The caterpillar is the frangipani hornworm. The adult stage is a brown colored moth.  The caterpillars feed primarily on the leaves of frangipani but can feed on a few other plants in the same plant family, the Dogbane family.

Usually the plants survive the attacks of the caterpillars.  Since frangipani plants drop their leaves during the winter anyway, there would be little harm in letting them feed undisturbed now.  If there were repeated, serious defoliations earlier in the growing season it would be of more concern.

More information of the frangipani hornworm can be found here: 
http://edis.ifas.ufl.edu/in621