Accurate trajectory transformations for redundant and nonredundant robots

This paper presents and compares four simple numerical algorithms for transforming a parameterized curve (a path or trajectory) from task space to joint space. They are based on Newton´s method, but offer substantially better accuracy for a given step size by making use of the continuity properties of the curve. They work for mechanisms with general geometry, and in both redundant and nonredundant situations; but they do not work at singularities or when the trajectory is out of reach. Some simulation results are presented