# Trajectory Optimization for Manipulation of Deformable Objects: Assembly of Belt Drive Units

arXiv: https://arxiv.org/abs/2106.00898 · HTML: https://mlsanity.com/paper/2106.00898/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jun 2021.

## Built on by (most cited first, 11 of 11)

- [Factory: Fast Contact for Robotic Assembly](https://mlsanity.com/paper/2205.03532/) (2022)
- [Robust Pivoting: Exploiting Frictional Stability Using Bilevel Optimization](https://mlsanity.com/paper/2203.11412/) (2022)
- [Learning Robot Manipulation from Cross-Morphology Demonstration](https://mlsanity.com/paper/2304.03833/) (2023)
- [PYROBOCOP : Python-based Robotic Control & Optimization Package for Manipulation and Collision Avoidance](https://mlsanity.com/paper/2106.03220/) (2021)
- [Chance-Constrained Optimization in Contact-Rich Systems for Robust Manipulation](https://mlsanity.com/paper/2203.02616/) (2022)
- [Robust Pivoting Manipulation using Contact Implicit Bilevel Optimization](https://mlsanity.com/paper/2303.08965/) (2023)
- [Grasping Trajectory Optimization with Point Clouds](https://mlsanity.com/paper/2403.05466/) (2024)
- [Learning Quasi-Static 3D Models of Markerless Deformable Linear Objects for Bimanual Robotic Manipulation](https://mlsanity.com/paper/2309.07609/) (2023)
- [KnotDLO: Toward Interpretable Knot Tying](https://mlsanity.com/paper/2506.22176/) (2025)
- [Learning Pivoting Manipulation with Force and Vision Feedback Using Optimization-based Demonstrations](https://mlsanity.com/paper/2508.01082/) (2025)
- [SILO: Simulation-in-the-Loop Sim-to-Real Transfer for Multi-Stage Cable Routing](https://mlsanity.com/paper/2607.04616/) (2026)

## Abstract (arXiv)

This paper presents a novel trajectory optimization formulation to solve the robotic assembly of the belt drive unit. Robotic manipulations involving contacts and deformable objects are challenging in both dynamic modeling and trajectory planning. For modeling, variations in the belt tension and contact forces between the belt and the pulley could dramatically change the system dynamics. For trajectory planning, it is computationally expensive to plan trajectories for such hybrid dynamical systems as it usually requires planning for discrete modes separately. In this work, we formulate the belt drive unit assembly task as a trajectory optimization problem with complementarity constraints to avoid explicitly imposing contact mode sequences. The problem is solved as a mathematical program with complementarity constraints (MPCC) to obtain feasible and efficient assembly trajectories. We validate the proposed method both in simulations with a physics engine and in real-world experiments with a robotic manipulator.