# Provably Safe Tolerance Estimation for Robot Arms via Sum-of-Squares Programming

arXiv: https://arxiv.org/abs/2104.08896 · HTML: https://mlsanity.com/paper/2104.08896/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 18 references that are in the map.
- First posted on arXiv 18 Apr 2021.

## Builds on (most cited first, 3 of 3)

- [Algorithms for Verifying Deep Neural Networks](https://mlsanity.com/paper/1903.06758/) (2019)
- [The Convex Feasible Set Algorithm for Real Time Optimization in Motion Planning](https://mlsanity.com/paper/1709.00627/) (2017)
- [Contact-Rich Trajectory Generation in Confined Environments Using Iterative Convex Optimization](https://mlsanity.com/paper/2008.03826/) (2020)

## Built on by (most cited first, 6 of 6)

- [State-wise Safe Reinforcement Learning: A Survey](https://mlsanity.com/paper/2302.03122/) (2023)
- [GUARD: A Safe Reinforcement Learning Benchmark](https://mlsanity.com/paper/2305.13681/) (2023)
- [State-wise Constrained Policy Optimization](https://mlsanity.com/paper/2306.12594/) (2023)
- [Implicit Safe Set Algorithm for Provably Safe Reinforcement Learning](https://mlsanity.com/paper/2405.02754/) (2024)
- [Absolute Policy Optimization](https://mlsanity.com/paper/2310.13230/) (2023)
- [Absolute State-wise Constrained Policy Optimization: High-Probability State-wise Constraints Satisfaction](https://mlsanity.com/paper/2410.01212/) (2024)

## Abstract (arXiv)

Tolerance estimation problems are prevailing in engineering applications. For example, in modern robotics, it remains challenging to efficiently estimate joint tolerance, ie the maximal allowable deviation from a reference robot state such that safety constraints are still satisfied. This paper presented an efficient algorithm to estimate the joint tolerance using sum-of-squares programming. It is theoretically proved that the algorithm provides a tight lower bound of the joint tolerance. Extensive numerical studies demonstrate that the proposed method is computationally efficient and near optimal. The algorithm is implemented in the JTE toolbox and is available at urlhttps://github.com/intelligent-control-lab/Sum-of-Square-Safety-Optimization.