1. Route Planning & Simulation
Ming C. Lin
Department of Computer Science
University of North Carolina

2. 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

3. State of Art (II)
Game physics engines provides pseudo physical behavior that varies
Online multi-player games becomes increasingly popular

4. 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

5. 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.

6. Real-time Path Planning for Virtual Agents in Dynamic Environments
[Sud et al.; IEEE VR 2007]

7. Multi-Agent Navigation Graph
Unified data structure for path planning of multiple agents
Computed using 1st and 2nd order Voronoi diagrams 11

8. 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 12

9. 1st Order Voronoi Diagram (VD1)
Agents
Static Obstacle

10. 1st Order Voronoi Diagram (VD1)
Agents
Static Obstacle

11. 2nd Order Voronoi Diagram (VD2)

12. VD1 and VD2
VD1
VD2

13. Voronoi Graphs
VG1 U
VG2

14. 2nd nearest nbr graph 2nd order Voronoi graph 1st order Voronoi graph
VG2 captures inter-agent proximity,

15. MaNG Subset of the 2nd nearest neighbor graph Static Obstacle
So we remove edges corresponding to static obstacles.
Static Obstacle

16. 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

17. MaNG: Planner For each agent: Connect agent (source) to VG2 edges

18. MaNG: Planner For each agent: Connect agent (source) to VG2 edges
Connect destination to VG1 edges

19. MaNG: Planner For each agent: Connect agent (source) to VG2 edges
Connect destination to VG1 edges
Assign edge weights 8 3 4 2 3 6 5 2 1 7 2 3 1 3

20. MaNG: Planner For each agent: Connect agent (source) to VG2 edges
Connect destination to VG1 edges
Assign edge weights
Graph search 8 3 4 2 3 6 5 2 1 7 2 3 1 3

21. MaNG: Planner For each time step: Compute MaNG once
Compute paths for all agents from same MaNG

22. 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

23. MaNG Computation Computing exact Voronoi diagram difficult
Non-linear boundaries
High complexity

24. MaNG Computation Computing exact Voronoi diagram difficult
Compute Discrete Voronoi Diagram (DVD)
Compute closest site at finite set of points
Show grid.

25. 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)
Please refer to paper for more details

26. Demos
Fruit stealing
Crowds in urban environment

27. Demos Fruit stealing Crowds in urban environment Dynamic goal update
Swarming behavior observed
Crowds in urban environment

28. 100 Agent simulation at 9 fps
Demo: Stealing Fruit
- As fruits stolen, they disappear
Talk about camera angles
100 Agent simulation at 9 fps 34

29. Demos Fruit stealing Crowds in small urban environment
Dynamic obstacles

30. 100 Agent simulation at 10 fps
Demos: Crowd
As agents approach the goals, they leave the environment. New agents are also inserted into the environment from the buildings or the road
100 Agent simulation at 10 fps 36

31. Motivation Traditional approaches Better motion paths
Randomized, only considers agent geometry
Not realistic motion
Better motion paths
Requires smoother paths, incorporating physics
Start
Goal

32. Traditional: Straight-line links
Motivation
Traditional approaches
Randomized, only considers agent geometry
Not realistic motion
Better motion paths
Requires smoother paths, incorporating physics
Traditional: Straight-line links
Start
Goal

33. Motivation Traditional approaches Better motion paths
Randomized, only considers agent geometry
Not realistic motion
Better motion paths
Requires smoother paths, incorporating physics
Better: Smoother path
Goal
Start

34. 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

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

36. 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

37. 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

38. Planning Architecture

39. Applied to Deformable Agents
Motion equations:
Particle motion in a mass-spring lattice
Artificial forces:
Volume preservation
Obstacle avoidance
Collision resolution
Goal seeking

40. Algorithm Overview Roadmap Generation Path Estimation Path Query
Advance simulation while satisfy constraints
min E(x) subject to V(x) ≤ 
Non-penetration
Volume Preservation

41. Deforming cylinder in a tunnel; agent must deform to exit.
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

42. Applied to Deformable Agents

43. Highly Articulated Chains
Motion equations:
Articulated body motion equation
Artificial forces:
Joint configuration
Path following
Obstacle avoidance
Collision resolution

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

45. Reducing dimensionality
Based on “adaptive forward dynamics”
Adaptively determine which sub-bodies behave most like rigid bodies and rigidify them
All joints simulated
At each step, 25 most important joints are simulated

46. System Demonstrations
Chain with 300 joints must navigate a sequence of walls
Chain with 600 joints must travel through a tunnel

47. Cable Routing on Bridge
A snake robot of 500 links and 500 DOFs
with only 70 DOFs used in this bridge scene

48. Search and Rescue
A snake robot with 2,000 joints searches for a cavity in debris and then exits

49. Pipe inspection
A snake robot with 2,000 joints inspects pipes for a leak by coiling around it

50. Video Demonstration

51. 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
In medical and surgical procedures, flexible catheters or small tubes are often inserted in human vessels. Catheters can be used to obtain diagnostic information such as measures of blood pressure or blood flow. They can also be used to deliver contrast agents to enhance imaging techniques or to deliver treatment to a specific location. With this third ability, catheters are becoming important tools to fight cancer. For example,………..

52. 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
In a procedure called liver chemoembolization, the application we focus on, a catheter is used to deliver chemotherapy drugs directly to the main blood vessel supplying a liver tumor. The catheter is inserted in the femoral artery and is advanced into the selected liver artery. A fluoroscopic display and the resistance felt by the catheter are used by the doctor to guide the catheter to the target. Once the catheter is in place, chemotherapy drugs are injected through the catheter to the liver tumor.
tumor
catheter

53. 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.
Given this potential, we apply our motion planning techniques to this area. In this simulation, we used our motion planning technique to plan the path of a flexible catheter, inserted at the femoral artery, to a specific hepatic artery supplying a tumor inside the liver.
The environment consisted of 3D models of the liver and blood vessels obtained from the 4D NCAT phantom, a realistic computer model of the human body based on the Visible Human Male CT dataset from the National Library of Medicine
The catheter was modeled as a cylinder with a length of 100 cm and a diameter of 1.35 mm. The catheter model was deformable; it was set up to be flexible and snakelike so it could traverse the blood vessels, realistically.

54. Benchmark: Liver (Courtesy of JHU)
A bird’s eye
view of the
entire live &
arteries
jhu1 - The environment from the start. A small hole can be seen on the far left artery, which is where the catheter will enter the arteries.
jhu2 - A view looking from the top of the environment. Shows the liver and the complex arteries inside.
jhu4 - The back side of the environment, zoomed out so that the entire environment is visible
A catheter enters
the left artery.
A closer view
of liver and the
internal arteries

55. 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

56. 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

57. 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

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