# Folding Deformable Objects using Predictive Simulation and Trajectory Optimization

arXiv: https://arxiv.org/abs/1512.06922 · HTML: https://mlsanity.com/paper/1512.06922/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Dec 2015.

## Built on by (most cited first, 19 of 19)

- [PlasticineLab: A Soft-Body Manipulation Benchmark with Differentiable Physics](https://mlsanity.com/paper/2104.03311/) (2021)
- [Deep Imitation Learning of Sequential Fabric Smoothing From an Algorithmic Supervisor](https://mlsanity.com/paper/1910.04854/) (2019)
- [Mesh-based Dynamics with Occlusion Reasoning for Cloth Manipulation](https://mlsanity.com/paper/2206.02881/) (2022)
- [VisuoSpatial Foresight for Physical Sequential Fabric Manipulation](https://mlsanity.com/paper/2102.09754/) (2021)
- [Learning Latent Graph Dynamics for Visual Manipulation of Deformable Objects](https://mlsanity.com/paper/2104.12149/) (2021)
- [Self-supervised Cloth Reconstruction via Action-conditioned Cloth Tracking](https://mlsanity.com/paper/2302.09502/) (2023)
- [SculptBot: Pre-Trained Models for 3D Deformable Object Manipulation](https://mlsanity.com/paper/2309.08728/) (2023)
- [Cloth-Splatting: 3D Cloth State Estimation from RGB Supervision](https://mlsanity.com/paper/2501.01715/) (2025)
- [Cloth Manipulation Using Random-Forest-Based Imitation Learning](https://mlsanity.com/paper/1802.09661/) (2018)
- [InstructionBench: An Instructional Video Understanding Benchmark](https://mlsanity.com/paper/2504.05040/) (2025)
- [Learn2Fold: Structured Origami Generation with World Model Planning](https://mlsanity.com/paper/2603.29585/) (2026)
- [Robot Deformable Object Manipulation via NMPC-generated Demonstrations in Deep Reinforcement Learning](https://mlsanity.com/paper/2502.11375/) (2025)
- [Cloth Manipulation Planning on Basis of Mesh Representations with Incomplete Domain Knowledge and Voxel-to-Mesh Estimation](https://mlsanity.com/paper/2103.08137/) (2021)
- [Learning a General Model: Folding Clothing with Topological Dynamics](https://mlsanity.com/paper/2504.20720/) (2025)
- [Recognising Known Configurations of Garments For Dual-Arm Robotic Flattening](https://mlsanity.com/paper/2205.00225/) (2022)
- [Co-manipulation of soft-materials estimating deformation from depth images](https://mlsanity.com/paper/2301.05609/) (2023)
- [Topological reconstruction of sampled surfaces via Morse theory](https://mlsanity.com/paper/2405.17257/) (2024)
- [Imitation Learning-Based Path Generation for the Complex Assembly of Deformable Objects](https://mlsanity.com/paper/2505.24339/) (2025)
- [Dynamic robotic cloth folding with efficient Koopman operator-based model predictive control](https://mlsanity.com/paper/2605.18373/) (2026)

## Abstract (arXiv)

Robotic manipulation of deformable objects remains a challenging task. One such task is folding a garment autonomously. Given start and end folding positions, what is an optimal trajectory to move the robotic arm to fold a garment? Certain trajectories will cause the garment to move, creating wrinkles, and gaps, other trajectories will fail altogether. We present a novel solution to find an optimal trajectory that avoids such problematic scenarios. The trajectory is optimized by minimizing a quadratic objective function in an off-line simulator, which includes material properties of the garment and frictional force on the table. The function measures the dissimilarity between a user folded shape and the folded garment in simulation, which is then used as an error measurement to create an optimal trajectory. We demonstrate that our two-arm robot can follow the optimized trajectories, achieving accurate and efficient manipulations of deformable objects.