History of centrifugal and centripetal forces: Difference between revisions

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[[File:Velocity obstacle.svg|thumb|right|The velocity obstacle ''VO''<sub>''AB''</sub> for a robot ''A'', with position '''x'''<sub>''A''</sub>, induced by another robot ''B'', with position '''x'''<sub>''B''</sub> and velocity '''v'''<sub>''B''</sub>.]]
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In [[robotics]] and [[motion planning]], a '''velocity obstacle''', commonly abbreviated '''VO''', is the set of all [[velocity|velocities]] of a [[robot]] that will result in a [[collision]] with another robot at some moment in time, assuming that the other robot maintains its current velocity.<ref name="fiorini98" >{{cite journal
  |author=Fiorini, P.; Shiller, Z.
  |date=July 1998
  |title=Motion planning in dynamic environments using velocity obstacles
  |doi=10.1177/027836499801700706
  |journal=The International Journal of Robotics Research
  |publisher=[[SAGE Publications]]
  |location=[[Thousand Oaks, California|Thousand Oaks, Calif.]]
  |volume=17
  |issue=7
  |pages=760–772
  |issn=0278-3649
}}</ref> If the robot chooses a velocity inside the velocity obstacle then the two robots will eventually collide, if it chooses a velocity outside the velocity obstacle, such a collision is guaranteed not to occur.<ref name="fiorini98" />
 
This algorithm for robot collision avoidance has been repeatedly rediscovered and published under different names:
in 1989 as a maneuvering-board approach,<ref name="tychonieivich89">{{cite conference
  |author=Tychonievich, L. P.; Zaret, D.; Mantegna, R.; Evans, R.; Muehle, E.; Martin, S.
  |year=1989
  |title=A maneuvering-board approach to path planning with moving obstacles
  |conference=International Joint conference on Artificial Intelligence (IJCAI)
  |pages=1017–1021
}}</ref>
in 1993 it was first introduced as the "velocity obstacle",<ref name="fiorini93">{{cite conference
  |author=Fiorini, P.; Shiller, Z.
  |year=1993
  |title=Motion planning in dynamic environments using the relative velocity paradigm
  |conference=IEEE Conference on Robotics and Automation
  |pages=560–565
}}</ref>
in 1998 as collision cones,<ref name="chakravarthy98">{{cite journal
  |doi=10.1109/3468.709600
  |author=Chakravarthy, A.; Ghose, D.
  |title=Obstacle avoidance in a dynamic environment: A collision cone approach
  |journal=IEEE Transactions on Systems, Man and Cybernetics—Part A: Systems and Humans
  |volume=28
  |issue=5
  |pages=562–574
  |date=September 1998
}}</ref>
and in 2009 as forbidden velocity maps.<ref name="">{{cite conference
  |author=Damas, B.; Santos-Victor, J.
  |title=Avoiding moving obstacles: the forbidden velocity map
  |conference=IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
  |year=2009
  |pages=4393–4398
}}</ref>
The same algorithm has been used in maritime port navigation since at least 1903.<ref name="miller03">{{cite book
  |author=Miller, F. S.; Everett, A. F.
  |title=Instructions for the Use of Martin’s Mooring Board and Battenberg’s Course Indicator
  |publisher=Authority of the Lords of Commissioners of the Admirality
  |year=1903
}}</ref>
 
The velocity obstacle for a robot <math>A</math> induced by a robot <math>B</math> may be formally written as
 
:<math>
VO_{A|B} = \{ \mathbf{v}\,|\, \exists t > 0 : (\mathbf{v} - \mathbf{v}_B)t \in D(\mathbf{x}_B - \mathbf{x}_A, r_A + r_B) \}
</math>
 
where <math>A</math> has [[position (vector)|position]] <math>\mathbf{x}_A</math> and [[radius]] <math>r_A</math>, and <math>B</math> has position <math>\mathbf{x}_B</math>, radius <math>r_B</math>, and velocity <math>\mathbf{v}_B</math>.  The notation <math>D(\mathbf{x}, r)</math> represents a [[disk (mathematics)|disc]] with [[centroid|center]] <math>\mathbf{x}</math> and radius <math>r</math>.
 
