We examine the persistent random motion of self-propelled rods (SPR) as a function of the area fraction phi and study the effect of steric interactions on their diffusion properties. SPR of length l and width w are fabricated with a spherocylindrical head attached to a beaded chain tail, and show directed motion on a vibrated substrate. The mean square displacement (MSD) on the substrate grows linearly with time t for phi<w/l, before displaying caging as phi is increased, and stops well below the close packing limit. Direction autocorrelations decay progressively slower with phi. We describe the observed decrease of SPR propagation speed c(phi) with a tube model. Further, MSD parallel to the SPR collapse with tau=l/c(phi) and scales as (lt/tau);{2}, and MSD in the perpendicular direction grows progressively slower than l{2}t/tau with phi, consistent with dynamics inside a thinning tube.