Minimally sufficient structures for information-feedback policies
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912238413021184 |
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| author | Sakcak, Basak Weinstein, Vadim K. Timperi, Kalle G. LaValle, Steven M. |
| author_facet | Sakcak, Basak Weinstein, Vadim K. Timperi, Kalle G. LaValle, Steven M. |
| contents | In this paper, we consider robotic tasks which require a desirable outcome to be achieved in the physical world that the robot is embedded in and interacting with. Accomplishing this objective requires designing a filter that maintains a useful representation of the physical world and a policy over the filter states. A filter is seen as the robot's perspective of the physical world based on limited sensing, memory, and computation and it is represented as a transition system over a space of information states. To this end, the interactions result from the coupling of an internal and an external system, a filter, and the physical world, respectively, through a sensor mapping and an information-feedback policy. Within this setup, we look for sufficient structures, that is, sufficient internal systems and sensors, for accomplishing a given task. We establish necessary and sufficient conditions for these structures to satisfy for information-feedback policies that can be defined over the states of an internal system to exist. We also show that under mild assumptions, minimal internal systems that can represent a particular plan/policy described over the action-observation histories exist and are unique. Finally, the results are applied to determine sufficient structures for distance-optimal navigation in a polygonal environment. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_13852 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Minimally sufficient structures for information-feedback policies Sakcak, Basak Weinstein, Vadim K. Timperi, Kalle G. LaValle, Steven M. Robotics In this paper, we consider robotic tasks which require a desirable outcome to be achieved in the physical world that the robot is embedded in and interacting with. Accomplishing this objective requires designing a filter that maintains a useful representation of the physical world and a policy over the filter states. A filter is seen as the robot's perspective of the physical world based on limited sensing, memory, and computation and it is represented as a transition system over a space of information states. To this end, the interactions result from the coupling of an internal and an external system, a filter, and the physical world, respectively, through a sensor mapping and an information-feedback policy. Within this setup, we look for sufficient structures, that is, sufficient internal systems and sensors, for accomplishing a given task. We establish necessary and sufficient conditions for these structures to satisfy for information-feedback policies that can be defined over the states of an internal system to exist. We also show that under mild assumptions, minimal internal systems that can represent a particular plan/policy described over the action-observation histories exist and are unique. Finally, the results are applied to determine sufficient structures for distance-optimal navigation in a polygonal environment. |
| title | Minimally sufficient structures for information-feedback policies |
| topic | Robotics |
| url | https://arxiv.org/abs/2502.13852 |