A New Trajectory Deformation Algorithm Based on Affine Transformations

Abstract

We propose a new approach to deform robot trajectories based on affine transformations. At the heart of our approach is the concept of affine invariance: Trajectories are deformed in order to avoid unexpected obstacles or to achieve new objectives but, at the same time, certain definite features of the original motions are preserved. Such features include, for instance, trajectory smoothness, periodicity, affine velocity, or more generally, all affine-invariant features, which are of particular importance in human-centered applications. Furthermore, this approach enables one to “convert” the constraints and optimization objectives regarding the deformed trajectory into constraints and optimization objectives regarding the matrix of the deformation in a natural way, making constraints satisfaction and optimization substantially easier and faster in many cases. As illustration, we present an application to the transfer of human movements to humanoid robots while preserving equiaffine velocity, a well-established invariant of human hand movements. Building on the presented affine deformation framework, we finally revisit the concept of trajectory redundancy from the viewpoint of group theory.