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{{Short description|Use of a robot to maximize the knowledge over a particular area}}
{{For|the exploration problem in recreational mathematics|jeep problem}}

In [[robotics]], the '''exploration problem''' deals with the use of a [[robot]] to maximize the [[knowledge]] over a particular area. The exploration problem arises in [[robotic mapping]] and [[search & rescue]] situations, where an environment might be dangerous or inaccessible to humans.<ref name=Trun2005>{{cite book
| author = Thrun, S.
| author-link1 = Sebastian Thrun
| author2 = Burgard, W.
| author-link2 = Wolfram Burgard
| author3 = Fox, D.
| author-link3 = Dieter Fox
| title = Probabilistic Robotics
| publisher = [[MIT Press]]
| location = Cambridge
| year = 2005
| isbn = 978-0-262-20162-9
}}</ref>

==Overview==
The exploration problem naturally arises in situations in which a robot is utilized to survey an area that is dangerous or inaccessible for humans. The field of robotic explorations draws from various fields of [[information gathering]] and [[decision theory]], and have been studied as far back as the 1950s.

The earliest work in robotic exploration was done in the context of simple finite state automata known as bandits, where algorithms were designed to distinguish and map different states in a [[finite-state automaton]]. Since then, the primary emphasis has been shifted to the robotics system development domain, where exploration-algorithms guided robot have been used to survey volcanos,<ref name=Bares1999>{{cite journal
| author = Bares, J.E.
|author2=Wettergreen, D.S.
| year = 1999
| title = Dante II: Technical Description, Results, and Lessons Learned
| journal = The International Journal of Robotics Research
| volume = 18
| issue = 7
| pages = 621
| doi = 10.1177/02783649922066475
|citeseerx=10.1.1.41.8358
|s2cid=9772668
}}</ref> search and rescue, and abandoned mines mapping.<ref name=Thrun2003>{{cite conference
| author = Thrun, S.
|author2=Hahnel, D. |author3=Ferguson, D. |author4=Montemerlo, M. |author5=Triebel, R. |author6=Burgard, W. |author7=Baker, C. |author8=Omohundro, Z. |author9=Thayer, S. |author10= Whittaker, W.
| year = 2003
| title = A system for volumetric robotic mapping of abandoned mines
| book-title = Robotics and Automation, 2003. Proceedings. ICRA'03. IEEE International Conference on
| volume = 3
|doi=10.1109/ROBOT.2003.1242260 }}</ref> Current state of the art system include advanced techniques on active localization, [[simultaneous localization and mapping]] (SLAM) based exploration, and multi-agent cooperative exploration.

==Information gain==
The key concept in the exploration problem is the notion of information gain, that is, the amount of knowledge acquired while pushing the frontiers. A probabilistic measure of information gain is defined by the entropy

: <math>H_p(x)=-\int p(x) \log p(x) \, dx.</math>

The function <math>H_p(x)</math> is maximized if ''p'' is a uniform distribution and minimized when ''p'' is a point mass distribution. By minimizing the [[expected value|expected]] entropy of belief, information gain is maximized as

: <math>I_b(u) = H_p(x)-E_z \left[ H_b(x'|z,u) \right].</math>

== See also ==
* [[Kidnapped robot problem]]
* [[Wake-up robot problem]]

==References==
{{reflist}}

[[Category:Robot control]]

Exploration problem - Revision history

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