# Mediating between Contact Feasibility and Robustness of Trajectory Optimization through Chance Complementarity Constraints

arXiv: https://arxiv.org/abs/2105.09973 · HTML: https://mlsanity.com/paper/2105.09973/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 May 2021.

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

- [Robust Pivoting: Exploiting Frictional Stability Using Bilevel Optimization](https://mlsanity.com/paper/2203.11412/) (2022)
- [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)

## Abstract (arXiv)

As robots move from the laboratory into the real world, motion planning will need to account for model uncertainty and risk. For robot motions involving intermittent contact, planning for uncertainty in contact is especially important, as failure to successfully make and maintain contact can be catastrophic. Here, we model uncertainty in terrain geometry and friction characteristics, and combine a risk-sensitive objective with chance constraints to provide a trade-off between robustness to uncertainty and constraint satisfaction with an arbitrarily high feasibility guarantee. We evaluate our approach in two simple examples: a push-block system for benchmarking and a single-legged hopper. We demonstrate that chance constraints alone produce trajectories similar to those produced using strict complementarity constraints; however, when equipped with a robust objective, we show the chance constraints can mediate a trade-off between robustness to uncertainty and strict constraint satisfaction. Thus, our study may represent an important step towards reasoning about contact uncertainty in motion planning.