUTONOMOUS PEDESTRIANS

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  • Maintain separation
  • Only considers “temporary crowd”
  • Nearby agents moving with similar velocity
  • 𝑔

𝑗𝑘 = 𝑠𝑗 |𝑞 𝑗𝑘|−𝑒𝑛𝑗𝑜 𝑞

𝑗𝑘

  • Got some mathematical problems

University of North Carolina at Chapel Hill

From paper

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SLIDE 13

AUTONOMOUS PEDESTRIANS

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  • Avoid oncoming pedestrians
  • Classifies potential collisions with non-temporary

crowd members

  • Cross collisions
  • Head-on collisions
  • Considers most “imminent”
  • Turns from head-on
  • Changes speed for

cross collisions

University of North Carolina at Chapel Hill

From paper

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SLIDE 14

AUTONOMOUS PEDESTRIANS

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  • Avoid “dangerously” close pedestrians
  • Safety catch for when the previous two rules fail
  • If another pedestrian is in the safety zone:
  • Stop as quickly as possible
  • Turn away
  • Start again when it appears clear

University of North Carolina at Chapel Hill

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SLIDE 15

AUTONOMOUS PEDESTRIANS

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  • Validate against obstacles
  • Inter-agent rules can lead to obstacle collisions
  • The current velocity is validated against obstacles
  • Throws out agent-responses
  • Applies voodoo to know when slowing should
  • ccur
  • (Not described in the paper)

University of North Carolina at Chapel Hill

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SLIDE 16

VELOCITY-SPACE MODELS

16

  • Performs optimization in geometric space using
  • ptimization techniques
  • Here at UNC we primarily use models of this type

University of North Carolina at Chapel Hill

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SLIDE 17

VELOCITY-SPACE MODELS

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  • Paris et al., 2007

University of North Carolina at Chapel Hill

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SLIDE 18

VELOCITY-SPACE MODELS

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  • Paris et al., 2007

University of North Carolina at Chapel Hill

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SLIDE 19

VELOCITY-SPACE MODELS

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  • Paris et al., 2007
  • Response is selected from the region with the

lowest cost

  • Cost is minimal where:
  • Section speed is close to desired speed
  • Section orientation is close to desired direction
  • Acceleration is limited (related to previous

rules)

  • Sections based on near time are more

important

University of North Carolina at Chapel Hill

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SLIDE 20
  • A set of velocities which will lead to an inevitable

collision.

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VELOCITY OBSTACLES

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SLIDE 21
  • Navigate by selecting “best” velocity outside of the
  • bstacle.

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VELOCITY OBSTACLES

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SLIDE 22
  • Velocity obstacle for moving objects is translated by

that object’s velocity.

  • This is the original VO formulation [Fiorini & Schiller

1998].

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VELOCITY OBSTACLES

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SLIDE 23
  • Predicting responsive obstacles

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VELOCITY OBSTACLES

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SLIDE 24

VELOCITY OBSTACLES

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  • Reciprocal Velocity Obstacles (RVO) - van den Berg,

et al., 2008

  • Assume:
  • Each agent is responsive
  • Each agent will take an equal share to avoid

collision

University of North Carolina at Chapel Hill

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SLIDE 25
  • RVO

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VELOCITY OBSTACLES

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SLIDE 26

VELOCITY OBSTACLES

26

  • RVO
  • It still assumes that it accurately predicts the other

agent’s future velocity

  • If the other agent has OTHER constraints that

prevent it from taking the expected velocity, the assumption is broken

  • That brings us to Optimal Reciprocal Collision

Avoidance (ORCA) – van den Berg, et al., 2009

University of North Carolina at Chapel Hill

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SLIDE 27

OPTIMAL RECIPROCAL COLLISION AVOIDANCE (ORCA)

  • Identify a collision
  • Linear extrapolation (constant velocity)

vi vj

27

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SLIDE 28
  • Identify a collision w.r.t. relative velocity and position
  • Linear interpolation (constant velocity)

vi vj

OPTIMAL RECIPROCAL COLLISION AVOIDANCE (ORCA)

vij

28

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SLIDE 29
  • Find alternate, collision-free relative velocity
  • Which one?

vi vj

OPTIMAL RECIPROCAL COLLISION AVOIDANCE (ORCA)

vij

? ? ? ? ? ?

29

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SLIDE 30
  • ORCA finds the relative velocity that requires the

smallest change to the current relative velocity

  • u is the change vector

vi vj

OPTIMAL RECIPROCAL COLLISION AVOIDANCE (ORCA)

vij u

30

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SLIDE 31
  • Share the displacement equally between the two

agents

vi vj

OPTIMAL RECIPROCAL COLLISION AVOIDANCE (ORCA)

vij u

31

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SLIDE 32
  • The change in velocity is enforced with a half-plane

constraint

  • All feasible pairs will change relative velocity by at

least u

Feasible for blue Feasible for yellow

OPTIMAL RECIPROCAL COLLISION AVOIDANCE (ORCA)

vj vi

32

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SLIDE 33
  • Multiple neighbors form multiple, simultaneous

constraints

  • Nearest feasible velocity to v0

OPTIMAL RECIPROCAL COLLISION AVOIDANCE (ORCA)

vi Feasible with respect to all neighbors vi

0 vi

vi vi vi vi vi

33

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SLIDE 34

OPTIMAL RECIPROCAL COLLISION AVOIDANCE (ORCA)

  • [van den Berg et al. 2009]

34

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SLIDE 35

VISION-BASED

35

  • Ondrej et al., 2010
  • Based on planning in “vision” space
  • Similar to optical flow
  • Detecting how quickly things change size and

heading

  • http://www.youtube.com/watch?feature=player_e

mbedded&v=586qhaDwr24

University of North Carolina at Chapel Hill

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SLIDE 36

AGGREGATE CROWDS

36

  • Narain, et al., 2009
  • Solves for velocity based on density constraints
  • Creates velocity and density fields
  • Projects preferred velocity onto the field and

solves the flow such that maximum density is never exceeded

  • http://www.youtube.com/watch?v=pqBSNAOsMDc
  • In principle, still similar to previous pedestrian

models

University of North Carolina at Chapel Hill

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SLIDE 37

CONTINUUM CROWD

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  • Treuille et al., 2006
  • Does not use the global-local decomposition
  • Solves globally at each time step w.r.t. dynamic

entities

  • http://www.youtube.com/watch?v=lGOvYyJ6r1c

University of North Carolina at Chapel Hill

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SLIDE 38

CONTINUUM CROWD

38

  • Treuille et al., 2006
  • Computes a “unit-cost” field
  • Minimizes
  • Path length
  • Travel time
  • Discomfort
  • A true potential field model

University of North Carolina at Chapel Hill

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SLIDE 39

CONTINUUM CROWD

39

  • Treuille et al., 2006
  • Assumes limited number of unique groups
  • Groups share
  • Goal
  • Preferred speed
  • Discomfort fields

University of North Carolina at Chapel Hill

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SLIDE 40

QUESTIONS?

40 University of North Carolina at Chapel Hill