Reactive and Potential Field Planners

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Reactive and Potential Field Planners
David Johnson

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

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

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

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

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

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

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

Path Followed by Bug-2? Start Finish

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

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

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

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!

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

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

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

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

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

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

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

Attractive Potential Field

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

Repulsive Potential Field

Vector Sum of Two Fields

Resulting Robot Trajectory

Main Problem

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

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.

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.

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

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

Kappa = 3 Target Obstacle

Increase Kappa Kappa = 4

Sphere World: 5 Obstacles
Kappa = 5.6 No local minima