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. in 2014 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 orien-
tation with this formulation, producing a motion pattern highly deviant from the
desired and highlight its source. A correct formulation is then proposed that alle-
viates 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.