If they're dead set on you not traveling, then you probably don't want to do it until you know they can be comfortable with it. If you just take off now, they could have panic attacks and set off a heart attack (I had a panic attack and those SUCK). I would recommend living like you're homeless in your home town. If this is too humiliating, then don't act like a total hippy and/or bum. Try WWOOFing in your home town, it's fun, you get to work, get a little bit of money for luxuries (tobacco, ganja, booze, most times they'll provide these regardless). Just do the things you want to do, float the river, skateboard, bike, hike, fish, hunt, farm, play with legos, whatever. Do something that your parents will see is not bad. If they're afraid you're going to get killed, ask them to pay for a good martial arts class (check out a few places to decide your form of martial art) so you can know how to defend yourself, but rest assured, you probably won't need this while traveling, but it will boost your parents confidence in you. If they believe you have issues with substances, well they could imagine terrible stuff on the street and that really is out there, then make principals that you will follow (make it something you agree with, not something for them), and make it clear to them that this is what you do, not that other crap.
You are in control of this situation, not them, so control it, don't yell at them, don't get physical, this never works, be subtle, be effective, be positive, be like a rolling stone (not like dynamite). Sure you could live with your friends, but this can build tension. Learn to live like you're homeless, because then you will force yourself out of your comfort zone and to get in touch with survival instincts which you (maybe) never knew you had. Hell you can camp out in your parents yard, they'll think it's crazy, but let them know you're preparing for traveling because that's what you want to do and you will continue to be curious until you do.
Make it clear that you are not dropping out of college, simply making yourself a higher priority for the time being. You will learn new respect, new confidence, new knowledge and new insight to your own being, while traveling, that would take exponentially longer to learn at home. Let them to delay traveling will not only delay what you want to do, but it will also create a distraction to your education.
This should only take a couple/few weeks before they get a bit acclimated to you being a traveler, then you can start taking mini trips. Come back home just to show them cool souvenirs, tell them your stories (EVERY detail, even the drugs you did, if you don't want to tell them about the drugs you do, don't do the drugs that you don't want to talk about). They might act like they don't care, they might be thrilled, who knows, just tell them and tell them every minute detail (don't leave out the crazy axe murdering methed out drug dealer). If you leave out the parts that make them think/say "What happened? Shit! Be careful", then you're leaving out the parts that prove to them that the scary stuff won't kill you. Total honesty, don't edit your experiences for anybody, for any reason.
Most importantly:
KEEP IN TOUCH WITH THEM EVERY DAY. I know this can be hard to do, but make it a habit, otherwise they're going to worry about you. When I traveled for 3 months, I lost my cellphone and could rarely contact my folks, I traveled across country and hadn't talked to my folks in weeks. My dad, the least worrisome person I know, ex-hitchhiker, once was a climbing bum in Yosemite, WORRIED HIS ASS OFF! I'm my dad's best friend, I am his apprentice, his closest relative, his prodigy, the beholder of his legacy, I am his inspiration, and I didn't have the decency to borrow somebody's cell phone to call him every step of the way (payphone? PSH!! yea right!). My dad worried his ASS off about me, and he didn't have anywhere to turn to for comfort except the bar and the bottle. If you want to see your parents become a wreck, that will do it. If you love your parents, KEEP IN TOUCH WITH THEM EVERY DAY. I don't care if you have to borrow somebody's laptop at starbucks to send your mom a message on facebook, send them a post card in the mail, fax them, ANYTHING! This is THE MOST important thing to do while traveling (eating can wait, you parents won't eat for days if they don't here from you). Not calling parents is worse than leaving a dog locked in a car on a hot summer day. The dog will be rescued by any decent person, your parents can only be rescued by YOU.