Methods, apparatus, and systems for performing minimally invasive surgery through an aperture of a patient. In accordance with a method, parameters are received from an input device associated with a surgeon, the parameters indicating a desired state of an end effector of a surgical instrument oriented through the aperture. The surgical instrument is included in a mechanical assembly having a first set of joints. Instructions are then computed for controlling the mechanical assembly using the received parameters by computing instructions for controlling a second set joints, the second set of joints including the first set of joints and an additional joint, the additional joint being absent from the mechanical assembly. The mechanical assembly is then driven so as to move the end effector toward the desired state based on the computed instructions.