A mathematical characterization of minimally sufficient robot brains
Sakcak, Basak; Timperi, Kalle G; Weinstein, Vadim; LaValle, Steven M (2023-09-19)
Sakcak, Basak
Timperi, Kalle G
Weinstein, Vadim
LaValle, Steven M
Sage publications
19.09.2023
Sakcak B, Timperi KG, Weinstein V, LaValle SM. A mathematical characterization of minimally sufficient robot brains. The International Journal of Robotics Research. 2024;43(9):1342-1362. doi:10.1177/02783649231198898
https://rightsstatements.org/vocab/InC/1.0/
Sakcak B, Timperi KG, Weinstein V, LaValle SM. A mathematical characterization of minimally sufficient robot brains. The International Journal of Robotics Research. 2024;43(9):1342-1362. doi:10.1177/02783649231198898. Copyright © 2023 The Author(s). DOI: doi:10.1177/02783649231198898.
https://rightsstatements.org/vocab/InC/1.0/
Sakcak B, Timperi KG, Weinstein V, LaValle SM. A mathematical characterization of minimally sufficient robot brains. The International Journal of Robotics Research. 2024;43(9):1342-1362. doi:10.1177/02783649231198898. Copyright © 2023 The Author(s). DOI: doi:10.1177/02783649231198898.
https://rightsstatements.org/vocab/InC/1.0/
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:oulu-202404152709
https://urn.fi/URN:NBN:fi:oulu-202404152709
Tiivistelmä
Abstract
This paper addresses the lower limits of encoding and processing the information acquired through interactions between an internal system (robot algorithms or software) and an external system (robot body and its environment) in terms of action and observation histories. Both are modeled as transition systems. We want to know the weakest internal system that is sufficient for achieving passive (filtering) and active (planning) tasks. We introduce the notion of an information transition system (ITS) for the internal system which is a transition system over a space of information states that reflect a robot’s or other observer’s perspective based on limited sensing, memory, computation, and actuation. An ITS is viewed as a filter and a policy or plan is viewed as a function that labels the states of this ITS. Regardless of whether internal systems are obtained by learning algorithms, planning algorithms, or human insight, we want to know the limits of feasibility for given robot hardware and tasks. We establish, in a general setting, that minimal information transition systems (ITSs) exist up to reasonable equivalence assumptions, and are unique under some general conditions. We then apply the theory to generate new insights into several problems, including optimal sensor fusion/filtering, solving basic planning tasks, and finding minimal representations for modeling a system given input-output relations.
This paper addresses the lower limits of encoding and processing the information acquired through interactions between an internal system (robot algorithms or software) and an external system (robot body and its environment) in terms of action and observation histories. Both are modeled as transition systems. We want to know the weakest internal system that is sufficient for achieving passive (filtering) and active (planning) tasks. We introduce the notion of an information transition system (ITS) for the internal system which is a transition system over a space of information states that reflect a robot’s or other observer’s perspective based on limited sensing, memory, computation, and actuation. An ITS is viewed as a filter and a policy or plan is viewed as a function that labels the states of this ITS. Regardless of whether internal systems are obtained by learning algorithms, planning algorithms, or human insight, we want to know the limits of feasibility for given robot hardware and tasks. We establish, in a general setting, that minimal information transition systems (ITSs) exist up to reasonable equivalence assumptions, and are unique under some general conditions. We then apply the theory to generate new insights into several problems, including optimal sensor fusion/filtering, solving basic planning tasks, and finding minimal representations for modeling a system given input-output relations.
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