We describe the resolutions of some old and new problems in locomotion (motion planning). One of these problems is the following. We have $n$ pointwise particles in $d$-space. In each move, one of them jumps over another and lands on its other side at the same distance. What conditions need to be satisfied by the initial configuration to make sure that there is a finite sequence of moves that takes the particles simultaneously arbitrarily close to any $n$ pre-assigned positions. The solution is joint work with Gábor Tardos.