Washbasin-cleaning robot can imitate human motions and adapt its knowledge flexibly to different situations

Robots are supposed to do boring or unpleasant jobs for us. However, tedious tasks such as cleaning the bathroom are challenging to automate. How is it possible to calculate the movement of a robot arm so that it can reach every part of a washbasin? What if the basin has unusually curved edges? How much force should be applied at which point?