An optimal path-generation algorithm for manufacturing of arbitrarily curved surfaces using uncalibrated vision

Multiple industrial manufacturing tasks require a complex path to be followed precisely over an arbitrary surface which has a geometry that is not known with precision. Examples of such tasks include welding, glue-application, cutting, plasma-spraying, etc., over commercial plates whose geometry cannot be known in advance. Such processes are in general referred to as surface manufacturing. In this work, a path is traced over the surface in an optimal fashion, using the concept of geodesic mapping. By definition, a geodesic line is the shortest line that joins two points over a surface whose algebraic representation is known. Such an optimal solution of a problem, associated with variational calculus, is the approach employed for mapping complex paths, defined in a data base, over a surface of arbitrary geometry. The straight-line segments in which a complex path can be divided are mapped onto an arbitrary surface as geodesic lines. The presented algorithm enables a user to interact with the system in a simple and efficient manner using a commercial computer pointing device. The algorithm was tested experimentally in an industrial maneuver involving arc welding, using an industrial robot and a method of vision-based, robot guidance known as camera-space manipulation. This method has the advantage of not requiring calibration of optical or mechanical components.