a sheet of paper may need to come to a full stop as discussed above a nominal path may be generated by prescribing a path velocity v similarly a nominal angular velocity u03c9 may be generated the path may be chosen to correct for a certain input registration error in developing a nominal path for a particular application a reference path velocity v may be used for a registration distance the reference velocity may be a constant velocity a nominal angular velocity may be determined and used together with the reference velocity to prescribe a path on the sheet of paper it may be desirable to have velocity independent paths for example it may be desirable to construct an angular velocity u03c9 as a function of the coordinate s along the path for example when the reference velocity is constant and equal to unity then a nominal s may be expressed as when the reference velocity is a constant v c but not equal to unity the corresponding angular velocity u03c9 may be expressed as when the reference velocity is a variable v t the angular velocity w s may be expressed as the equations associated with non constant reference velocity may be solved numerically in view of the above an angular velocity profile u03c9 s may be obtained as a function of coordinate s along the path in order to follow the same path for different path velocities v t the position s along a path may need to be determined this determination may be based on the integration of the equations discussed above in real time control this determination may mean adding a u03b4s v t u00d7.