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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.

No MeSH data available.


Related in: MedlinePlus

Hexapod set-up.Left-hand side: The simulated hexapod with a display of the joint configurations. Right-hand side: Visualization of the target walking pattern. The plot shows which leg touched the ground at which point in time. Blue areas refer to a contact with a the ground, while orange areas refer to points in time during which the correspond leg did not touch the ground. The different legs are plotted over the y-axis, while each point on the x-axis refers to a single point in time.
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pcbi.1004427.g007: Hexapod set-up.Left-hand side: The simulated hexapod with a display of the joint configurations. Right-hand side: Visualization of the target walking pattern. The plot shows which leg touched the ground at which point in time. Blue areas refer to a contact with a the ground, while orange areas refer to points in time during which the correspond leg did not touch the ground. The different legs are plotted over the y-axis, while each point on the x-axis refers to a single point in time.

Mentions: In the previous sections we have derived a theoretical bound for the complexity of a CRBM based policy. In this section, we want to evaluate that bound experimentally. For this purpose, we chose a six-legged walking machine (hexapod) as our experimental platform (see Fig 7 left panel), because it has a well-studied morphology in the context of artificial intelligence, with one of its first appearances as Ghengis [47]. The purpose of this section is not to develop an optimal walking strategy for this system. Contrary, this morphology was chosen, because the tripod gait (see Fig 7 right panel) is known to be one of the optimal locomotion behaviors, which can be implemented efficiently in various ways. This said, learning a control for this gait is not trivial, and hence it is a good testbed to evaluate our complexity bound for CRBM based policies.


A Theory of Cheap Control in Embodied Systems.

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

Hexapod set-up.Left-hand side: The simulated hexapod with a display of the joint configurations. Right-hand side: Visualization of the target walking pattern. The plot shows which leg touched the ground at which point in time. Blue areas refer to a contact with a the ground, while orange areas refer to points in time during which the correspond leg did not touch the ground. The different legs are plotted over the y-axis, while each point on the x-axis refers to a single point in time.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi.1004427.g007: Hexapod set-up.Left-hand side: The simulated hexapod with a display of the joint configurations. Right-hand side: Visualization of the target walking pattern. The plot shows which leg touched the ground at which point in time. Blue areas refer to a contact with a the ground, while orange areas refer to points in time during which the correspond leg did not touch the ground. The different legs are plotted over the y-axis, while each point on the x-axis refers to a single point in time.
Mentions: In the previous sections we have derived a theoretical bound for the complexity of a CRBM based policy. In this section, we want to evaluate that bound experimentally. For this purpose, we chose a six-legged walking machine (hexapod) as our experimental platform (see Fig 7 left panel), because it has a well-studied morphology in the context of artificial intelligence, with one of its first appearances as Ghengis [47]. The purpose of this section is not to develop an optimal walking strategy for this system. Contrary, this morphology was chosen, because the tripod gait (see Fig 7 right panel) is known to be one of the optimal locomotion behaviors, which can be implemented efficiently in various ways. This said, learning a control for this gait is not trivial, and hence it is a good testbed to evaluate our complexity bound for CRBM based policies.

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