Route Planning

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Route Planning Simulation

• Ming C. Lin
• Department of Computer Science
• University of North Carolina
• http//www.cs.unc.edu/lin
• http//www.cs.unc.edu/geom
• lin_at_cs.unc.edu

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State of Art (I)

• Wide variety of technology, e.g. JSAF, OneSAF,
  DARWAR, etc.
• Existing systems are very powerful and offer
• Many capabilities
• Flexibility to incorporate new technologies
• e.g. GPU-based LoS computations

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State of Art (II)

• Game physics engines provides pseudo physical
  behavior that varies
• Online multi-player games becomes increasingly
  popular

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What Changes in Simulations

• Yesterday tanks, vehicles, vessels, planes on
  open terrain and airspace
• Today teams of soldiers on foot, civilians,
  insurgency, cluttered urban scenes, dynamic
  terrains civil infrastructures

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New Needs

• Add more realistic and higher fidelity
  simulations, especially for urban
  simulations/scenarios.
• Require modeling/simulation of civilians many
  independent agents or heterogeneous crowds
• Physics-based computations weather effects,
  deformable robots, explosions, entity simulation,
  spatialized sound effects, shadows, environmental
  effects, etc.

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Gaming Technologies for Training?

• Significant advances in rendering, modeling
  simulation
• Physics not quite there yet
• But, different focuses end goals
• Visually believable, not accurate or reflective
  of real situations
• Lower fidelity than what may be required for
  effective, reliable training

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Some Issues

• Performance vs. Fidelity
• Validation and Verification
• Assessment Evaluation
• Correct training
• Performance enhancement
• Cost saving

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Speed vs. Fidelity/Accuracy

• Multiresolution framework
• Perception-based
• Data driven Physics New Math

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Real-time Path Planning for Virtual Agents in
Dynamic Environments
Sud et al. IEEE VR 2007
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Overview
At each time step
Environment (Static Obstacles, Dynamic
Obstacles, and Agents)
Scripted Behaviors
Multi-agent Navigation Graph
Update
Local Dynamics Collision Detection
Forces to move along path
Path to goal
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Multi-Agent Navigation Graph

• Unified data structure for path planning of
  multiple agents
• Computed using 1st and 2nd order Voronoi diagrams

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Multi-Agent Navigation Graph

• Unified data structure for path planning of
  multiple agents
• Computed using 1st and 2nd order Voronoi diagrams
• Advantage
• Provides pairwise proximity information for all
  agents simultaneously
• Compute collision free paths of all agents from
  single MaNG

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1st Order Voronoi Diagram (VD1)
Agents
Static Obstacle
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1st Order Voronoi Diagram (VD1)
Agents
Static Obstacle
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2nd Order Voronoi Diagram (VD2)
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VD1 and VD2
VD1
VD2
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Voronoi Graphs
VG1
VG2
U
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2nd nearest nbr graph
2nd order Voronoi graph
1st order Voronoi graph
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MaNG

• Subset of the 2nd nearest neighbor graph

Static Obstacle
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Multi-Agent Navigation Graph

• Unified data structure for path planning of
  multiple agents
• Computed using 1st and 2nd order Voronoi diagrams
• Advantage Reduce omputation of many 1st order
  Voronoi graphs to computation of a single MaNG

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MaNG Planner

• For each agent
• Connect agent (source) to VG2 edges

Agent
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MaNG Planner

• For each agent
• Connect agent (source) to VG2 edges
• Connect destination to VG1 edges

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MaNG Planner

• For each agent
• Connect agent (source) to VG2 edges
• Connect destination to VG1 edges
• Assign edge weights

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3
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1
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3
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MaNG Planner

• For each agent
• Connect agent (source) to VG2 edges
• Connect destination to VG1 edges
• Assign edge weights
• Graph search

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3
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MaNG Planner

• For each time step
• Compute MaNG once
• Compute paths for all agents from same MaNG

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MaNG Planner

• 2nd order Voronoi diagram gives proximity to
  closest obstacle
• Sud et al.06
• Compute force fields at each step
• Repulsive forces from closest obstacle

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MaNG Computation

• Computing exact Voronoi diagram difficult
• Non-linear boundaries
• High complexity

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MaNG Computation

• Computing exact Voronoi diagram difficult
• Compute Discrete Voronoi Diagram (DVD)
• Compute closest site at finite set of points

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MaNG Computation

• Computing exact Voronoi diagram difficult
• Compute Discrete Voronoi Diagram (DVD)
• Interactive computation using GPU Sud et al. 06
• Culling techniques for fast 2D computation (paper)

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Undersampling

• Fixed grid resolution on GPU

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Undersampling

• Disconnected Voronoi regions
• Complex graph
• Solution Local tests to reduce graph complexity
  without changing connectivity (paper)

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Demos

• Fruit stealing
• Crowds in urban environment

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Demos

• Fruit stealing
• Dynamic goal update
• Swarming behavior observed
• Crowds in urban environment

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Demo Stealing Fruit
100 Agent simulation at 9 fps
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Demos

• Fruit stealing
• Crowds in small urban environment
• Dynamic obstacles

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Demos Crowd
100 Agent simulation at 10 fps
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Motivation

• Traditional approaches
• Randomized, only considers agent geometry
• Not realistic motion
• Better motion paths
• Requires smoother paths, incorporating physics

