Sorry I was away at work when you got back to me.
With problem cats, I recommend at least one more litter pan than cats, so if she is an only cat, I would have two. I am not familiar with the litter robot, but many cats do not like litter pans that make noises, or are covered, so I would have an uncovered litter pan.
I would try adding Cat Attract to the litter; it is an herbal product that gets many problem cats in the litter box. Catnip is another thing to try.
Use unscented, clumping litter.
Keep as many doors closed as possible, to limit her access to furniture.
I would not discount the red blood cells in her urine. Has an Xray been done to be sure she does not have bladder stones?
The first thing I do when a cat is not using the litter box is to find out if this is all behavior, or if it could be a physical problem. If she has any crystals in her urine, or stones in her bladder, that can cause stinging or burning with urination, as well as an urgency to urinate. If you Xray her and there are no stones, and you do a urinalysis that shows no crystals, no blood cells , and a pH of 6.5, then I would assume it is behavioral. If Cat Attract does not help, I might consider anti anxiety medication.
My cat did not like using a litter box with other cats, and got to be really bad. I "retrained" her like I train a new kitten. I put her in a bathroom with food and water and litter, and only let her out when she emptied her bladder in the litter. Gradually she learned that the price of freedom was using the litter, and she got to be outside more and more, but she always had to be confined with the litter for part of the day.
Let me know what else I can answer. Rebecca