<< Chapter < Page Chapter >> Page >

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.


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


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


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

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get the best Algebra and trigonometry course in your pocket!

Source:  OpenStax, Geometric methods in structural computational biology. OpenStax CNX. Jun 11, 2007 Download for free at http://cnx.org/content/col10344/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Geometric methods in structural computational biology' conversation and receive update notifications?