By proxy. Trans Saharan trade was never pre-organized, state-driven or institutionalized, it was a journey of nomadic Arab tribes who would just make enough of a profit to survive. Each trade route was known intimately and passed down through generations but not generally well known; shifting sands also made the journey treacherous for anyone who didn't know what they were doing.

Besides, each trade route depended on small oases that could be stopped at and used to keep the traders (and their camels) going. An organized overland trade would have used up these limited resources and killed the routes altogether. It's also worth pointing out that the Sahara has been dessicating, in all directions, for as long as we know. So the route in the 1400s would have been more manageable and not nearly as far as it is today.