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We study the problem of determining optimal coordinated motions for two disc robots in an otherwise obstacle-free plane.
Convexity
H. G. Eggleston · 1958
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A Collection of Mathematical Problems: Problems in Modern Mathematics
Stanislaw Marcin Ulam · 1964
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The "most economical" displacement of a segment (in russian)
A. B. Gurevich · 1975
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On the piano movers’ problem: III. coordinating the motion of several independent bodies: the special case of circular bodies moving amidst polygonal barriers
Jacob T Schwartz and Micha Sharir · 1983
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On the complexity of motion planning for multiple independent objects; pspace- hardness of the "warehouseman’s problem"
J.E. Hopcroft, J.T. Schwartz, and M. Sharir · 1984
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Strong NP-hardness of moving many discs
Paul G. Spirakis and Chee-Keng Yap · 1984
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Coordinating the motion of several discs
Chee Yap · 1984
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Reducing multiple object motion planning to graph searching
J E Hopcroft and G T Wolfong · 1986
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Coordinated motion planning for two independent robots
Micha Sharir and Shmuel Sifrony · 1991
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Optimal motion planning for a rod in the plane subject to velocity constraints
Yui-Bin Chen and Doug Ierardi · 1993
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Shortest paths for line segments
Christian Icking, Günter Rote, Emo Welzl, and Chee-Keng Yap · 1993
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Time-optimal motion of two omnidirectional robots carrying a ladder under a velocity constraint
Zhengyuan Chen, Ichiro Suzuki, and Masafumi Yamashita · 1997
Cited alongside, same era.
Using a PRM planner to compare centralized and decoupled planning for multi-robot systems
Gildardo Sánchez-Ante and Jean-Claude Latombe · 2002
Cited alongside, same era.
Moving coins
Manuel Abellanas, Sergey Bereg, Ferran Hurtado, Alfredo García Olaverri, David Rappaport, and Javier Tejel · 2004
Cited alongside, same era.
Sliding Disks in the Plane
Sergey Bereg, Adrian Dumitrescu, and János Pach · 2005
Cited alongside, same era.
On Reconfiguration of Disks in the Plane and Related Problems
Adrian Dumitrescu and Minghui Jiang · 2009
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Finding optimal solutions to cooperative pathfinding problems
Trevor Standley · 2010
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On Ulam’s problem of path planning, and “How to move heavy furniture"
Erik I Verriest · 2011
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M*: A complete multirobot path planning algorithm with performance bounds
Glenn Wagner and Howie Choset · 2011
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Trajectory Planning and Assignment in Multirobot Systems
Matthew Turpin, Nathan Michael, and Vijay Kumar · 2013
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Efficient Multi-robot Motion Planning for Unlabeled Discs in Simple Polygons
Aviv Adler, Mark de Berg, Dan Halperin, and Kiril Solovey · 2015
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Pspace-completeness of sliding-block puzzles and other problems through the nondeterministic constraint logic model of computation
Robert A. Hearn and Erik D. Demaine · 2005
Cited alongside, same era.
Planning algorithms
Steven M. LaValle · 2006
Cited alongside, same era.
Metric structures for Riemannian and non-Riemannian spaces
Misha Gromov · 2007
Cited alongside, same era.
On the hardness of unlabeled multi-robot motion planning
Kiril Solovey and Dan Halperin · 2015
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Motion planning for unlabeled discs with optimality guarantees
Kiril Solovey, Jingjin Yu, Or Zamir, and Dan Halperin · 2015
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