On the complexity of parametrized motion planning algorithms
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911705872728064 |
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| author | Daundkar, Navnath Jauhari, Ekansh |
| author_facet | Daundkar, Navnath Jauhari, Ekansh |
| contents | We study a probabilistic variant of the r-th sequential parametrized topological complexity, which bounds this classical invariant from below and measures the difficulty in constructing permissive parametrized motion planning algorithms. On one hand, we use cohomology to show that this new invariant behaves similarly to the classical invariant on Fadell-Neuwirth fibrations and oriented sphere bundles; on the other hand, we use equivariant homotopy theory to prove that its behavior is wildly different on bundles whose fibers are real projective spaces and whose structure groups are special orthogonal groups. We also explore several other features of our invariant and its relationships with various other invariants motivated by topological robotics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17629 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the complexity of parametrized motion planning algorithms Daundkar, Navnath Jauhari, Ekansh Algebraic Topology 55S40, 55M30, (Primary) 55R10, 70Q05, 55R25, 55R91(Secondary) We study a probabilistic variant of the r-th sequential parametrized topological complexity, which bounds this classical invariant from below and measures the difficulty in constructing permissive parametrized motion planning algorithms. On one hand, we use cohomology to show that this new invariant behaves similarly to the classical invariant on Fadell-Neuwirth fibrations and oriented sphere bundles; on the other hand, we use equivariant homotopy theory to prove that its behavior is wildly different on bundles whose fibers are real projective spaces and whose structure groups are special orthogonal groups. We also explore several other features of our invariant and its relationships with various other invariants motivated by topological robotics. |
| title | On the complexity of parametrized motion planning algorithms |
| topic | Algebraic Topology 55S40, 55M30, (Primary) 55R10, 70Q05, 55R25, 55R91(Secondary) |
| url | https://arxiv.org/abs/2508.17629 |