Method of real-time machine path planning from a math model

#This invention relates to control of multi-axis machines and particularly to driving such machines from a mathematical model corresponding to the machine path and for real time path planning.

#Because the styling of an automobile is so critical to customer acceptance, considerable effort is expended in designing and accurately representing the visible inner and outer surfaces of the vehicle. Most of this design effort has historically involved the creation of concept designs (artist sketches, renderings and drawings) followed by the sculpturing of 3/8 or full scale clay models. It has been proposed to integrate computer aided design (CAD) systems into this design process. Models designed or represented within such CAD systems can be rendered on a two-dimensional graphics screen using color and shading to produce life-like images of the defining mathematical surfaces. Despite these powerful CAD design and evaluation tools, designers and others find it necessary to create, view and evaluate a hard, physical, three-dimensional realization of the mathematical model in order to effectively evaluate a particular concept. Hard models are also needed to evaluate the aerodynamic performance of a proposed design. Once a model has been designed on a CAD system, an accurate, hard model ideally should be produced rapidly with minimal user involvement. In the best of situations, hard model generation would proceed so rapidly that the process of CAD design and model realization/evaluation could proceed interactively.

#Prior attempts to use the CAD mathemetical models as data sources for numerically controlled milling machine control resulted in the procedure of calculating all the points for the cutting tool path and storing the points in the N/C machine. Because so many points are required to define the cutting path for the entire model, the time required is burdensome. For a three-axis milling machine, many hours are required to calculate the points from the CAD model. For instance, a pre-cutting path generation time of 14 hours is required for a 3/8 scale concept model. For a five-axis machine, even more time may be required to calculate the tool path. According to the present invention, a more efficient way of generating a tool path from CAD data and transferring it to the cutting machine permits cutting to begin in a minute (instead of hours or days) from the beginning of the calculations. Thereafter, the tool path calculation proceeds in real time and is fed to the machine one line at a time so that minimal data storage space is required. The cutting machine may be an N/C milling machine which can cut any hardness material from clay to steel with high accuracy, or a robot carrying a mill which is faster, less expensive and more flexible than most milling machines but has lower accuracy.

#The above and other advantages of the invention will become more apparent from the following description taken in conjunction with the accompanying drawings wherein like references refer to like parts and wherein:

#FIG. 1 is a schematic drawing of a system for carrying out the method of the invention;

#FIG. 2 is a schematic drawing illustrating the transformation from two dimensional parametric space to three dimensional Cartesian space by a mathematical model;

#The ensuing description is directed to a method of path planning of a robot for cutting a clay model of a vehicle. The method has much broader applications, however. For example, the robot may be used for trajectory tracking functions such as spray painting or applying sealant to a vehicle body. The path planning method can be applied to machines other than robots such as 3-axis or 5-axis milling machines to realize efficient tool path planning and the virtual elimination of computation time while maintaining the very high accuracy of such milling machines.

#The diagram of FIG. 1 shows a system to rapidly cut 3/8 scale clay models designed on a computer aided design (CAD) system 10. Mathematical surfaces of vehicle exteriors can be rapidly designed at a CAD system terminal, and color images of almost photographic realism can be quickly generated and displayed on two-dimensional console screens. The designed surface or math model is transferred to a microprocessor based computer 12 by direct line connection or by other means such as floppy discs. The computer 12 which is a VAX (TM) for instance, is directly coupled by a serial data link 13 to a robot controller 14 which comprises a main central processing unit (CPU) and a path CPU. The robot controller 14, in turn, controls a robot 16 having a plurality of joints 18 and carrying a milling cutter 20. A mass of clay 22 is positioned to be shaped by the cutter 20 to give three-dimensional reality to the math surface. The resulting model can be evaluated for appearance by observation and for aerodynamics by wind tunnel tests. Any changes can be incorporated into the math model by the CAD system 10 and can be immediately recut by the robot, addressing only the region incorporating the change.

#The math model of a surface provided by the CAD 10 typically uses B-spline formulas which relate parametric space to real world Cartesian space. The spline surface is a linear combination of control points weighted by separable bivariate tensor-product B-splines. This well known mathematical process is fully set forth in the publications, Besl, P. J., "Geometric Modeling and Computer Vision", Proceedings of the IEEE, Vol. 76, No. 8, August 1988, and de Boor, Practical Guide to Splines", Springer-Verlag, New York, which are incorporated herein by reference. As illustrated in FIG. 2, the corresponding surface in parametric space 27 is a plane defined by the parameters u and v. It is necessary to use techniques that marry the purely geometric information provided by the mathematical surface definitions with physical smoothness requirements demanded by robot tool tip motions (requirements on velocities and accelerations) in order to calculate paths in the parametric space that can later be tracked to produce Cartesian motions which accurately follow the desired space curves on the surface in the real world Cartesian space.