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>.]] | |||
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}} | |||
Revision as of 08:15, 21 January 2014
In robotics and motion planning, a velocity obstacle, commonly abbreviated VO, is the set of all 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.[1] 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.[1]
This algorithm for robot collision avoidance has been repeatedly rediscovered and published under different names: in 1989 as a maneuvering-board approach,[2] in 1993 it was first introduced as the "velocity obstacle",[3] in 1998 as collision cones,[4] and in 2009 as forbidden velocity maps.[5] The same algorithm has been used in maritime port navigation since at least 1903.[6]
The velocity obstacle for a robot induced by a robot may be formally written as
where has position and radius , and has position , radius , and velocity . The notation represents a disc with center and radius .
Variations include common velocity obstacles (CVO),[7] finite-time-interval velocity obstacles (FVO),[8] generalized velocity obstacles (GVO),[9] hybrid reciprocal velocity obstacles (HRVO),[10] nonlinear velocity obstacles (NLVO),[11] reciprocal velocity obstacles (RVO),[12] and recursive probabilistic velocity obstacles (PVO).[13]
References
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