The Vector Field Histogram

1
The Vector Field Histogram

• Erick Tryzelaar
• November 14, 2001
• Robotic Motion Planning
• A Method Developed by J. Borenstein and
• Y. Koren

2
The Problem

• To simultaneously
• Detect, and avoid, unknown obstacles in real-time
• Steer in the best direction that leads to some
  target, ktarg
• Do it as quickly as possible

3
The Solution The Vector Field Histogram (VFH)

• The first step generates a 2D Cartesian
  coordinate from each range sensor, and increments
  that position in the histogram grid C
• Note this method does not depend on a specific
  sensor model

4
The Solution, Continued (2)

• The next step filters this two dimensional grid
  down into a one dimensional structure
• The final step calculates the steering angle and
  the velocity controls from this structure

5
First, Some Terminology

• VCP
• The center point of the robot
• Obstacle vector
• A vector pointing from a cell in C to the VCP

Robot
VCP
6
Step 2 Mapping 2D onto 1D

• In order to simplify calculations, the 2D grid
  used in this step is a window of C, with constant
  dimensions, and centered on the VCP, called the
  active grid, or C.

7
Step 2 Continued (2)

• This is then mapped onto a 1D structure known as
  a polar histogram, or H. A polar histogram is a
  one-dimensional grid comprising of n angular
  sections with width a

Figure included with permission from J. Borenstein
8
Step 2 Continued (3)

• In order to generate H, we must first map every
  cell in C onto a 1D point in Hs coordinate
  system

9
Step 2 Continued (4)
Figure included with permission from J. Borenstein
10
Step 2 Continued (5)

• Because H at this point contains discrete points,
  a smoothing function can be applied in order to
  better approximate the environment

11
Step 3 Computing the Steering Direction

• A typical polar histogram contains peaks, or
  sectors with a high polar obstacle density (POD),
  and valleys, sectors that contain low PODs
• A valley below some threshold is called a
  candidate valley

Figure included with permission from J. Borenstein
12
Step 3 Continued (2)

• From all the candidate valleys, the valley
  closest to the ktarg is selected
• The type of the valley is dependant on the some
  consecutive number of sectors, Smax, under the
  threshold
• Wide is greater than Smax
• Narrow is less than Smax

13
Step 3 Continued (3)

• In that valley, kn is selected from the first or
  the last sector, whichever is closer to ktarg
• Wide valleys kf kn Smax, which results in kf
  in the valley
• Narrow valleys kf is the last sector in the
  valley
• Then q (kn kf)/2

14
Step 3 Selecting the Threshold

• If set too high, the robot may be too close to an
  obstacle, and moving too quickly in order to
  prevent a collision
• However, if set too low, VFH can miss some valid
  candidate valleys
• Generally, the threshold does not need much
  tuning, unless the application of the robot
  requires very fast navigation of tightly packed
  obstacles

15
Step 3 Speed Controls
16
Comparison to Potential Fields

• Influences of a bad sensor read is minimized
  because it is averaged out with prior data
• Instability in traveling down a narrow corridor
  is eliminated because the polar histogram varies
  only slightly between sonar reads
• The repulsive forces from obstacles cannot
  counterbalance the attractive force from the
  target and trap the robot in a local minima, as
  VFH only tries to drive through the best possible
  valley, regardless if it leads away from the
  target

17
Comparison, Continued (2)

• However, VFH cannot not solve all the limitations
  inherent with the potential field method
• Nothing prevents the robot from being caught in a
  real local minima, or a cycle
• When this occurs, a global path planner must be
  used to generate intermediary targets for the VFH
  until it is out of the trap

Robot
ktarg