  In terms of Rudyak's generalization of Farber's topological complexity of the
path motion planning problem in robotics, we give a complete description of the
topological instabilities in any sequential motion planning algorithm for a
system consisting of non-colliding autonomous entities performing tasks in
space whilst avoiding collisions with several moving obstacles. The Isotopy
Extension Theorem from manifold topology implies, somewhat surprisingly, that
the complexity of this problem coincides with the complexity of the
corresponding problem in which the obstacles are stationary.
