A robotic cleaning apparatus for cleaning a toilet includes a cleaning head, an articulated body, and a controller. The articulated body coupled to the cleaning head and mountable to the toilet. The body having one or more actuators that collectively move the cleaning head into contact with surfaces of the toilet bowl and toilet seat when the articulated body is mounted to the toilet. The controller communicatively coupled to the one or more actuators to send control signals that, when the articulated body is mounted to the toilet, direct the one or more actuators to move the cleaning head to a plurality of positions and determine an angular orientation of the toilet seat based at least in part on the plurality of positions. The cleaning head is in contact with the toilet seat or a rim of the toilet bowl in each of the positions.