# 0.7 Robotic path planning and protein modeling  (Page 2/3)

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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.

find the 15th term of the geometric sequince whose first is 18 and last term of 387
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
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