  In this paper we study paramertized motion planning algorithms which provide
universal and flexible solutions to diverse motion planning problems. Such
algorithms are intended to function under a variety of external conditions
which are viewed as parameters and serve as part of the input of the algorithm.
Continuing a recent paper, we study further the concept of parametrized
topological complexity. We analyse in full detail the problem of controlling a
swarm of robots in the presence of multiple obstacles in Euclidean space which
served for us a natural motivating example. We present an explicit parametrized
motion planning algorithm solving the motion planning problem for any number of
robots and obstacles.. This algorithm is optimal, it has minimal possible
topological complexity for any d odd. Besides, we describe a modification of
this algorithm which is optimal for d even. We also analyse the parametrized
topological complexity of sphere bundles using the Stiefel - Whitney
characteristic classes.
