1. The Vector Field Histogram Erick Tryzelaar November 14, 2001 Robotic Motion Planning A Method Developed by J. Borenstein and Y. Koren

2. 24-700 Robotic Motion Planning2 The Problem To simultaneously: Detect, and avoid, unknown obstacles in real-time Steer in the best direction that leads to some target, k targ Do it as quickly as possible

3. 24-700 Robotic Motion Planning3 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. 24-700 Robotic Motion Planning4 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. 24-700 Robotic Motion Planning5 First, Some Terminology VCP The center point of the robot Obstacle vector A vector pointing from a cell in C* to the VCP VCP Robot

6. 24-700 Robotic Motion Planning6 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. 24-700 Robotic Motion Planning7 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  Figure included with permission from J. Borenstein

8. 24-700 Robotic Motion Planning8 Step 2: Continued (3) In order to generate H, we must first map every cell in C* onto a 1D point in H’s coordinate system

9. 24-700 Robotic Motion Planning9 Step 2: Continued (4) Figure included with permission from J. Borenstein

10. 24-700 Robotic Motion Planning10 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. 24-700 Robotic Motion Planning11 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 POD’s A valley below some threshold is called a candidate valley Figure included with permission from J. Borenstein

12. 24-700 Robotic Motion Planning12 Step 3: Continued (2) From all the candidate valleys, the valley closest to the k targ is selected The type of the valley is dependant on the some consecutive number of sectors, S max, under the threshold Wide is greater than S max Narrow is less than S max

13. 24-700 Robotic Motion Planning13 Step 3: Continued (3) In that valley, k n is selected from the first or the last sector, whichever is closer to k targ Wide valleys: k f = k n ± S max, which results in k f in the valley Narrow valleys: k f is the last sector in the valley Then  = (k n + k f )/2

14. 24-700 Robotic Motion Planning14 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. 24-700 Robotic Motion Planning15 Step 3: Speed Controls

16. 24-700 Robotic Motion Planning16 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. 24-700 Robotic Motion Planning17 Comparison, Continued (2) However, VFH can 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 k targ