Transitioning from PhD in biomedical engineering to software dev (have 5-6 software experience working for a team during PhD)?
I have been in both industry and academia, both as a software developer and lecturer, and here two points that might help you: 


You Diplomas: You non-software related diplomas, does not hold you back on finding good software development jobs. It is how much you know about software development. In fact, you have a good story on saying that you are chasing what you like.
Choose Your Side: Ok, so you been involved with robotics, so probably you enjoy logic and reasoning more than shapes and colors. Therefore I would suggest to look into back-end development sort of things (e.g., Python, Java development), rather than front-end design and implementation. 
Your CV: In you cv include any software development experience, even if it is by using an obscure software or programming language. Also, do not hide your academic past, simply explain that is what you did enjoy then and now you enjoy doing software development.