Since the caterpillars are coming from eggs laid on the branches in the tree canopy, duct tape, sticky tape, tanglefoot etc. will have no effect.

Bt, Bacillus thuringiensis, is a biocontrol that will attack all manner of larval caterpillar. It is considered organic and is available at virtually any garden center or by mail order. It is harmless to any other organisms so no negative impact on bees or other pollinators. For a small tree, it is easily sprayed on with a hand sprayer but you might need more elaborate equipment with large trees.

Blasting them off the tree with a strong stream of water can also help. Any that survive this vigorous dislodgement are rapidly gobbled up by birds.