Fundamental Limits for Sensor-Based Robot Control

TL;DR

This paper establishes fundamental theoretical limits on robot control performance based on sensor information, using information theory and dynamic programming, validated through diverse robotic examples.

Contribution

It introduces a novel information-theoretic framework and algorithms to quantify the maximum achievable performance given sensor constraints in robot control tasks.

Findings

Derived upper bounds on robot control performance based on sensor information.

Validated bounds through examples including POMDP, object catching, and obstacle avoidance.

Demonstrated the bounds' tightness by comparing with actual control policies.

Abstract

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).