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Motivation

• Traditional approaches
• Randomized, only considers agent geometry
• Not realistic motion
• Better motion paths
• Requires smoother paths, incorporating physics

Traditional Straight-line links
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Motivation

• Traditional approaches
• Randomized, only considers agent geometry
• Not realistic motion
• Better motion paths
• Requires smoother paths, incorporating physics

Better Smoother path
Goal
Start
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Motivation Performance

• Motion planning is exponential in agent degrees
  of freedom
• Traditional Intractable for very high number of
  joints, many agents, or incorporating dynamics

300 rotational joints
2,500 rotational joints
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Applications

• Autonomous vehicles
• Search and rescue
• Medical simulations
• Virtual prototyping
• Cable planning
• Multi-agent planning
• Character animation
• Molecular modeling
• Many more!

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Physically-based Motion Planning (PMP)

• Novel motion planning approach
• Goal Generate realistic paths in a practical
  amount of time for very complex situations

Planned trajectory for a deforming sphere
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Physically-based Motion Planning

• Approach Bias the planning search by artificial
  workspace forces and agent motion equations
• Obstacle avoidance
• Guiding paths
• Energy functions
• Agent behavior
• Sensing information

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Planning Architecture
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Applied to Deformable Agents

• Motion equations
• Particle motion in a mass-spring lattice
• Artificial forces
• Volume preservation
• Obstacle avoidance
• Collision resolution
• Goal seeking

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Algorithm Overview

• Roadmap Generation
• Path Estimation
• Path Query
• Advance simulation while satisfy constraints
• min E(x) subject to ?V(x) ?
• Non-penetration
• Volume Preservation

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GPU Acceleration

• GPUs can be utilized to
• accelerate collision detection
• high-level path generation
• link queries
• These optimizations allow each simulation step to
  be computed much faster, thus allowing more
  complex planning scenarios to be solved in a
  reasonable amount of time.

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Benchmark Scenarios
Deforming cylinder in a tunnel agent must deform
to exit.
Deforming sphere in a cup agent deforms to
quickly get to and enter the cup
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Applied to Deformable Agents
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Highly Articulated Chains

• Motion equations
• Articulated body motion equation
• Artificial forces
• Joint configuration
• Path following
• Obstacle avoidance
• Collision resolution

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Challenges

• Chain planning and simulation is expensive
• Each joint adds exponentially
• Exploit temporal coherence to reduce adaptively
  reduce problem dimensionality
• Goal Fewer active joints

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Reducing dimensionality

• Based on adaptive forward dynamics
• Adaptively determine which sub-bodies behave most
  like rigid bodies and rigidify them

At each step, 25 most important joints are
simulated
All joints simulated
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System Demonstrations
Chain with 300 joints must navigate a sequence of
walls
Chain with 600 joints must travel through a tunnel
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Cable Routing on Bridge
A snake robot of 500 links and 500 DOFs with
only 70 DOFs used in this bridge scene
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Search and Rescue

• A snake robot with 2,000 joints searches for a
  cavity in debris and then exits

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Pipe inspection

• A snake robot with 2,000 joints inspects pipes
  for a leak by coiling around it

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Video Demonstration
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Catheterization Procedures

• In medical and surgical procedures, flexible
  catheters are often inserted in human vessels to
• Obtain diagnostic information (blood pressure or
  flow)
• Enhance imaging with the injection of contrast
  agents
• Provide a mechanism to deliver treatment to a
  specific area

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Liver Chemoembolization

• Catheter is used to inject chemotherapy drugs
  directly to the blood vessel supplying a liver
  tumor
• Catheter is inserted into the femoral artery
  (near the groin) and advanced into the selected
  liver artery

• A fluoroscopic display and the resistance felt
  from the catheter are used to determine how it
  should be advanced, withdrawn, or rotated
• Chemotherapy drugs followed by embolizing agents
  are injected through the catheter into the liver
  tumor

tumor
catheter
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Motion Planning Application

• Application to plan the path of a flexible
  catheter, inserted at the femoral artery, to a
  specific liver artery supplying a tumor

• Environment 3D models of the liver and blood
  vessels obtained from the 4D NCAT phantom, a
  realistic computer model of the human body
• Catheter was modeled as a snake robot with 2500
  joints with only 10 of joints simulated to
  achieve 10x speed up.

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Benchmark Liver (Courtesy of JHU)
A birds eye view of the entire live arteries
A catheter enters the left artery.
A closer view of liver and the internal arteries
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Applied to multiple agents

• Motion equation
• Each agent as constrained particle motion
• Artificial forces
• Roadmap following
• Obstacle/other agent avoidance
• For human agents Social forces

10 red agents among moving spheres
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Reactive Deformation Roadmaps (RDR)

• PMP not restricted to agents
• Reactive roadmaps
• Adjust to moving obstacles, changing environments
• Particle motion
• Physically-based limits on elasticity

Link removed
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Reactive Deformation Roadmap

• Blend together ideas from decoupled planning,
  fast path and roadmap modification, and
  replanning into a single unified framework
• Useful for modeling of heterogeneous crowds as
  well

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PMP Conclusions

• General framework practical planning of complex
  agents
• Incorporates kinematic/geometic, dynamic, and
  mechanical constraints
• Tighter coupling with agent allows adjustable
  behavior