# MMP++: Motion Manifold Primitives with Parametric Curve Models

arXiv: https://arxiv.org/abs/2310.17072 · HTML: https://mlsanity.com/paper/2310.17072/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 49 references that are in the map.
- First posted on arXiv 26 Oct 2023.

## Builds on (most cited first, 14 of 14)

- [Diffusion Policy: Visuomotor Policy Learning via Action Diffusion](https://mlsanity.com/paper/2303.04137/) (2023)
- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [Learning Stable Deep Dynamics Models](https://mlsanity.com/paper/2001.06116/) (2020)
- [The Riemannian Geometry of Deep Generative Models](https://mlsanity.com/paper/1711.08014/) (2017)
- [Neural Dynamic Policies for End-to-End Sensorimotor Learning](https://mlsanity.com/paper/2012.02788/) (2020)
- [Dynamic Movement Primitives in Robotics: A Tutorial Survey](https://mlsanity.com/paper/2102.03861/) (2021)
- [A survey of robot learning from demonstrations for Human-Robot Collaboration](https://mlsanity.com/paper/1710.08789/) (2017)
- [Kernelized Movement Primitives](https://mlsanity.com/paper/1708.08638/) (2017)
- [Autoencoding Under Normalization Constraints](https://mlsanity.com/paper/2105.05735/) (2021)
- [Learning Riemannian Manifolds for Geodesic Motion Skills](https://mlsanity.com/paper/2106.04315/) (2021)
- [Geometric Autoencoders -- What You See is What You Decode](https://mlsanity.com/paper/2306.17638/) (2023)
- [Learning Contracting Vector Fields For Stable Imitation Learning](https://mlsanity.com/paper/1804.04878/) (2018)
- [On Explicit Curvature Regularization in Deep Generative Models](https://mlsanity.com/paper/2309.10237/) (2023)
- [A Geometric Perspective on Autoencoders](https://mlsanity.com/paper/2309.08247/) (2023)

## Built on by (most cited first, 5 of 5)

- [Motion Manifold Flow Primitives for Task-Conditioned Trajectory Generation under Complex Task-Motion Dependencies](https://mlsanity.com/paper/2407.19681/) (2024)
- [Differentiable Motion Manifold Primitives for Reactive Motion Generation under Kinodynamic Constraints](https://mlsanity.com/paper/2410.12193/) (2024)
- [Riemannian Time Warping: Multiple Sequence Alignment in Curved Spaces](https://mlsanity.com/paper/2506.01635/) (2025)
- [LEGO: Latent-space Exploration for Geometry-aware Optimization of Humanoid Kinematic Design](https://mlsanity.com/paper/2604.08636/) (2026)
- [Let the Dynamics Flow: Stable Flow Matching Dynamical Systems](https://mlsanity.com/paper/2606.03834/) (2026)

## Abstract (arXiv)

Motion Manifold Primitives (MMP), a manifold-based approach for encoding basic motion skills, can produce diverse trajectories, enabling the system to adapt to unseen constraints. Nonetheless, we argue that current MMP models lack crucial functionalities of movement primitives, such as temporal and via-points modulation, found in traditional approaches. This shortfall primarily stems from MMP's reliance on discrete-time trajectories. To overcome these limitations, we introduce Motion Manifold Primitives++ (MMP++), a new model that integrates the strengths of both MMP and traditional methods by incorporating parametric curve representations into the MMP framework. Furthermore, we identify a significant challenge with MMP++: performance degradation due to geometric distortions in the latent space, meaning that similar motions are not closely positioned. To address this, Isometric Motion Manifold Primitives++ (IMMP++) is proposed to ensure the latent space accurately preserves the manifold's geometry. Our experimental results across various applications, including 2-DoF planar motions, 7-DoF robot arm motions, and SE(3) trajectory planning, show that MMP++ and IMMP++ outperform existing methods in trajectory generation tasks, achieving substantial improvements in some cases. Moreover, they enable the modulation of latent coordinates and via-points, thereby allowing efficient online adaptation to dynamic environments.