Affine trajectory deformation for redundant manipulators

We propose a new method to smoothly deform trajectories of redundant manipulators in order to deal with unforeseen perturbations or to retarget captured motions into new environments. This method is based on the recently-developed affine deformation framework, which offers such advantages as closed-form solutions, one-step computation and no trajectory re-integration. Satisfaction of inequality constraints and dynamics optimization are seamlessly integrated into the framework. Applications of the method to interactive motion editing and motion transfer to humanoid robots are presented. Building on these developments, we offer a brief discussion of the concept of redundancy from the viewpoint of group theory.