The crate is zip tied to the rack, and a piece of carpet is placed on top. A short leash ties the dogs in so that they cannot jump out and away. The bungee cord on the side keeps the U-lock in place while I ride.
On the front of the bike a special rack clips into a mount, and the crate is permanently zip-tied to the rack. The bike folds up into a bag, and so the zip ties on the back rack are cut off after every ride with the dogs -- about 10 cents worth of plastic.