# Differentiable Motion Manifold Primitives for Reactive Motion Generation under Kinodynamic Constraints

arXiv: https://arxiv.org/abs/2410.12193 · HTML: https://mlsanity.com/paper/2410.12193/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 29 references that are in the map.
- First posted on arXiv 16 Oct 2024.

## Builds on (most cited first, 11 of 11)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [Motion Planning Networks: Bridging the Gap Between Learning-based and Classical Motion Planners](https://mlsanity.com/paper/1907.06013/) (2019)
- [On Explicit Curvature Regularization in Deep Generative Models](https://mlsanity.com/paper/2309.10237/) (2023)
- [GuSTO: Guaranteed Sequential Trajectory Optimization via Sequential Convex Programming](https://mlsanity.com/paper/1903.00155/) (2019)
- [Constrained Motion Planning Networks X](https://mlsanity.com/paper/2010.08707/) (2020)
- [A Geometric Perspective on Autoencoders](https://mlsanity.com/paper/2309.08247/) (2023)
- [Sampling-based optimal kinodynamic planning with motion primitives](https://mlsanity.com/paper/1809.02399/) (2018)
- [MMP++: Motion Manifold Primitives with Parametric Curve Models](https://mlsanity.com/paper/2310.17072/) (2023)
- [State Supervised Steering Function for Sampling-based Kinodynamic Planning](https://mlsanity.com/paper/2206.07227/) (2022)
- [Motion Manifold Flow Primitives for Task-Conditioned Trajectory Generation under Complex Task-Motion Dependencies](https://mlsanity.com/paper/2407.19681/) (2024)

## Built on by (most cited first, 1 of 1)

- [Non-Prehensile Throwing: A Reinforcement Learning Perspective](https://mlsanity.com/paper/2609.00771/) (2026)

## Abstract (arXiv)

Real-time motion generation -- which is essential for achieving reactive and adaptive behavior -- under kinodynamic constraints for high-dimensional systems is a crucial yet challenging problem. We address this with a two-step approach: offline learning of a lower-dimensional trajectory manifold of task-relevant, constraint-satisfying trajectories, followed by rapid online search within this manifold. Extending the discrete-time Motion Manifold Primitives (MMP) framework, we propose Differentiable Motion Manifold Primitives (DMMP), a novel neural network architecture that encodes and generates continuous-time, differentiable trajectories, trained using data collected offline through trajectory optimizations, with a strategy that ensures constraint satisfaction -- absent in existing methods. Experiments on dynamic throwing with a 7-DoF robot arm demonstrate that DMMP outperforms prior methods in planning speed, task success, and constraint satisfaction.