# Fundamental Limits for Sensor-Based Robot Control

arXiv: https://arxiv.org/abs/2202.00129 · HTML: https://mlsanity.com/paper/2202.00129/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 47 references that are in the map.
- First posted on arXiv 31 Jan 2022.

## Builds on (most cited first, 10 of 10)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [On Variational Bounds of Mutual Information](https://mlsanity.com/paper/1905.06922/) (2019)
- [Understanding the Limitations of Variational Mutual Information Estimators](https://mlsanity.com/paper/1910.06222/) (2019)
- [Information-Theoretic Bounded Rationality](https://mlsanity.com/paper/1512.06789/) (2015)
- [Learning Task-Driven Control Policies via Information Bottlenecks](https://mlsanity.com/paper/2002.01428/) (2020)
- [pomdp_py: A Framework to Build and Solve POMDP Problems](https://mlsanity.com/paper/2004.10099/) (2020)
- [How Are Learned Perception-Based Controllers Impacted by the Limits of Robust Control?](https://mlsanity.com/paper/2104.00827/) (2021)
- [Understanding Robust Control Theory Via Stick Balancing](https://mlsanity.com/paper/1606.03520/) (2016)
- [Toward a language-theoretic foundation for planning and filtering](https://mlsanity.com/paper/1807.08856/) (2018)
- [Robust Control Under Uncertainty via Bounded Rationality and Differential Privacy](https://mlsanity.com/paper/2109.08262/) (2021)

## Built on by (most cited first, 1 of 1)

- [Belief-Conditioned One-Step Diffusion: Real-Time Trajectory Planning with Just-Enough Sensing](https://mlsanity.com/paper/2508.12166/) (2025)

## Abstract (arXiv)

Our goal is to develop theory and algorithms for establishing fundamental limits on performance imposed by a robot's sensors for a given task. In order to achieve this, we define a quantity that captures the amount of task-relevant information provided by a sensor. Using a novel version of the generalized Fano inequality from information theory, we demonstrate that this quantity provides an upper bound on the highest achievable expected reward for one-step decision making tasks. We then extend this bound to multi-step problems via a dynamic programming approach. We present algorithms for numerically computing the resulting bounds, and demonstrate our approach on three examples: (i) the lava problem from the literature on partially observable Markov decision processes, (ii) an example with continuous state and observation spaces corresponding to a robot catching a freely-falling object, and (iii) obstacle avoidance using a depth sensor with non-Gaussian noise. We demonstrate the ability of our approach to establish strong limits on achievable performance for these problems by comparing our upper bounds with achievable lower bounds (computed by synthesizing or learning concrete control policies).