  We present a new approach to equivariant version of the topological
complexity, called a symmetric topological complexity. It seems that the
presented approach is more adequate for the analysis of an impact of symmetry
on the the motion planning algoritm than the one introduced and studied by
Colman and Grant. We show many bounds for the symmetric topological complexity
comparing it with already known invariants and prove that in the case of a free
action it is equal to the Farber's topological complexity of the orbit space.
We define the Whitehead version of it.
