Strict Standards: Non-static method DB::connect() should not be called statically, assuming $this from incompatible context in /group/project/aicat/web/lib/database.php on line 32

Strict Standards: Non-static method DB::parseDSN() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB.php on line 520

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB.php on line 557

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /group/project/aicat/web/lib/database.php on line 34

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /group/project/aicat/web/lib/database.php on line 92

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB/common.php on line 1009

Strict Standards: Non-static method DB::isManip() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB/common.php on line 2200

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /group/project/aicat/web/lib/database.php on line 97

Strict Standards: Non-static method DB::connect() should not be called statically, assuming $this from incompatible context in /group/project/aicat/web/lib/database.php on line 32

Strict Standards: Non-static method DB::parseDSN() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB.php on line 520

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB.php on line 557

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /group/project/aicat/web/lib/database.php on line 34
Catalogue of Artificial Intelligence Techniques

Catalogue of Artificial Intelligence Techniques

   

Jump to: Top | Entry | References | Comments

View Maths as: Images | MathML


Strict Standards: Non-static method DB::isManip() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB/common.php on line 2200

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB/common.php on line 1217

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB/common.php on line 1666

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB.php on line 1387

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB/common.php on line 1683

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /group/project/aicat/web/lib/database.php on line 113

Strict Standards: Non-static method DB::isManip() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB/common.php on line 2200

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB/common.php on line 1217

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB/common.php on line 1666

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB.php on line 1387

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB/common.php on line 1683

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /group/project/aicat/web/lib/database.php on line 113

Strict Standards: Non-static method DB::isManip() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB/common.php on line 2200

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB/common.php on line 1217

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB/common.php on line 1666

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB.php on line 1387

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB/common.php on line 1683

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /group/project/aicat/web/lib/database.php on line 113

Strict Standards: Non-static method DB::isManip() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB/common.php on line 2200

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB/common.php on line 1217

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB/common.php on line 1666

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB.php on line 1387

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB/common.php on line 1683

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /group/project/aicat/web/lib/database.php on line 113

Dynamic Programming

Aliases: Variational Dynamic Programming

Keywords: dynamic programming, path, planning, robot manipulation

Categories: Robotics


Author(s): Carmen Istrate

Dynamic programming as a technique was developed in the 1950s by Richard Bellman, as a method of making decisions over time or stages. It has found many applications since, and is by no means restricted to decision making over time. The principle of DP is to divide a problem into subproblems, which are in turn divided into further subproblems. The deepest level subproblems are first evaluated, followed by the ones immediately depending on them, and so on, up to the original problem. This is a bottom-up approach. The efficiency of DP relies on the fact that subproblems are characterised by their state, so subproblems with the same state will have identical optimal solutions, and are therefore equivalent as far as the optimisation is concerned.

An important application in the field of Artificial Intelligence has been the use of DP methods to solve robot path planning problems. This avoids the problem specific heuristics, like potential functions, which have been used to model fields that would attract the robot towards its target, and therefore makes it possible to solve higher dimension path finding problems. The generality of this method makes it applicable to a wide range of manipulation task planning problems, which would otherwise be difficult to model with problem specific heuristics.

The method consists in iteratively improving an initial path (possibly colliding with obstacles). At each iteration, the program performs a search over a k-dimensional submanifold of the n-dimensional configuration space containing the current path. In practice, k is chosen as 2,3 or 4, for performance issues. The k-dimensional manifold is an arbitrarily chosen ruled surface, containing the current path. This surface is quantised into a k-dimensional grid of configurations, and is then searched with Dijkstra's algorithm, which has an additive cost function proportional to the number of configurations colliding with obstacles. Therefore it is certain that fewer points will collide with obstacles in the new path. The search is repeated until a clear path is obtained.


References:


Strict Standards: Non-static method DB::isManip() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB/common.php on line 2200

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB/common.php on line 1217

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB/common.php on line 1666

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB.php on line 1387

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB/common.php on line 1683

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /group/project/aicat/web/lib/database.php on line 113


Comments:


Strict Standards: Non-static method DB::isManip() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB/common.php on line 2200

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB/common.php on line 1217

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB/common.php on line 1666

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB.php on line 1387

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /usr/share/pear/DB/common.php on line 1683

Strict Standards: Non-static method DB::isError() should not be called statically, assuming $this from incompatible context in /group/project/aicat/web/lib/database.php on line 113
Add Comment

No comments.