# A Recurrent Differentiable Engine for Modeling Tensegrity Robots Trainable with Low-Frequency Data

arXiv: https://arxiv.org/abs/2203.00041 · HTML: https://mlsanity.com/paper/2203.00041/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 50 references that are in the map.
- First posted on arXiv 28 Feb 2022.

## Builds on (most cited first, 25 of 25)

- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Learning agile and dynamic motor skills for legged robots](https://mlsanity.com/paper/1901.08652/) (2019)
- [DiffTaichi: Differentiable Programming for Physical Simulation](https://mlsanity.com/paper/1910.00935/) (2019)
- [Graph networks as learnable physics engines for inference and control](https://mlsanity.com/paper/1806.01242/) (2018)
- [Closing the Sim-to-Real Loop: Adapting Simulation Randomization with Real World Experience](https://mlsanity.com/paper/1810.05687/) (2018)
- [Active Domain Randomization](https://mlsanity.com/paper/1904.04762/) (2019)
- [A Differentiable Physics Engine for Deep Learning in Robotics](https://mlsanity.com/paper/1611.01652/) (2016)
- [gradSim: Differentiable simulation for system identification and visuomotor control](https://mlsanity.com/paper/2104.02646/) (2021)
- [Flexible Neural Representation for Physics Prediction](https://mlsanity.com/paper/1806.08047/) (2018)
- [Scalable Differentiable Physics for Learning and Control](https://mlsanity.com/paper/2007.02168/) (2020)
- [DiSECt: A Differentiable Simulation Engine for Autonomous Robotic Cutting](https://mlsanity.com/paper/2105.12244/) (2021)
- [MotionRNN: A Flexible Model for Video Prediction with Spacetime-Varying Motions](https://mlsanity.com/paper/2103.02243/) (2021)
- [Interpretable Social Anchors for Human Trajectory Forecasting in Crowds](https://mlsanity.com/paper/2105.03136/) (2021)
- [Bi-directional Domain Adaptation for Sim2Real Transfer of Embodied Navigation Agents](https://mlsanity.com/paper/2011.12421/) (2020)
- [Differentiable Physics Models for Real-world Offline Model-based Reinforcement Learning](https://mlsanity.com/paper/2011.01734/) (2020)
- [Differentiable Molecular Simulations for Control and Learning](https://mlsanity.com/paper/2003.00868/) (2020)
- [Encoding Physical Constraints in Differentiable Newton-Euler Algorithm](https://mlsanity.com/paper/2001.08861/) (2020)
- [Interactive Differentiable Simulation](https://mlsanity.com/paper/1905.10706/) (2019)
- [Deep Reinforcement Learning for Tensegrity Robot Locomotion](https://mlsanity.com/paper/1609.09049/) (2016)
- [A First Principles Approach for Data-Efficient System Identification of Spring-Rod Systems via Differentiable Physics Engines](https://mlsanity.com/paper/2004.13859/) (2020)
- [A Differentiable Newton Euler Algorithm for Multi-body Model Learning](https://mlsanity.com/paper/2010.09802/) (2020)
- [Sim2Sim Evaluation of a Novel Data-Efficient Differentiable Physics Engine for Tensegrity Robots](https://mlsanity.com/paper/2011.04929/) (2020)
- [A Bio-Inspired Tensegrity Manipulator with Multi-DOF, Structurally Compliant Joints](https://mlsanity.com/paper/1604.08667/) (2016)
- [Design, Simulation, and Testing of a Flexible Actuated Spine for Quadruped Robots](https://mlsanity.com/paper/1804.06527/) (2018)
- [Compensation for undefined behaviors during robot task execution by switching controllers depending on embedded dynamics in RNN](https://mlsanity.com/paper/2003.04862/) (2020)

## Built on by (most cited first, 2 of 2)

- [Real2Sim2Real Transfer for Control of Cable-driven Robots via a Differentiable Physics Engine](https://mlsanity.com/paper/2209.06261/) (2022)
- [Prof. Robot: Differentiable Robot Rendering Without Static and Self-Collisions](https://mlsanity.com/paper/2503.11269/) (2025)

## Abstract (arXiv)

Tensegrity robots, composed of rigid rods and flexible cables, are difficult to accurately model and control given the presence of complex dynamics and high number of DoFs. Differentiable physics engines have been recently proposed as a data-driven approach for model identification of such complex robotic systems. These engines are often executed at a high-frequency to achieve accurate simulation. Ground truth trajectories for training differentiable engines, however, are not typically available at such high frequencies due to limitations of real-world sensors. The present work focuses on this frequency mismatch, which impacts the modeling accuracy. We proposed a recurrent structure for a differentiable physics engine of tensegrity robots, which can be trained effectively even with low-frequency trajectories. To train this new recurrent engine in a robust way, this work introduces relative to prior work: (i) a new implicit integration scheme, (ii) a progressive training pipeline, and (iii) a differentiable collision checker. A model of NASA's icosahedron SUPERballBot on MuJoCo is used as the ground truth system to collect training data. Simulated experiments show that once the recurrent differentiable engine has been trained given the low-frequency trajectories from MuJoCo, it is able to match the behavior of MuJoCo's system. The criterion for success is whether a locomotion strategy learned using the differentiable engine can be transferred back to the ground-truth system and result in a similar motion. Notably, the amount of ground truth data needed to train the differentiable engine, such that the policy is transferable to the ground truth system, is 1% of the data needed to train the policy directly on the ground-truth system.