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In the above figures, the configuration space is two dimensional because the robot has two degrees of freedom. If the heading of the robot mattered (i.e., if the robot were not circular), then a configuration would consist of a position and an orientation. The configuration space would therefore be three dimensional. If the robot had a rotatable joint, this would add another degree of freedom and another dimension to the C-space.

The path planning problem

The robotic path planning problem is, given a robot, a work space, and starting and goal configurations for the robot in the work space, find a collision-free path for the robot from the starting configuration to the goal, if one exists. Otherwise determine that no such path exists. An extensive introduction to the path planning problem and existing solutions may be found in .

Early approaches to path planning included:

  • Construction of visibility graphs between the vertices of C-space obstacles.
  • Decomposition of the C-space, effectively into subproblems.
  • Potential field methods, in which the goal exerts an attractive force on the robot, and the obstacles exert repulsive forces.
The first two methods scale poorly with the dimensionality of the C-space, since the complexity of the C-space affects their run time. Potential fields are subject to local minima. A robot moving down the potential gradient might get stuck in a potential well before it reaches the global potential minimum at the goal.

Sampling-based path planning

One solution to the scalability problem was to find methods whose run time does not depend on the dimensionality of the C-space, but on some other factor. This led to sampling-based path planning. Rather than making some explicit analysis of the whole C-space, sampling based planners built their representation of C-space by sampling random configurations and using a fast collision checker to determine whether they are in collision.

The basis of many modern sampling-based planners is the Probabilistic Roadmap Method (PRM) . Although the implementation details can become complicated, the basic algorithmic framework is quite straightforward and easy to understand.

    The prm algorithmic framework:

  • Randomly sample a large number of points in C-space, keeping any that are not in collision. This creates a point set in C-space.
  • Using a local planner , attempt to connect pairs of samples that are relatively close to each other by thoroughly sampling and collision checking configurations between them. This creates a graph data structure called a roadmap.
  • To query the roadmap, first attempt to connect the start and goal configurations to the existing graph. If that is successful, search the graph for a path from start to goal using any standard graph search method (often A*).
PRM implementations vary in terms of how the points are sampled--remember that random does not mean uniformly at random--as well as in how the local planner attempts to connect nearby configurations.

Configuration space for path planning

A configuration space in which we wish to build a Probabilistic Roadmap.

Sampling

Random points in the configuration space are tested for collision with obstacles. Collision-free points are kept.

Connection

The roadmap is constructed by connecting nearby samples. Many collision checks are made along each edge to ensure that the connection is legitimate.

Query

The start and goal configurations are connected to their nearest neighbors in the roadmap. A graph search is then made to find the shortest path in the roadmap from start to goal.

Questions & Answers

how can chip be made from sand
Eke Reply
are nano particles real
Missy Reply
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
Lohitha
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Geometric methods in structural computational biology. OpenStax CNX. Jun 11, 2007 Download for free at http://cnx.org/content/col10344/1.6
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