A correct formulation for the Orientation Dynamic Movement Primitives for robot control in the Cartesian space

Dynamic movement primitives (DMP) are an efficient way for learning and reproducing complex robot behaviors. A singularity free DMP formulation for orientation in the Cartesian space is proposed by Ude et al. [1] and has been largely adopted by the research community. In this work, we demonstrate the undesired oscillatory behavior that may arise when controlling the robot’s orientation with this formulation, producing a motion pattern highly deviant from the desired and highlight its source. A correct formulation is then proposed that alleviates such problems while guaranteeing generation of orientation parameters that lie in SO(3). We further show that all aspects and advantages of DMP including ease of learning, temporal and spatial scaling and the ability to include coupling terms are maintained in the proposed formulation. Simulations and experiments with robot control in SO(3) are performed to demonstrate the performance of the proposed formulation and compare it with the previously adopted one.