# Planning in the Belief Space

Reliable planning under uncertainty is crucial in many application endeavors in which the platform operates in full or partial autonomy, such as autonomous navigation and exploration, monitoring, surveillance and robotic surgery. Autonomous operation in complex unknown scenarios involves a deep intertwining of estimation and planning capabilities. The platform has to fuse sensor measurements in order to infer its state and to build a model of the surrounding environment. Moreover, accomplishing given goals with high accuracy and robustness requires accounting for different sources of uncertainty within motion planning. Consequently, planning should be done in the /belief space/, a problem also known as partially observable Markov decision process (POMDP).

In this research we develop approaches for planning under uncertainty when the environment model in which the platform operates is unknown or uncertain, and in lack of sources of absolute information (e.g. no GPS). We represent the platform state and the state of the surrounding environment within the /generalized/ belief space, and investigate approaches for planning in the continuous domain, avoiding discretizing the state and control space.

Below is a demonstration of this concept in an autonomous navigation scenario where the platform has to visit a number of goals (denoted by green color) while operating in unknown GPS-deprived environment. The planning algorithm tradeoffs between reaching the goals, control effort and uncertainty. Whenever uncertainty exceeds a threshold, the platform is guided towards previously observed regions to perform loop closure, thereby reducing uncertainty.

## Related Publications:

### Articles

• V. Indelman. Cooperative Multi-Robot Belief Space Planning for Autonomous Navigation in Unknown Environments. Autonomous Robots, Special Issue on Active Perception, accepted, 2017. doi:10.1007/s10514-017-9620-6
[BibTeX] [URL] [PDF]
@Article{Indelman17arj,
author = {V. Indelman},
title = {Cooperative Multi-Robot Belief Space Planning for Autonomous Navigation in Unknown Environments},
journal = {Autonomous Robots, Special Issue on Active Perception, accepted},
year = 2017,
pdf = "http://indelman.github.io/ANPL-Website/Publications/Indelman17arj.pdf",
doi = "10.1007/s10514-017-9620-6",
researchtopic = {BeliefSpacePlanning},
}

• V. Indelman, L. Carlone, and F. Dellaert. Planning in the Continuous Domain: a Generalized Belief Space Approach for Autonomous Navigation in Unknown Environments. International Journal of Robotics Research, 34(7):849-882, 2015.
[BibTeX] [URL] [PDF]
@Article{Indelman15ijrr,
author = {V. Indelman and L. Carlone and F. Dellaert},
title = {Planning in the Continuous Domain: a Generalized Belief Space Approach for Autonomous Navigation in Unknown Environments},
journal = "International Journal of Robotics Research",
year = 2015,
volume = 34,
number = 7,
pages = "849-882",
url = "http://ijr.sagepub.com/content/34/7/849.full.pdf+html",
pdf = "http://indelman.github.io/ANPL-Website/Publications/Indelman15ijrr.pdf",
researchtopic = {BeliefSpacePlanning},
}

### In Collections

• V. Indelman. Towards Cooperative Multi-Robot Belief Space Planning in Unknown Environments. In Robotics Research, Springer Tracts in Advanced Robotics. Springer, 2017. doi:10.1007/978-3-319-51532-8_27
[BibTeX]
@incollection{Indelman17chapter,
booktitle={Robotics Research},
title={Towards Cooperative Multi-Robot Belief Space Planning in Unknown Environments},
publisher={Springer},
author={V. Indelman},
year={2017},
doi = "10.1007/978-3-319-51532-8_27",
researchtopic = {BeliefSpacePlanning},
}

• V. Indelman, L. Carlone, and F. Dellaert. Towards Planning in Generalized Belief Space. In Robotics Research, The 16th International Symposium ISRR, volume 114 of Springer Tracts in Advanced Robotics, pages 593-609. Springer, 2016.
[BibTeX] [URL] [PDF]
@incollection{Indelman16chapter,
booktitle={Robotics Research, The 16th International Symposium ISRR},
title={Towards Planning in Generalized Belief Space},
publisher={Springer},
author={V. Indelman and L. Carlone and F. Dellaert},
pages="593-609",
volume = {114},
year={2016},
pdf = "http://indelman.github.io/ANPL-Website/Publications/Indelman16chapter.pdf",
researchtopic = {BeliefSpacePlanning},
}

### In Proceedings

• E. Farhi and V. Indelman. Towards Efficient Inference Update through Planning via JIP – Joint Inference and Belief Space Planning. In IEEE International Conference on Robotics and Automation (ICRA), May 2017.
[BibTeX] [PDF]
@InProceedings{Farhi17icra,
author = {E. Farhi and V. Indelman},
title = {Towards Efficient Inference Update through Planning via JIP - Joint Inference and Belief Space Planning},
booktitle = "IEEE International Conference on Robotics and Automation (ICRA)",
year = 2017,
month = "May",
pdf = "http://indelman.github.io/ANPL-Website/Publications/Farhi17icra.pdf",
location = {Singapore},
researchtopic = {BeliefSpacePlanning, CBS},
}

