# Robust Pivoting: Exploiting Frictional Stability Using Bilevel Optimization

arXiv: https://arxiv.org/abs/2203.11412 · HTML: https://mlsanity.com/paper/2203.11412/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 25 references that are in the map.
- First posted on arXiv 22 Mar 2022.

## Builds on (most cited first, 13 of 13)

- [GelSlim: A High-Resolution, Compact, Robust, and Calibrated Tactile-sensing Finger](https://mlsanity.com/paper/1803.00628/) (2018)
- [Tactile-RL for Insertion: Generalization to Objects of Unknown Geometry](https://mlsanity.com/paper/2104.01167/) (2021)
- [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 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)
- [Application of Wrench based Feasibility Analysis to the Online Trajectory Optimization of Legged Robots](https://mlsanity.com/paper/1712.06833/) (2017)
- [Local Trajectory Stabilization for Dexterous Manipulation via Piecewise Affine Approximations](https://mlsanity.com/paper/1909.08045/) (2019)
- [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, 8 of 8)

- [Imperative Learning: A Self-supervised Neuro-Symbolic Learning Framework for Robot Autonomy](https://mlsanity.com/paper/2406.16087/) (2024)
- [Simultaneous Contact-Rich Grasping and Locomotion via Distributed Optimization Enabling Free-Climbing for Multi-Limbed Robots](https://mlsanity.com/paper/2207.01418/) (2022)
- [Robust Pivoting Manipulation using Contact Implicit Bilevel Optimization](https://mlsanity.com/paper/2303.08965/) (2023)
- [Is Linear Feedback on Smoothed Dynamics Sufficient for Stabilizing Contact-Rich Plans?](https://mlsanity.com/paper/2411.06542/) (2024)
- [Generalizable Human-Robot Collaborative Assembly Using Imitation Learning and Force Control](https://mlsanity.com/paper/2212.01434/) (2022)
- [Hierarchical Contact-Rich Trajectory Optimization for Multi-Modal Manipulation using Tight Convex Relaxations](https://mlsanity.com/paper/2503.07963/) (2025)
- [A Virtual Reality Teleoperation Interface for Industrial Robot Manipulators](https://mlsanity.com/paper/2305.10960/) (2023)
- [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 interaction with uncertainty in physical properties of the object. In this paper, we study robust optimization for control of pivoting manipulation in the presence of uncertainties. We present insights about how friction can be exploited to compensate for the inaccuracies in the estimates of the physical properties during manipulation. In particular, we derive analytical expressions for stability margin provided by friction during pivoting manipulation. This margin is then used in a bilevel trajectory optimization algorithm to design a controller that maximizes this stability margin to provide robustness against uncertainty in physical properties of the object. We demonstrate our proposed method using a 6 DoF manipulator for manipulating several different objects.