A novel DMP formulation for global and frame independent spatial scaling in the task space

In this work we study the DMP spatial scaling in the Cartesian space. The DMP framework is claimed to have the
ability to generalize learnt trajectories to new initial and goal positions, maintaining the desired kinematic pattern. However we show that the existing formulations present problems in trajectory spatial scaling when used in the Cartesian space for a wide variety of tasks and examine their cause. We then propose a novel formulation alleviating these problems. Trajectory generalization analysis, is performed by deriving the trajectory tracking dynamics. The proposed formulation is compared with the existing ones through simulations and experiments on a KUKA LWR 4+ robot.