Fundamental limits for sensor-based robot control

Anirudha Majumdar, Zhiting Mei, Vincent Pacelli

Research output: Contribution to journalArticlepeer-review


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's 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).

Original languageEnglish (US)
Pages (from-to)1051-1069
Number of pages19
JournalInternational Journal of Robotics Research
Issue number12
StatePublished - Oct 2023
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Software
  • Modeling and Simulation
  • Mechanical Engineering
  • Electrical and Electronic Engineering
  • Artificial Intelligence
  • Applied Mathematics


  • Fundamental performance bounds
  • generalized Fano’s inequality
  • task-relevant information


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