IMMP++: Isometric Motion Manifold Primitives with Parametric Curve Models

The Motion Manifold Primitive (MMP) produces, for a given task, a continuous manifold of trajectories, each of which can successfully complete the task, addressing the challenge of high dimensionality in trajectory data. However, the discrete-time trajectory representations used in existing MMP methods lack important functionalities of movement primitives (e.g., temporal modulation, via-points modulation, etc.) found in other conventional methods that employ parametric curve representations. To address these limitations, we introduce Motion Manifold Primitives++ (MMP++), which combines the advantages of the MMP and conventional methods by applying the MMP framework to the parametric curve representations. However, we observe that the performance of MMP++ can sometimes degrade significantly due to geometric distortion in the latent space -- by distortion, we mean that similar motions are not located nearby in the latent space. To mitigate this issue, we propose Isometric Motion Manifold Primitives++ (IMMP++), where the latent coordinate space preserves the geometry of the manifold. Experimental results with 2-DoF planar motions and 7-DoF robot arm tasks demonstrate that MMP++ and IMMP++ outperform existing methods, in some cases by a significant margin, while maintaining the advantages of parametric curve representations.