# Contact-Implicit Trajectory Optimization for Dynamic Object Manipulation

arXiv: https://arxiv.org/abs/2103.01104 · HTML: https://mlsanity.com/paper/2103.01104/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2021.

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

- [Physics-Driven Data Generation for Contact-Rich Manipulation via Trajectory Optimization](https://mlsanity.com/paper/2502.20382/) (2025)
- [Contact Points Discovery for Soft-Body Manipulations with Differentiable Physics](https://mlsanity.com/paper/2205.02835/) (2022)
- [Learning Reusable Manipulation Strategies](https://mlsanity.com/paper/2311.03293/) (2023)
- [Jacta: A Versatile Planner for Learning Dexterous and Whole-body Manipulation](https://mlsanity.com/paper/2408.01258/) (2024)
- [One-Shot Manipulation Strategy Learning by Making Contact Analogies](https://mlsanity.com/paper/2411.09627/) (2024)
- [RAPID: Robot Agentic Programming from Demonstrations](https://mlsanity.com/paper/2609.30249/) (2026)
- [Learning Pivoting Manipulation with Force and Vision Feedback Using Optimization-based Demonstrations](https://mlsanity.com/paper/2508.01082/) (2025)
- [Approximately Optimal Global Planning for Contact-Rich SE(2) Manipulation on a Graph of Reachable Sets](https://mlsanity.com/paper/2601.10827/) (2026)
- [Shooting for Contact: Contact-Implicit Multiple Shooting for Dynamic Motion Retargeting](https://mlsanity.com/paper/2608.03116/) (2026)

## Abstract (arXiv)

We present a reformulation of a contact-implicit optimization (CIO) approach that computes optimal trajectories for rigid-body systems in contact-rich settings. A hard-contact model is assumed, and the unilateral constraints are imposed in the form of complementarity conditions. Newton's impact law is adopted for enhanced physical correctness. The optimal control problem is formulated as a multi-staged program through a multiple-shooting scheme. This problem structure is exploited within the FORCES Pro framework to retrieve optimal motion plans, contact sequences and control inputs with increased computational efficiency. We investigate our method on a variety of dynamic object manipulation tasks, performed by a six degrees of freedom robot. The dynamic feasibility of the optimal trajectories, as well as the repeatability and accuracy of the task-satisfaction are verified through simulations and real hardware experiments on one of the manipulation problems.