Topology of Parametrized Motion Planning Algorithms

We introduce and study a new concept of parametrized topological complexity: invariant motivated by the motion planning problem robotics. In setting, algorithm has high degree universality flexibility can function under variety external conditions (such as positions obstacles). explicitly compute complexity obstacle-avoiding collision-free many particles (robots) in 3-dimensional space. Our results show that be significantly higher than standard (nonparametrized) invariant.