Obstacle Count Independent RealTime Collision Avoidance

1
Obstacle Count Independent Real-Time Collision
Avoidance

• Michael Greenspan and Nestor Burtnyk
• ENSC887 Presentation
• Wayne Chen
• Nov. 15, 2004

2
Overview

• Motivation
• Previous Work
• The Algorithms
• Voxel Map Maintenance
• Spherical Model Generation
• Real-Time Collision Detection Algorithm
• Experimental Results
• Comparison to Other Algorithms

3
Motivation

• to detect potential collisions and prevent
  their occurrence by redirecting the motion of the
  robot
• Real-Time
• Obstacle Count Independent
• Relevant applications
• Direct teleoperation
• Sensor-based control

4
Previous Work

• Model-Based vs. Sensor-Based

• Collision between geometric primitives
• Two convex polyhedra Lozano-Perez
• Two convex polytopes Gilbert
• Sphere vs. Polyhedra Dodds
• Dynamic spheres Tornero
• ? obstacle count dependent -gt too many
  comparisons!

5
Previous Work (continued)

• Hierarchical spherical representation Wavish
• ? efficient only when no collision
• Pre-calculated Look-Up Table
• Discrete C-Space Lozano-Perez
• ? exponential to number of dof
• Discrete R-Space (Voxel Map)
• Voxels vs. Voxels Duffy
• Spheres vs. Voxels (This paper!)

6
Voxel Map Maintenance

• 3 workspace element types
• Static, movabily static, dynamic
• Contains distance to closest obstacle
• Voxel map operations
• Add obstacles explosion
• Remove obstacles explosionimplosion
• Same idea as Brush Fire

7
Voxel Map Add Obstacle
6
8
Voxel Map Remove Obstacle
2
6
9
Voxel Map - Remarks

• Key any voxel remaining nearer to a prior
  obstacle remains unchanged
• Operates in local region of obstacle
• Voxel Influence Zone
• Voronoi regions
• k?O(n), k ? 1.

10
Spherical Model Generation

• Model must satisfy
• Coverage
• Goodness of Fit
• Compactness
• of spheres ? performance

11
Spherical Model Generation

• Sphere Generation
• Input polyhedra, overshoot, spacing
• Sphere Pruning
• Single Sphere Enclosure
• Multiple Sphere Enclosure

12
Sphere Generation - Rules

• Voxel resolution spacing
• exterior, boundary, or interior.
• Voxels only exterior and boundary are set
  values.
• Sphere
• Only at boundary and interior
• One sphere centred at each voxel

13
Sphere Generation
14
Sphere Pruning

• Sphere is redundant if it does not add coverage.
• Single Sphere Enclosure
• Check distance b/w centres ? radius?

15
Sphere Pruning

• Multiple Sphere Enclosure
• Most spheres pruned in this step
• How to check?
• Create candidate sphere set
• Create a temp voxel map running through all
  spheres.
• Increment voxel value for each sphere enclosure
• If value gt 2, can take out a sphere.

16
Sphere Pruning
(a)
17
Sphere Generation - Parameters
18
Sphere Generation Puma 560

• 509 spheres used here.

19
Real-Time Collision Detection

• Off-line computation
• Manipulator spheres
• Obstacles numbers in voxel map
• On-line actual collision check
• collision if (sphere radius gt voxel value)
• Otherwise sphere radius ? voxel value distance
  to closest obstacle

20
Real-Time Collision Detection
21
Real-Time Collision Detection

• For (all links)
• calculate link frame transform
• for (all spheres in link frame)
• transform sphere centre
• index voxel at sphere centre
• sphere clearance voxel value sphere radius
• if (sphere clearance gt 0)
• sphere is collision-free
• else
• sphere is in collision
• link is in collision
• manipulator is in collision

22
Experimental Results

• Efficiency O(s)
• Obstacle Count Independent
• Example
• CPU Speed 2 MFLOP/sec (66MHz 486)
• Computation 50 FLOP/sphere
• Real-Time Constraint 50Hz Controller

23
Experimental Results

• Collision avoidance
• 0th order stop
• 1st order stop colliding component
• 2nd order alter path
• Currently only 0th order achieved.

24
Experimental Results

• First setup direct teleoperation
• Robot controlled with joystick
• Controller running 28 msec
• Total voxel map 2m (2cm resolution)
• Total of spheres 509
• Workspace 527 polygons
• Result (66MHz PC)
• Off-line computation 15 seconds
• On-line computation 10 msec

25
Experimental Results

• Setup 2 path planning of manipulator

26
Experimental Results

• Results
• Search space exponential to n (6)
• Algorithm helps reduce base of exponential
  relationship
• Path generated in 6 seconds (4 MFLOPS CPU)

27
Comparison

• A Fast Procedure for Computing the Distance
  between Complex Objects in Three-Dimensional
  Space Gilbert, et al.
• A Fast Algorithm for Incremental Distance
  Calculation Lin and Canny
• Obstacle Count Independent Real-Time Collision
  Avoidance Greenspan and Burtnyk

28
Comparison

• (Review) Gilberts Algorithm

29
Comparison

• (Review) Gilberts Algorithm
• Reduce problem to finding distance b/w origin and
  K1?K2.
• Compute distance

30
Comparison

• (Review) Lins Algorithm
• Preprocessing polytopes

31
Comparison

• (Review) Lins Algorithm
• Find closest features (V,E,F) between polyhedras
  (6 cases)
• 3 applicability tests (mutual test)
• Point Vertex
• Point Edge
• Point Face
• Then find distance between these features

32
Comparison

• (Review) Lins Algorithm

33
Comparison Algorithm Nature
34
Comparison Algorithm Nature
35
Comparison Algorithm Nature
36
Comparison Algorithm Nature
37
Comparison Algorithm Nature
38
Comparison Efficiency
39
Comparison Run Time
Gilbert Algorithm (Harris 800) (CPU 0.23
MFLOP/sec)
Lin Algorithm (Sun4 SPARC) (CPU 1.4 MFLOP/sec)
Greenspan Algorithm (CPU1 1.7 MFLOP/sec) (CPU2
4 MFLOP/sec)
1. Direct Manipulation lt10msec 2. Planning 6
seconds
40
Comparison Applications