# Learning Equality Constraints for Motion Planning on Manifolds

arXiv: https://arxiv.org/abs/2009.11852 · HTML: https://mlsanity.com/paper/2009.11852/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Sep 2020.

## Built on by (most cited first, 9 of 9)

- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [ReKep: Spatio-Temporal Reasoning of Relational Keypoint Constraints for Robotic Manipulation](https://mlsanity.com/paper/2409.01652/) (2024)
- [Learning Models as Functionals of Signed-Distance Fields for Manipulation Planning](https://mlsanity.com/paper/2110.00792/) (2021)
- [Regularized Deep Signed Distance Fields for Reactive Motion Generation](https://mlsanity.com/paper/2203.04739/) (2022)
- [Gaussian Process Constraint Learning for Scalable Chance-Constrained Motion Planning from Demonstrations](https://mlsanity.com/paper/2112.04612/) (2021)
- [A Survey on the Integration of Machine Learning with Sampling-based Motion Planning](https://mlsanity.com/paper/2211.08368/) (2022)
- [Physics-informed Neural Motion Planning on Constraint Manifolds](https://mlsanity.com/paper/2403.05765/) (2024)
- [Toward Generalist Neural Motion Planners for Robotic Manipulators: Challenges and Opportunities](https://mlsanity.com/paper/2603.24318/) (2026)
- [Entropy Transformer Networks: A Learning Approach via Tangent Bundle Data Manifold](https://mlsanity.com/paper/2307.12517/) (2023)

## Abstract (arXiv)

Constrained robot motion planning is a widely used technique to solve complex robot tasks. We consider the problem of learning representations of constraints from demonstrations with a deep neural network, which we call Equality Constraint Manifold Neural Network (ECoMaNN). The key idea is to learn a level-set function of the constraint suitable for integration into a constrained sampling-based motion planner. Learning proceeds by aligning subspaces in the network with subspaces of the data. We combine both learned constraints and analytically described constraints into the planner and use a projection-based strategy to find valid points. We evaluate ECoMaNN on its representation capabilities of constraint manifolds, the impact of its individual loss terms, and the motions produced when incorporated into a planner.