  We analyze both the s- and p-wave collision induced frequency shifts and
propose a over-$\pi$ pulse scheme to cancel the shifts in optical lattice
clocks interrogated by a Rabi pulse. The collisional frequency shifts are
analytically solved as a function of the pulse area and the inhomogeneity of
the Rabi frequencies. Experimentally measured collisional frequency shifts in
an Yb optical lattice clock are in good agreement with the analytical
calculations. Based on our analysis, the over-$\pi$ pulse combined with a small
inhomogeneity below 0.1 allows a fractional uncertainty on a level of
$10^{-18}$ in both Sr and Yb optical lattice clocks by canceling the
collisional frequency shift.
