Bounded deviation joint path algorithms for piecewise cubic polynomial trajectories

Presented are three bounded deviation joint path (BDJP) algorithms which generate only enough intermediate knots, sampled from a smooth Cartesian path, for piecewise cubic polynomial joint trajectories. The first algorithm is basically the one proposed by R.H. Taylor (1979), and it is based on position transformations. The second algorithm utilizes inverse velocity transformations, and direct velocity transformations are used in the third algorithm. The proposed BDJP algorithms are aimed to be used in process applications of industrial robots, such as arc welding and contour grinding, in which the desired Cartesian paths are smooth free-formed curves and it is necessary to keep the manipulator acceptably close to the desired path