# Robust Pivoting Manipulation using Contact Implicit Bilevel Optimization

arXiv: https://arxiv.org/abs/2303.08965 · HTML: https://mlsanity.com/paper/2303.08965/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 56 references that are in the map.
- First posted on arXiv 15 Mar 2023.

## Builds on (most cited first, 20 of 20)

- [GelSlim: A High-Resolution, Compact, Robust, and Calibrated Tactile-sensing Finger](https://mlsanity.com/paper/1803.00628/) (2018)
- [Tactile Dexterity: Manipulation Primitives with Tactile Feedback](https://mlsanity.com/paper/2002.03236/) (2020)
- [Trajectory Optimization for Manipulation of Deformable Objects: Assembly of Belt Drive Units](https://mlsanity.com/paper/2106.00898/) (2021)
- [Simultaneous Tactile Exploration and Grasp Refinement for Unknown Objects](https://mlsanity.com/paper/2103.00655/) (2021)
- [Robust Pivoting: Exploiting Frictional Stability Using Bilevel Optimization](https://mlsanity.com/paper/2203.11412/) (2022)
- [Robust Trajectory Optimization over Uncertain Terrain with Stochastic Complementarity](https://mlsanity.com/paper/2009.12409/) (2020)
- [Risk-Aware Motion Planning for a Limbed Robot with Stochastic Gripping Forces Using Nonlinear Programming](https://mlsanity.com/paper/2006.02656/) (2020)
- [PYROBOCOP : Python-based Robotic Control & Optimization Package for Manipulation and Collision Avoidance](https://mlsanity.com/paper/2106.03220/) (2021)
- [Imitation and Supervised Learning of Compliance for Robotic Assembly](https://mlsanity.com/paper/2111.10488/) (2021)
- [Simultaneous Tactile Estimation and Control of Extrinsic Contact](https://mlsanity.com/paper/2303.03385/) (2023)
- [Application of Wrench based Feasibility Analysis to the Online Trajectory Optimization of Legged Robots](https://mlsanity.com/paper/1712.06833/) (2017)
- [Contact-Implicit Trajectory Optimization using Orthogonal Collocation](https://mlsanity.com/paper/1809.06436/) (2018)
- [Manipulation with Shared Grasping](https://mlsanity.com/paper/2006.02996/) (2020)
- [Simultaneous Contact-Rich Grasping and Locomotion via Distributed Optimization Enabling Free-Climbing for Multi-Limbed Robots](https://mlsanity.com/paper/2207.01418/) (2022)
- [Local Trajectory Stabilization for Dexterous Manipulation via Piecewise Affine Approximations](https://mlsanity.com/paper/1909.08045/) (2019)
- [Design of Adaptive Compliance Controllers for Safe Robotic Assembly](https://mlsanity.com/paper/2204.10447/) (2022)
- [Tactile-Filter: Interactive Tactile Perception for Part Mating](https://mlsanity.com/paper/2303.06034/) (2023)
- [Stability Analysis of Discrete-Time Linear Complementarity Systems](https://mlsanity.com/paper/2012.13287/) (2020)
- [Mediating between Contact Feasibility and Robustness of Trajectory Optimization through Chance Complementarity Constraints](https://mlsanity.com/paper/2105.09973/) (2021)
- [Chance-Constrained Optimization in Contact-Rich Systems for Robust Manipulation](https://mlsanity.com/paper/2203.02616/) (2022)

## Built on by (most cited first, 3 of 3)

- [Is Linear Feedback on Smoothed Dynamics Sufficient for Stabilizing Contact-Rich Plans?](https://mlsanity.com/paper/2411.06542/) (2024)
- [Hierarchical Contact-Rich Trajectory Optimization for Multi-Modal Manipulation using Tight Convex Relaxations](https://mlsanity.com/paper/2503.07963/) (2025)
- [Learning Pivoting Manipulation with Force and Vision Feedback Using Optimization-based Demonstrations](https://mlsanity.com/paper/2508.01082/) (2025)

## Abstract (arXiv)

Generalizable manipulation requires that robots be able to interact with novel objects and environment. This requirement makes manipulation extremely challenging as a robot has to reason about complex frictional interactions with uncertainty in physical properties of the object and the environment. In this paper, we study robust optimization for planning of pivoting manipulation in the presence of uncertainties. We present insights about how friction can be exploited to compensate for inaccuracies in the estimates of the physical properties during manipulation. Under certain assumptions, we derive analytical expressions for stability margin provided by friction during pivoting manipulation. This margin is then used in a Contact Implicit Bilevel Optimization (CIBO) framework to optimize a trajectory that maximizes this stability margin to provide robustness against uncertainty in several physical parameters of the object. We present analysis of the stability margin with respect to several parameters involved in the underlying bilevel optimization problem. We demonstrate our proposed method using a 6 DoF manipulator for manipulating several different objects. We also design and validate an MPC controller using the proposed algorithm which can track and regulate the position of the object during manipulation.