This change is coming... and fast. I've often thought about this recently and I think it will come from a slightly unexpected angle - not for convenience, but for insurance purposes.
For example, take the heavy road transport industry. Insurance is a necessity to protect business from catastrophic loss (and often a legislated requirement). Insurers have to take into account the level of risk when setting a premium. No matter how well trained and experienced a driver is, they are prone to lapses in concentrations, fatigue, errors in judgement and limitations due to illness or injury. Enter a self driving truck (a robot on wheels), that executes the same work without limitations, without getting tired, with more situational awareness and without making mistakes.
It becomes simple mathematics.The risk of a self driving truck causing damage and loss is less than a human operated one. Therefore the insurance premium for a self driving truck becomes lower by comparison. Combined with the ability of a self driving truck to essentially work 24/7, eventually, a tipping point will be reached where it becomes uneconomic to run a heavy road transport business without self driving trucks. This will happen far quicker than when internal combustion driven trucks replaced horse drawn carts.
You could apply this line of thinking to nearly every unskilled or semi-skilled service currently dependant on human labour.
As for personal assistance droids, I think these may take a little longer to be ubiquitous in society. Currently, they are primarilly limited by power. However, once the next advances in battery technology occurs (again, not far away), there will undoubtedly be big leaps forward.