# Non-prehensile Planar Manipulation via Trajectory Optimization with Complementarity Constraints

arXiv: https://arxiv.org/abs/2109.13145 · HTML: https://mlsanity.com/paper/2109.13145/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Sep 2021.

## Built on by (most cited first, 13 of 13)

- [Flow Matching Imitation Learning for Multi-Support Manipulation](https://mlsanity.com/paper/2407.12381/) (2024)
- [DyWA: Dynamics-adaptive World Action Model for Generalizable Non-prehensile Manipulation](https://mlsanity.com/paper/2503.16806/) (2025)
- [Physics-Driven Data Generation for Contact-Rich Manipulation via Trajectory Optimization](https://mlsanity.com/paper/2502.20382/) (2025)
- [Nonprehensile Planar Manipulation through Reinforcement Learning with Multimodal Categorical Exploration](https://mlsanity.com/paper/2308.02459/) (2023)
- [CORN: Contact-based Object Representation for Nonprehensile Manipulation of General Unseen Objects](https://mlsanity.com/paper/2403.10760/) (2024)
- [ROS-PyBullet Interface: A Framework for Reliable Contact Simulation and Human-Robot Interaction](https://mlsanity.com/paper/2210.06887/) (2022)
- [Learning Visuotactile Estimation and Control for Non-prehensile Manipulation under Occlusions](https://mlsanity.com/paper/2412.13157/) (2024)
- [Dynamic object goal pushing with mobile manipulators through model-free constrained reinforcement learning](https://mlsanity.com/paper/2502.01546/) (2025)
- [Is Linear Feedback on Smoothed Dynamics Sufficient for Stabilizing Contact-Rich Plans?](https://mlsanity.com/paper/2411.06542/) (2024)
- [Incremental Few-Shot Adaptation for Non-Prehensile Object Manipulation using Parallelizable Physics Simulators](https://mlsanity.com/paper/2409.13228/) (2024)
- [Hierarchical Contact-Rich Trajectory Optimization for Multi-Modal Manipulation using Tight Convex Relaxations](https://mlsanity.com/paper/2503.07963/) (2025)
- [Physics-Informed Eikonal Caging for Whole-Arm Manipulation Planning](https://mlsanity.com/paper/2606.22143/) (2026)
- [Learning Pivoting Manipulation with Force and Vision Feedback Using Optimization-based Demonstrations](https://mlsanity.com/paper/2508.01082/) (2025)

## Abstract (arXiv)

Contact adaption is an essential capability when manipulating objects. Two key contact modes of non-prehensile manipulation are sticking and sliding. This paper presents a Trajectory Optimization (TO) method formulated as a Mathematical Program with Complementarity Constraints (MPCC), which is able to switch between these two modes. We show that this formulation can be applicable to both planning and Model Predictive Control (MPC) for planar manipulation tasks. We numerically compare: (i) our planner against a mixed integer alternative, showing that the MPCC planer converges faster, scales better with respect to time horizon, and can handle environments with obstacles; (ii) our controller against a state-of-the-art mixed integer approach, showing that the MPCC controller achieves better tracking and more consistent computation times. Additionally, we experimentally validate both our planner and controller with the KUKA LWR robot on a range of planar manipulation tasks.