• T. Regev and V. Indelman. Multi-Robot Decentralized Belief Space Planning in Unknown Environments via Efficient Re-Evaluation of Impacted Paths. In IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), October 2016.
[BibTeX] [PDF] [Slides]
@inproceedings{Regev16iros,
author = {T. Regev and V. Indelman},
title = {Multi-Robot Decentralized Belief Space Planning in Unknown Environments via Efficient Re-Evaluation of Impacted Paths},
booktitle = "IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)",
year = 2016,
month = "October",
location = {Daejeon, Korea},
pdf = "http://indelman.github.io/ANPL-Website/Publications/Regev16iros.pdf",
slides = "http://indelman.github.io/ANPL-Website/Publications/Regev16iros_ppt.pdf",
researchtopic = {BeliefSpacePlanning, CBS},
}

• V. Indelman. Towards Cooperative Multi-Robot Belief Space Planning in Unknown Environments. In International Symposium on Robotics Research (ISRR), September 2015.
[BibTeX] [PDF] [Slides]
@InProceedings{Indelman15isrr,
author = {V. Indelman},
title = {Towards Cooperative Multi-Robot Belief Space Planning in Unknown Environments},
booktitle = "International Symposium on Robotics Research (ISRR)",
year = 2015,
month = "September",
location = {Italy},
pdf = "http://indelman.github.io/ANPL-Website/Publications/Indelman15isrr.pdf",
slides = "http://indelman.github.io/ANPL-Website/Publications/Indelman15isrr_ppt.pdf",
researchtopic = {BeliefSpacePlanning},
}

• V. Indelman. Towards Multi-Robot Active Collaborative State Estimation via Belief Space Planning. In IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), September 2015.
[BibTeX] [PDF] [Slides] [Video]
@InProceedings{Indelman15iros,
author = {V. Indelman},
title = {Towards Multi-Robot Active Collaborative State Estimation via Belief Space Planning},
booktitle = "IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)",
year = 2015,
month = "September",
location = {Germany},
pdf = "http://indelman.github.io/ANPL-Website/Publications/Indelman15iros.pdf",
slides = "http://indelman.github.io/ANPL-Website/Publications/Indelman15iros_ppt.pdf",
researchtopic = {BeliefSpacePlanning},
}

• V. Indelman. On Multi-Robot Active Collaborative Inference in Unknown Environments via Belief Space Planning. In Principles of Multi-Robot Systems, workshop in conjunction with Robotics Science and Systems (RSS) Conference, July 2015.
[BibTeX] [PDF] [Poster]
@InProceedings{Indelman15rss_ws_b,
author = {V. Indelman},
title = {On Multi-Robot Active Collaborative Inference in Unknown Environments via Belief Space Planning},
booktitle = {Principles of Multi-Robot Systems, workshop in conjunction with Robotics Science and Systems (RSS) Conference},
year = 2015,
month = "July",
location = {Italy},
researchtopic = {BeliefSpacePlanning},
}

• V. Indelman, L. Carlone, and F. Dellaert. Planning Under Uncertainty in the Continuous Domain: a Generalized Belief Space Approach. In IEEE International Conference on Robotics and Automation (ICRA), June 2014.
[BibTeX] [PDF] [Slides]
@InProceedings{Indelman14icra_a,
author = {V. Indelman and L. Carlone and F. Dellaert},
title = {Planning Under Uncertainty in the Continuous Domain: a Generalized Belief Space Approach},
booktitle = "IEEE International Conference on Robotics and Automation (ICRA)",
year = 2014,
month = "June",
location = {Hong Kong, China},
pdf = "http://indelman.github.io/ANPL-Website/Publications/Indelman14icra_a.pdf",
slides = "http://indelman.github.io/ANPL-Website/Publications/Indelman14icra_a_ppt.pdf",
researchtopic = {BeliefSpacePlanning},
}

• V. Indelman, L. Carlone, and F. Dellaert. Towards Planning in Generalized Belief Space. In International Symposium on Robotics Research (ISRR), December 2013.
[BibTeX] [PDF] [Slides]
@InProceedings{Indelman13isrr,
author = {V. Indelman and L. Carlone and F. Dellaert},
title = {Towards Planning in Generalized Belief Space},
booktitle = "International Symposium on Robotics Research (ISRR)",
year = 2013,
month = "December",
location = {Singapore},
pdf = "http://indelman.github.io/ANPL-Website/Publications/Indelman13isrr.pdf",
slides = "http://indelman.github.io/ANPL-Website/Publications/Indelman13isrr_ppt.pdf",
researchtopic = {BeliefSpacePlanning},
}