  The Topological complexity a la Farber $\text{TC}(-)$ is a homotopy invariant
which have interesting applications in Robotics, specifically, in the robot
motion planning problem. In this work we calculate the topological complexity
of the configuration space of $k$ distinct rigid bodies without collisions in
$\mathbb{R}^d$, for $d=2,3$. Furthermore, we present optimal algorithms which
can be used in designing practical systems controlling motion of many rigid
bodies moving in space without collisions. The motion planning algorithms we
present in this work are easily implementable in practice.
