A robotic system and methods are disclosed. A common axis is defined for an instrument and an energy applicator extending from the instrument. A manipulator has a plurality of links and actuators configured to move the links to position the instrument and energy applicator. A force/torque sensor coupled to the manipulator generates an output in response to forces/torques applied to the instrument. Controller(s) defines a centering point that intersects the common axis. Controller(s) model the instrument and the energy applicator as a virtual rigid body and determine forces/torques to apply to the virtual rigid body, which are determined, in part, based on the output of the force/torque sensor. Controller(s) control the manipulator to advance the energy applicator based on the determined forces/torques applied to the virtual rigid body and reorient the instrument such that the common axis pivots about the centering point during advancement of the energy applicator.