My friend has two daughters ages 18 months and 3 years. when her first was 20 months old, she took a week with NO commitments, put her daughter in panties (she said that they thought of pull ups as diapers so they were ineffective), gave her lots of water, and took her to the bathroom every HALF hour on the dot for a week. She gave her 3 m&ms when she would GO, not sit but GO. and more if it was poop. she potty trained her daughter in a week. occasionally there is a "i forgot to pull my panties off first" etc, but they are potty trained. her second was at 18 months, but she was interested in it because her sister was sitting on the potty.
every kiddo is different. what works for one may not work for the other. but if the kid begins to really feel wet and uncomfortable, then they may be able to potty train faster. like i said, pull ups are like diapers to their little minds, so i would highly recommend panties. but you have to be very consistent with every half hour on the dot or you will have messes to clean up. pull ups are a good idea for at night though, since kids even up to 5 and fully potty trained may not wake up enough to realize they have to go in the middle of the night, and could have bedwetting longer than potty training. but in the morning take them off and put them on the potty first thing, then panties til bedtime. keep in mind boys generally take longer to potty train.
good luck, and hope it works for you! also, let them see you go potty and make a game of it, because they are big enough to imitate. and they have to be old enough to sit on their potty and reach the floor. my DD is 13 months old, but shes petite and cant reach the floor yet. i still occasionally sit her on her potty, even though i know she probably wont go, before bathtime, and when i go, and i tell her that i am going in the big potty and explain what i am doing, so she learns that potties are where mommy goes pee pee so she will go pee pee in a potty too. imitation time is a great way for them to learn at this age. i do not expect her to be potty trained right now, but i want her to associate potty with pee pee, and she can understand a lot more now than people give her credit for. she can follow basic commands now, like go find daddy, or come here, or drink your water, or walk like a big girl. so i believe if i do that at least once a day, by the time she is big enough to potty train she will already have an idea of whats going on. but for them to be able to sit independently on the potty they really need to reach the floor. she can sit just fine, but her balance on a potty where she cant reach the floor is iffy, and i have to hold her.
like i said, good luck! :D