Industrial robot motion involving a generation of small shapes and features presents a different set of problems than traditional robot motion.  Small motion is much more affected by friction, backlash, and other sources of lost motion.  This effect is more pronounced on the major axes, especially where backlash is not biased to one direction by the effects of gravity, e.g., at a first axis associated with a robot base secured to a floor. 
Various methods have been attempted to mitigate the effects of friction, backlash, and other sources of lost motion.  One known method relies on fixing the major axes and most minor axes, and moving only one or more of the wrist axes.  While this eliminates the major source of path error in short moves, a side effect is that the robot's path cannot generally be maintained.  Applications such as water jet cutting have had some tolerance for path deviation, as long as the deviation is along the tool approach vector.  However, the known applications with tolerance for path deviation still sacrifice orientation. 
Further known methods for controlling robot motion involving small shapes and features are described, for example, in U.S. Pat.  No.  7,209,802 to Jerregard et al.,  U.S. Pat.  No.  6,064,168 to Tao et al.,  and U.S. Pat.  No.  4,969,722 to Akeel, the entire disclosures of which are hereby incorporated herein by reference. 
U.S. Pat.  No.  7,209,802 to Jerregard et al.  discloses a method for controlling a robot wherein the procedure is carried out with the robot while maintaining the robot immobile in axes that are not required to carry out the procedure.  The method permits operations to be carried out by industrial robots by minimizing the number of axes/shafts that are moved during any procedure.  By minimizing or eliminating movement of a shaft or axis, the amount of friction/tolerance that must be accounted for in the procedure is reduced.  This allows procedures to be carried out with greater precision.  Specifically, one or more of the arms will be immobile about one or more axes of movement during the processing, such as hole cutting.  Excluding one or more axes reduces the influence of friction and tolerances for the robot/manipulator when following a given path.  Typically, all axes that are not used will be totally inactive or still during a procedure.  Best tolerances may be achieved when using as few axes as possible during a procedure.  Usually, only one or more axes are moved, which are located closest to the process and/or tool. 
The Jerregard et al.  method specifically describes cutting a circular hole in a workpiece.  Initially, the robot is centered above the origin of the circle.  The tool center point (TCP) is moved to coincide with the wrist center point (WCP).  All reorientations of the robot will maintain immobile the axes that are to be static or still during the hole cutting.  Next, it is determined how the axes that are to be mobile during the hole cutting are to be moved to carry out the hole cutting.  For example, a relationship in a first plane is determined between a reorientation angle alpha and a radius of the circle to be cut.  This first plane may be the X-Z plane in a XYZ coordinate system.  During this measurement, the other axes of the robot may remain stationary.  A similar relationship for an angle gamma may then be determined in a second plane.  This second plane may be perpendicular to the first plane.  This second plane may be the Y-Z plane.  During the determination of the relationship between the reorientation angle gamma and the radius, the angle alpha may be held at 0.  As the relationships are determined, maximum and minimum values may be determined for each angle.  After determining the angles that the relevant axes are displaced to carry out the hole cutting, the hole may be cut. 
U.S. Pat.  No.  6,064,168 to Tao et al.  discloses a method of controlling movement of a robot that includes moving only the wrist portion about two of the wrist axes to achieve a repeated and cyclical movement, such as a back-and-forth movement of the tool relative to a preselected path.  Since only the wrist is moved, the range of available tool positions can be determined.  In most instances, the desired position of the tool as it deviates from the path is outside of the range of available tool positions, given that only the wrist will move.  The method of this invention includes determining a target position within the range of available positions that best corresponds to the desired position of the tool.  A unique inverse kinematics solution, which includes fixing one of the wrist axes, is used to determine the wrist orientation required to place the tool into the target position. 
In general terms, Tao et al.  discloses a method for controlling movement of a tool that is supported by a robot having a wrist that is moveable about a plurality of wrist axes that are associated with a wrist origin.  The method includes several basic steps.  First, the tool is positioned adjacent a preselected tool path by moving the robot arm into an appropriate orientation.  The wrist origin is then moved along a wrist path that corresponds to the preselected tool path.  While the wrist origin is moving along the wrist path, the robot wrist moves so that the tool is moved in a first direction away from the preselected tool path.  Only the robot wrist moves about at least one of the wrist axes to move the tool away from the path.  After the tool has reached a desired distance from the preselected path, it is then moved in a second direction back toward the path by moving only the robot wrist.  The movement of the tool toward and away from the path is cyclically repeated while the wrist origin moves along the wrist path.  The method of Tao et al.  achieves a weaving-like motion of a tool such as a welding torch by moving only the robot wrist. 
U.S. Pat.  No.  4,969,722 to Akeel discloses a device for delivering a collimated beam, such as a laser beam, along a beam path to a workpiece.  The device includes a relatively simple focusing lens means to allow the generation of a curve on the workpiece at high speeds and trace curves having various radii on the workpiece.  The focusing lens is driven by a single gear mechanism to control both focusing and the radii of the curves traced on the workpiece.  The device includes a rotational first axis, a housing means defining an internal cavity and a focusing lens received within the internal cavity and intersecting the first axis for focusing the beam.  The lens is rotatably supported on the first axis and has a focal point along a focal axis offset a first distance from the first axis at the lens means.  A continuous, unobstructed hollow passage extends along and surrounds the first axis to the lens so that a beam traveling along the first axis is deflected by the lens from the first axis to travel along a focused beam axis inclined with respect to the first and focal axes and to intersect the focal axis at the focal point.  Rotation of the lens about the first axis causes the focal point to trace a curve on the workpiece. 
Generally, Akeel describes a device having an independent rotational second axis on which the lens is rotatably supported.  Rotation of the lens about the second axis varies the distance between the first axis and the focal axis.  The lens is supported in a first housing part linearly movable relative to a second housing part along the focal axis.  In one embodiment of Akeel, a gear mechanism in cooperation with coupling means drives the first housing part along the focal axis for controlling the location of the focal point relative to the workpiece.  The gear rotates the first and second housing parts together about the second axis to vary the first distance between the first and focal axes.  A low-cost, low-weight adjustable beam shifting and focusing arrangement is provided.  The device has particularly utility in cutting operations, such as metal cutting operations wherein circles have to be cut in metal at high speed.  The device is usually associated with control means and feedback sensors that are necessary for the automatic and programmed operation of the device. 
Shortcomings of known systems and methods include: limited cutting approach orientation changes; typical cuts tend to have conical sides; the methods work best with thin materials; part Z placement variation causes formation of elliptical holes; the methods work best with tooling with an approach axis close to the wrist center, which causes limited robot reach; the methods are primarily applicable to short moves; and a Z path is not generally maintained by the methods. 
There is a continuing need for a system and method that maintains cutting approach orientation, allows formation of cuts with substantially squared sides, works well with thin or thick materials, maintains hole accuracy regardless of part Z coordinate placement, allows use of standard water jet tooling for full robot reach, and maintains the robot path in XYZ coordinates during operation.