Taciana O. Souza, Cesar A. Ipanaque Zapata
Published 2024-01-19Version 1
In this paper we discover a connection between the Milnor fibration theory and current research trends in topological robotics. The configuration space and workspace are often described as subspaces of some Euclidean spaces. The work map is a continuous map which assigns to each state of the configuration space the position of the end-effector at that state. The tasking planning problem consists in study the complexity and design of algorithms controlling the task performed by the robot manipulator. We study the tasking planning problem for the Milnor fibration of analytic function-germs in the real and complex cases. The tasking algorithms strongly depends of the Milnor fibration theorem.
Comments: 19 pages. Comments are welcome. arXiv admin note: text overlap with arXiv:2208.10672, arXiv:1910.00157
Topological complexity of motion planning
Topological complexity of n points on a tree
Category and Topological Complexity of the configuration space $F(G\times \mathbb{R}^n,k)$
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