Parametrized topological complexity of collision-free motion planning in the plane
This work addresses motion planning for robotics or autonomous systems in planar environments, but it is incremental as it builds on prior research in 3D space.
The paper tackles the problem of parameterized motion planning for multiple points in the plane, moving without collision and avoiding obstacles with unknown positions, by analyzing it using algebraic and topological tools distinct from the 3D case.
Parametrized motion planning algorithms have high degrees of universality and flexibility, as they are designed to work under a variety of external conditions, which are viewed as parameters and form part of the input of the underlying motion planning problem. In this paper, we analyze the parameterized motion planning problem for the motion of many distinct points in the plane, moving without collision and avoiding multiple distinct obstacles with a priori unknown positions. This complements our prior work [arXiv:2009.06023], where parameterized motion planning algorithms were introduced, and the obstacle-avoiding collision-free motion planning problem in three-dimensional space was fully investigated. The planar case requires different algebraic and topological tools than its spatial analog.