Do domesticated animals have control over their karma? Are domesticated animals able to generate their own karma, or is it down to their masters to ensure that they are set on the right path? I am talking particularly in regards to Pets, here.

My dog, Bronson, has epilepsy and fits on a regular basis, perhaps as a result of bad karma? To what extent can he help himself, and to what extent can I?
Are domesticated animals able to generate their own karma


Yes, they commit Kamma just like humans. But their range is limited compared to us. They are unable to commit highly potent good/bad Kamma except on rare occasions. Their minds are clouded by ignorance most of the time. So it's highly unlikely for them to commit a Triple Rooted Kamma required for a perfect human birth. 

Examples of animals committing good Kamma(first 2 are highly potent due to the purity of the recipient):  


Pārileyyaka the elephant and the monkey who took care of the Buddha in the forest.
Muchalinda the king cobra who sheltered the Buddha from rain in the 6th week after attaining enlightenment
Animals taking care of their offspring.



  their masters to ensure that they are set on the right path? To what extent can he help himself, and to what extent can I?


Yes, the owners can teach them good manners. Train them not to kill other animals, not to steal food from others. The more domesticated the animal is, the less bad Kamma it would commit. Also, you can have it listen to the Dhamma. It's a long shot, but it has worked on some occations. ex: The story of Manduka Devaputta


  My dog, Bronson, has epilepsy and fits on a regular basis, perhaps as
  a result of bad karma?


Yes, it is. This is called the Upattambaka(Supportive) Kamma. In case of lower births, this type of Kamma worsens the living conditions.