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On the “piano movers'” problem I. The case of a two‐dimensional rigid polygonal body moving amidst polygonal barriers
Abstract
We present an algorithm that solves a two‐dimensional case of the following problem which arises in robotics: Given a body B, and a region bounded by a collection of “walls”, either find a continuous motion connecting two given positions and orientations of B during which B avoids collision with the walls, or else establish that no such motion exists. The algorithm is polynomial in the number of walls (O(n5) if n is the number of walls), but for typical wall configurations can run more efficiently. It is somewhat related to a technique outlined by Reif.
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Citations
Cited by
Spatial Planning: A Configuration Space Approach
Lozano-Perez (1983) · IEEE Transactions on Computers · doi:10.1109/tc.1983.1676196 · Cited by 2,113
Robot Motion Planning: A Distributed Representation Approach
Barraquand, J., & Latombe, J.-C. (1991) · The International Journal of Robotics Research · doi:10.1177/027836499101000604 · Cited by 995
Lumelsky, V. J., & Stepanov, A. A. (1987) · Algorithmica · doi:10.1007/bf01840369 · Cited by 699
The evolution of robotics research
Garcia, E., Jimenez, M. A., De Santos, P. G., & Armada, M. (2007) · IEEE Robotics & Automation Magazine · doi:10.1109/mra.2007.339608 · Cited by 371
Metadata
- Authors
- Schwartz, J. T., & Sharir, M.
- Venue
- Communications on Pure and Applied Mathematics
- Publisher
- Wiley
- Published
- 1983-05
- Volume
- 36
- Issue
- 3
- Pages
- 345-398
- ISSN
- 0010-3640 (ISSN-L)
- 1097-0312
- OpenAlex
- W2001804342
- Cited by
- 454
- References
- 0
- FWCI
- 22.93
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: On the “piano movers'” problem I. The case of a two‐dimensional rigid polygonal body moving amidst polygonal barriers. https://app.cochat.ai/papers/10.1002/cpa.3160360305
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- Schwartz, J. T., & Sharir, M. (1983). On the “piano movers'” problem I. The case of a two‐dimensional rigid polygonal body moving amidst polygonal barriers. Communications on Pure and Applied Mathematics. https://doi.org/10.1002/cpa.3160360305
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