# Learning Orbitally Stable Systems for Diagrammatically Teaching

arXiv: https://arxiv.org/abs/2309.10298 · HTML: https://mlsanity.com/paper/2309.10298/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 30 references that are in the map.
- First posted on arXiv 19 Sep 2023.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Analyzing Inverse Problems with Invertible Neural Networks](https://mlsanity.com/paper/1808.04730/) (2018)
- [RoboTurk: A Crowdsourcing Platform for Robotic Skill Learning through Imitation](https://mlsanity.com/paper/1811.02790/) (2018)
- [Coupling-based Invertible Neural Networks Are Universal Diffeomorphism Approximators](https://mlsanity.com/paper/2006.11469/) (2020)
- [Neural Dynamic Policies for End-to-End Sensorimotor Learning](https://mlsanity.com/paper/2012.02788/) (2020)
- [Riemannian Motion Policies](https://mlsanity.com/paper/1801.02854/) (2018)
- [ImitationFlow: Learning Deep Stable Stochastic Dynamic Systems by Normalizing Flows](https://mlsanity.com/paper/2010.13129/) (2020)
- [Euclideanizing Flows: Diffeomorphic Reduction for Learning Stable Dynamical Systems](https://mlsanity.com/paper/2005.13143/) (2020)
- [Learning Contracting Vector Fields For Stable Imitation Learning](https://mlsanity.com/paper/1804.04878/) (2018)
- [Geometric Fabrics: Generalizing Classical Mechanics to Capture the Physics of Behavior](https://mlsanity.com/paper/2109.10443/) (2021)
- [An Energy-based Approach to Ensure the Stability of Learned Dynamical Systems](https://mlsanity.com/paper/2003.11290/) (2020)

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

- [RH20T-P: A Primitive-Level Robotic Dataset Towards Composable Generalization Agents](https://mlsanity.com/paper/2403.19622/) (2024)

## Abstract (arXiv)

Diagrammatic Teaching is a paradigm for robots to acquire novel skills, whereby the user provides 2D sketches over images of the scene to shape the robot's motion. In this work, we tackle the problem of teaching a robot to approach a surface and then follow cyclic motion on it, where the cycle of the motion can be arbitrarily specified by a single user-provided sketch over an image from the robot's camera. Accordingly, we contribute the Stable Diffeomorphic Diagrammatic Teaching (SDDT) framework. SDDT models the robot's motion as an Orbitally Asymptotically Stable (O.A.S.) dynamical system that learns to stablize based on a single diagrammatic sketch provided by the user. This is achieved by applying a diffeomorphism, i.e. a differentiable and invertible function, to morph a known O.A.S. system. The parameterised diffeomorphism is then optimised with respect to the Hausdorff distance between the limit cycle of our modelled system and the sketch, to produce the desired robot motion. We provide novel theoretical insight into the behaviour of the optimised system and also empirically evaluate SDDT, both in simulation and on a quadruped with a mounted 6-DOF manipulator. Results show that we can diagrammatically teach complex cyclic motion patterns with a high degree of accuracy.