Document Type
Article
Publication Date
6-16-2021
Abstract
We introduce and study a new concept of parametrized topological complexity: A topological invariant motivated by the motion planning problem of robotics. In the parametrized setting, a motion planning algorithm has a high degree of universality and flexibility and can function under a variety of external conditions (such as positions of obstacles). We explicitly compute the parametrized topological complexity of obstacle-avoiding collision-free motion of many particles (robots) in 3-dimensional space. Our results show that the parametrized topological complexity can be significantly higher than the standard (nonparametrized) invariant.
Publication Source (Journal or Book title)
SIAM Journal on Applied Algebra and Geometry
First Page
229
Last Page
249
Recommended Citation
Cohen, D., Farber, M., & Weinberger, S. (2021). Topology of parametrized motion planning algorithms. SIAM Journal on Applied Algebra and Geometry, 5 (2), 229-249. https://doi.org/10.1137/20M1358505