Just to let people know, Basic Income is just a safety net, is a reassurance for people to know that they wont go on hungry, sick and un-sheltered, is the same as universal healthcare and free tuition, they exist to assure you a minimum quality of life, but the safety nets still need to be taken care of, they need maintenance, for they don't come free, they have to be sustained by an active work force, that keeps on innovating and moving forward to a better work, just because you get a basic income, doesn't means that you can now detach yourself from society and leave it all in the hands of drones to manage.
For once the moment machines become able to self regulate and improve they will stop being machine and pass to be something else, an artificial organism or an advanced AI, which doesn't really has any duty to maintain us, secondly if management is still done by humans, the those humans have to be regulated by society in order to keep a check on power misuse, and a big part of that process comes from being an active member of society, being that as an artist, scientist, engineer, social worker, chef, nurse, teacher, etc.
Total automation and complete BI may make the concept of work as a form to acquire sustenance obsolete, but work will still serve as a form of regulating the system.