Please excuse me for any mistakes in the rendition!
Vidapi I think is similar to the Hindustani Raag Bhatiyar in the feel, although the latter includes ga3 and ni3.
Here's an abhang in Bhatiyar by Ranjani-Gayathri: http://www.youtube.com/watch?v=FiT7Hqk_uwg
Priya sisters have also sung a bhajan in this raag, "maare ghar aaoji"...
(I remember a documentary that used to come on Doordarshan years back- on the National Literacy Mission - in the voice of Kavitha Krishnamurthy, and I think that was also Bhatiyar... was a lovely tune and brings back fond memories of the DD days...)
Raga: Vidapi (S R1 M1 P D2 S, S D2 P M1 R1 S)
Lyrics: Sri Vadiraja
Tune: Smt Lalgudi Rajalakshmi