Variations include common velocity obstacles (CVO),<ref>{{cite conference
  |author=Abe, Y.; Yoshiki, M.
  |date=November 2001
  |title=Collision avoidance method for multiple autonomous mobile agents by implicit cooperation
  |doi=10.1109/IROS.2001.977147
  |conference=IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 01)
  |publisher=[[Institute of Electrical and Electronics Engineers|IEEE]].
  |location=[[New York City|New York, N.Y.]]
  |pages=1207–1212
}}</ref> finite-time-interval velocity obstacles (FVO),<ref>{{cite conference
  |author=Guy, S. J.; Chhugani, J.; Kim, C.; Satish, N.; Lin, M.; Manocha, D.; Dubey, P.
  |date=August 2009
  |title=ClearPath: Highly parallel collision avoidance for multi-agent simulation
  |doi=10.1145/1599470.1599494
  |conference=ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA 09)
  |publisher=[[Association for Computing Machinery|ACM]].|location=[[New York City|New York, N.Y.]]
  |pages=177–187
}}</ref> [[generalization|generalized]] velocity obstacles (GVO),<ref>{{cite conference
  |author=Wilkie, D.; v.d. Berg, J.; Manocha, D.
  |date=October 2009
  |title=Generalized velocity obstacles
  |doi=10.1109/IROS.2009.5354175
  |conference=IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 09)
  |publisher=[[Institute of Electrical and Electronics Engineers|IEEE]].  |location=[[New York City|New York, N.Y.]]
}}</ref> [[hybrid (biology)|hybrid]] reciprocal velocity obstacles (HRVO),<ref>{{cite conference
  |author=Snape, J.; v.d. Berg, J.; Guy, S. J.; Manocha, D.
  |date=October 2009
  |title=Independent navigation of multiple mobile robots with hybrid reciprocal velocity obstacles
  |url=http://gamma.cs.unc.edu/HRVO/
  |conference=IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 09)
  |publisher=[[Institute of Electrical and Electronics Engineers|IEEE]]  |location=[[New York City|New York, N.Y.]]
}}</ref> [[nonlinear system|nonlinear]] velocity obstacles (NLVO),<ref>{{cite conference
  |author=Large, F.; Sekhavat, S.; Shiller, Z.; Laugier, C.
  |date=December 2002
  |title=Using non-linear velocity obstacles to plan motions in a dynamic environment
  |doi=10.1109/ICARCV.2002.1238513
  |conference=IEEE International Conference on Control, Automation, Robotics and Vision (ICARCV 02)
  |publisher=[[Institute of Electrical and Electronics Engineers|IEEE]]
  |location=[[New York City|New York, N.Y.]]
  |pages=734–739
}}</ref>  reciprocal velocity obstacles (RVO),<ref>{{cite conference
  |last=v.d. Berg  |first=J.
  |last2=Lin  |first2=M.
  |last3=Manocha  |first3=D.
  |date=May 2008
  |title=Reciprocal velocity obstacles for real-time multi-agent navigation
  |doi=10.1109/ROBOT.2008.4543489|conference=IEEE International Conference on Robotics and Automation (ICRA 08)
  |publisher=[[Institute of Electrical and Electronics Engineers|IEEE]]
  |location=[[New York City|New York, N.Y.]]
  |pages=1928–1935
}}</ref> and [[recursion|recursive]] [[probability|probabilistic]] velocity obstacles (PVO).<ref>{{cite conference
  |author=Fulgenzi, C.; Spalanzani, A.; Laugier, C.
  |date=April 2007
  |title=Dynamic obstacle avoidance in uncertain environment combining PVOs and occupancy grid
  |doi=10.1109/ROBOT.2007.363554
  |conference=IEEE International Conference on Robotics and Automation (ICRA 07)
  |publisher=[[Institute of Electrical and Electronics Engineers|IEEE]]  |location=[[New York City|New York, N.Y.]]
  |pages=1610–1616
}}</ref>
 
== References ==
{{Reflist|colwidth=30em}}
 
[[Category:Geometric algorithms]]
[[Category:Multi-robot systems]]
[[Category:Robot kinematics]]
 
 
{{robo-stub}}

Latest revision as of 13:24, 22 April 2014

If an existing Word - Press code is found vulnerable, Word - Press will immediately issue an update for that. This means you can setup your mailing list and auto-responder on your wordpress site and then you can add your subscription form to any other blog, splash page, capture page or any other site you like. Your parishioners and certainly interested audience can come in to you for further information from the group and sometimes even approaching happenings and systems with the church. Keep reading for some great Word - Press ideas you can start using today. You can customize the appearance with PSD to Word - Press conversion .

As you know today Word - Press has turn out to be a tremendously popular open source publishing and blogging display place. If you wish to sell your services or products via internet using your website, you have to put together on the website the facility for trouble-free payment transfer between customers and the company. It allows Word - Press users to easily use HTML5 the element enable native video playback within the browser. It primarily lays emphasis on improving the search engine results of your website whenever a related query is typed in the search box. Many times the camera is following Mia, taking in her point of view in almost every frame.

The entrepreneurs can easily captivate their readers by using these versatile themes. After sending these details, your Word - Press blog will be setup within a few days. This platform can be customizedaccording to the requirements of the business. These frequent updates have created menace in the task of optimization. After that the developer adds the unordered list for navigations.

Numerous bloggers are utilizing Word - Press and with good reason. php file in the Word - Press root folder and look for this line (line 73 in our example):. Next you'll go by way of to your simple Word - Press site. There are many advantages of hiring Wordpress developers for Wordpress project development:. If your site does well you can get paid professional designer to create a unique Word - Press theme.

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