Mixed Orientation ProMPs and Their Application in Attitude Trajectory Planning

The application of motion primitives to encode robot motion has garnered considerable attention in the field of academic research. Existing models predominantly focus on reproducing task trajectory in relation to position, often neglecting the significance of orientation. Orientation Probabilistic Movement Primitives (ProMPs) indirectly encode motion primitives for attitude by utilizing their trajectory probabilities on Riemannian manifolds, specifically the 3-sphere \(\mathcal {S}^3\) . However, assuming a Gaussian distribution imposes constraints on its abilities. We propose Mixed Orientation ProMPs to enhance trajectory planning and minimize the occurrence of singular configurations. This model consists of multiple separate Gaussian distributions in the tangent space, enabling the approximation of any distribution. Furthermore, optimization objective functions of the Lagrangian type can incorporate constraints, such as singularity avoidance, and others. Finally, the effectiveness and reliability of the algorithm were validated through trajectory planning experiments conducted on the UR5 robotic arm.