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A Theory of Cheap Control in Embodied Systems.

Montúfar G, Ghazi-Zahedi K, Ay N - PLoS Comput. Biol. (2015)

Bottom Line: This embodied universal approximation is compared with the classical non-embodied universal approximation.To exemplify our approach, we present a detailed quantitative case study for policy models defined in terms of conditional restricted Boltzmann machines.The experiments indicate that the controller complexity predicted by our theory is close to the minimal sufficient value, which means that the theory has direct practical implications.

View Article: PubMed Central - PubMed

Affiliation: Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany.

ABSTRACT
We present a framework for designing cheap control architectures of embodied agents. Our derivation is guided by the classical problem of universal approximation, whereby we explore the possibility of exploiting the agent's embodiment for a new and more efficient universal approximation of behaviors generated by sensorimotor control. This embodied universal approximation is compared with the classical non-embodied universal approximation. To exemplify our approach, we present a detailed quantitative case study for policy models defined in terms of conditional restricted Boltzmann machines. In contrast to non-embodied universal approximation, which requires an exponential number of parameters, in the embodied setting we are able to generate all possible behaviors with a drastically smaller model, thus obtaining cheap universal approximation. We test and corroborate the theory experimentally with a six-legged walking machine. The experiments indicate that the controller complexity predicted by our theory is close to the minimal sufficient value, which means that the theory has direct practical implications.

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Related in: MedlinePlus

Locality of world-state transitions.At subsequent time steps, the knee of a robot can only move by a small amount. Only very few world state transitions are possible within one time step (e.g., transitions to neighboring positions). This hexapod is used in the experimental evaluation of our theory in “Experiments with a Hexapod”.
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pcbi.1004427.g004: Locality of world-state transitions.At subsequent time steps, the knee of a robot can only move by a small amount. Only very few world state transitions are possible within one time step (e.g., transitions to neighboring positions). This hexapod is used in the experimental evaluation of our theory in “Experiments with a Hexapod”.

Mentions: In the case of α, usually several actions a produce the same world state transition, such that, for any fixed world state w, α(w, ⋅; ⋅) is piece-wise constant with respect to a. Furthermore, for any given w, only very few states w′ ∈ 𝒲 are possible at the next time step, regardless of a, such that α(w, a; ⋅) assigns positive probability only to a very small subset of 𝒲. This means that rank(α) is usually much smaller than (∣𝒜∣ − 1) (the maximum theoretically possible rank). An example for this kind of constraints on α is a robot’s knee, which in a time step can only be moved to adjacent positions, as the one shown in Fig 4.


A Theory of Cheap Control in Embodied Systems.

Montúfar G, Ghazi-Zahedi K, Ay N - PLoS Comput. Biol. (2015)

Locality of world-state transitions.At subsequent time steps, the knee of a robot can only move by a small amount. Only very few world state transitions are possible within one time step (e.g., transitions to neighboring positions). This hexapod is used in the experimental evaluation of our theory in “Experiments with a Hexapod”.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4556690&req=5

pcbi.1004427.g004: Locality of world-state transitions.At subsequent time steps, the knee of a robot can only move by a small amount. Only very few world state transitions are possible within one time step (e.g., transitions to neighboring positions). This hexapod is used in the experimental evaluation of our theory in “Experiments with a Hexapod”.
Mentions: In the case of α, usually several actions a produce the same world state transition, such that, for any fixed world state w, α(w, ⋅; ⋅) is piece-wise constant with respect to a. Furthermore, for any given w, only very few states w′ ∈ 𝒲 are possible at the next time step, regardless of a, such that α(w, a; ⋅) assigns positive probability only to a very small subset of 𝒲. This means that rank(α) is usually much smaller than (∣𝒜∣ − 1) (the maximum theoretically possible rank). An example for this kind of constraints on α is a robot’s knee, which in a time step can only be moved to adjacent positions, as the one shown in Fig 4.

Bottom Line: This embodied universal approximation is compared with the classical non-embodied universal approximation.To exemplify our approach, we present a detailed quantitative case study for policy models defined in terms of conditional restricted Boltzmann machines.The experiments indicate that the controller complexity predicted by our theory is close to the minimal sufficient value, which means that the theory has direct practical implications.

View Article: PubMed Central - PubMed

Affiliation: Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany.

ABSTRACT
We present a framework for designing cheap control architectures of embodied agents. Our derivation is guided by the classical problem of universal approximation, whereby we explore the possibility of exploiting the agent's embodiment for a new and more efficient universal approximation of behaviors generated by sensorimotor control. This embodied universal approximation is compared with the classical non-embodied universal approximation. To exemplify our approach, we present a detailed quantitative case study for policy models defined in terms of conditional restricted Boltzmann machines. In contrast to non-embodied universal approximation, which requires an exponential number of parameters, in the embodied setting we are able to generate all possible behaviors with a drastically smaller model, thus obtaining cheap universal approximation. We test and corroborate the theory experimentally with a six-legged walking machine. The experiments indicate that the controller complexity predicted by our theory is close to the minimal sufficient value, which means that the theory has direct practical implications.

No MeSH data available.


Related in: MedlinePlus