Most probably this plant is Sesamum radiatum. As the features of Sesamum indicum and Sesamum radiatum are almost similar, I would suggest you to approach some appropriate authorities where plant identifications are done. It is better to get the plant authenticated before starting to work with it. Most of the organisations would issue you a certificate indicating the botanical name of the plant and other details. This would be useful in final reporting as well as in publications. Good Luck
It is looking like Sesamum indicum, please find my image. But Sesamum indicum leaves are not eaten. Fried seeds are edible, oil extracted from seeds is eaten. The oil is allergic to some women. It creates over bleeding.
I have not done any work on sesame in the past. However, I have seen the plant growing my colleague's field. The photographs appear to have some resemblance with Sesamum indicum but the actual varietal name would need a closer look at the life plant by a plant taxonomist.