1. Reactive and Potential Field Planners
David Johnson

2. Previously Use geometric reasoning to build path in environment
Visibility graphs
Cell decompositions
Use robot controls to generate forces to follow path
Such complete knowledge of environment is rare
May need to react to sensor data

3. A Simple Approach for Unknown Environments
Bug algorithms
Highlights the sort of approach needed for simple robots with simple sensors
From the text – but find the errata chapter online

4. Bug Algorithms Assumptions: The robot is modeled as a point
The obstacles are bounded and are finite
The robot senses perfectly its position and can measure traveled distance
The robot can perfectly detect contacts and their orientations
The robot can compute the direction to the goal and the distance between two points, and has small amount of memory
Finish
Start

5. Bug-0 Algorithm Bug-0 Repeat: Head toward the goal
Start
Finish
Bug-0
Repeat:
Head toward the goal
If the goal is attained then stop
If contact is made with an obstacle then follow the obstacle’s boundary (toward the left) until heading toward the goal is possible again.
Sort of like maze solving rules

6. Is Bug-0 Guaranteed to Work?
No!
Start
Finish
Start
Finish

7. Bug-1 Algorithm Bug-1: Repeat: Head toward the goal
If the goal is attained then stop
If contact is made with an obstacle then circumnavigate the obstacle (by wall-following), remember the closest point Li to the goal, and return to this point by the shortest wall-following path L2
Finish L1
Start

9. Bug-2 Algorithm Bug-2: Repeat:
Head toward the goal along the goal-line
If the goal is attained then stop
If a hit point is reached then follow the obstacle’s boundary (toward the left) until the goal-line is crossed at a leave point closer to the goal than the previous hit point
Finish
leave point
hit point
goal-line
Start

10. Path Followed by Bug-2?
Start
Finish

11. Which one --- Bug-1 or Bug-2 --- does better?
Bug-2 does better than Bug-1
Bug-1 does better than Bug-2
Start
Finish
Finish
Start

12. Bug1 vs. Bug2 Bug1 Bug2 Exhaustive search Optimal leave point
Performs better with complex obstacles
Bug2
Opportunistic (greedy) search
Performs better with simple obstacles

13. Kinds of sensors for Bug
Tactile sensing
Infinite number?
Goal beacon
Measure distance through
Signal strength
Time-of-flight
Phase
Wheel encoders
Orientation

14. Potential Field Planners
Can use range information better
Also tangent bug planner in text
Can also be used in known environment
Fast
Reactive to local data
Rather than
generate forces from path – old approach
generate path from forces!

15. Basic Idea Model physics of robot Attract to goal
Repulse from obstacles

16. Basic Idea Originally was described in terms of potentials
Potential energy is energy at a position (or configuration)
integral of force
Force is derivative of potential energy
Gradient in higher dimensions

17. Potential Field Path Planning
Potential function guides the robot as if it were a particle moving in a gradient field.
Analogy: robot is positively charged particle, moving towards negative charge goal
Obstacles have “repulsive” positive charge

18. Potential functions can be viewed as a landscape
Robot moves from high-value to low-value
Using a “downhill” path (i.e negative of the gradient).
This is known as gradient descent –follow a functional surface until you reach its minimum
Really, an extremum

19. How would you land on a maximum by moving downhill (jump onto small hill)

20. What kind of potentials/forces to use?
Want to
minimize travel time
have stability at goal
not crash

21. Attract to goal
Force is linear with distance
Like the spring force

22. Attractive Potential Field

23. Repulse from Obstacles
Use inverse quadratic
1/dist^2
What is that force law like?

24. Repulsive Potential Field

25. Vector Sum of Two Fields

26. Resulting Robot Trajectory

27. Main Problem

29. Some solutions to local minima
Build graph from local minima
Search graph
Random pertubation to escape
Make sure you don’t push into obstacle
Change parameters to get unstuck
Might not work
Build potential field with only one minimum
Navigation function

30. Rotational and Random Fields
Not gradients of potential functions
Adding a rotational field around obstacles
Breaks symmetry
Avoids some local minima
Guides robot around groups of obstacles
A random field gets the robot unstuck.
Avoids some local minima.

31. Navigation Function N(p)
A potential field leading to a given goal, with no local minima to get stuck in.
For any point p, N(p) is the minimum cost of any path to the goal.
Use a wavefront algorithm, propagating from the goal to the current location.
An active point updates costs of its 8 neighbors.
A point becomes active if its cost decreases.
Continue to the robot’s current position.

35. Sphere Worlds World in which Navigation Problem is solved
compact, connected subset of En
boundary formed by disjoint union of finite number of spheres
valid sphere world provided obstacle closures are contained within the workspace

36. MATLAB Simulation Target Obstacle Kappa = 3
Potential Field Level Curves
Obstacle

37. Plotting Navigation Function
Kappa = 3
Target
Obstacle

38. Increase Kappa
Kappa = 4

39. Sphere World: 5 Obstacles
Kappa = 5.6
No local minima

40. More Advanced Navigation Functions
Treat C-space as fluid flow simulation
Start is fluid source
Goal is fluid sink
Run FEA

41. Finding a Path Start at source Trace path along vector field
Can have non-point source and sinks
New sources are fast to compute