File:Astar progress animation.gif
Summary
Illustration of <a href="https://en.wikipedia.org/wiki/A*_search_algorithm" class="extiw" title="w:A* search algorithm">A* search algorithm</a>. The <a href="https://en.wikipedia.org/wiki/Graph_(mathematics)" class="extiw" title="w:Graph (mathematics)">graph</a> is created by uniform square discretization of a 2-dimensional planar region, placing a node in each discretized cell, and connecting each node with its 8 neighbors using bidirectional edges. Cost of edges are same as their Euclidean lengths. The gray shape represents an obstacle. The filled circles in red & green represent expanded nodes (nodes in closed set). The color indicate the g-value (red:lower g-value, green: higher g-value). The empty nodes with blue boundary are the ones in open set. The nodes of the graph are generated on the fly, and nodes falling inside the obstacle are discarded as inaccessible. The objective is to find the least cost path (restricted to the graph) from a given start to a given goal coordinate. The <a href="https://en.wikipedia.org/wiki/Consistent_heuristic" class="extiw" title="w:Consistent heuristic">heuristic (consistent)</a> used by a node is its <a href="https://en.wikipedia.org/wiki/Euclidean_distance" class="extiw" title="w:Euclidean distance">Euclidean distance</a> to goal. That is, ha(n) = |g - n|2, where n represents the Euclidean coordinate of the node n, g is the goal node, and | . |2 is the <a href="https://en.wikipedia.org/wiki/Norm_(mathematics)#Euclidean_norm" class="extiw" title="w:Norm (mathematics)">2-norm</a>. This is a typical example of <a href="https://en.wikipedia.org/wiki/motion_planning" class="extiw" title="w:motion planning">motion planning</a> in <a href="https://en.wikipedia.org/wiki/robotics" class="extiw" title="w:robotics">robotics</a> using A* search algorithm. Created using <a rel="nofollow" class="external text" href="http://code.google.com/p/yagsbpl/">YGSBPL graph-search library</a> and <a href="https://en.wikipedia.org/wiki/OpenCV" class="extiw" title="w:OpenCV">OpenCV</a>.
Licensing
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 06:12, 13 January 2017 | | 210 × 210 (50 KB) | 127.0.0.1 (talk) | Illustration of <a href="https://en.wikipedia.org/wiki/A*_search_algorithm" class="extiw" title="w:A* search algorithm">A* search algorithm</a>. The <a href="https://en.wikipedia.org/wiki/Graph_(mathematics)" class="extiw" title="w:Graph (mathematics)">graph</a> is created by uniform square discretization of a 2-dimensional planar region, placing a node in each discretized cell, and connecting each node with its 8 neighbors using bidirectional edges. Cost of edges are same as their Euclidean lengths. The gray shape represents an obstacle. The filled circles in red & green represent expanded nodes (nodes in closed set). The color indicate the g-value (red:lower g-value, green: higher g-value). The empty nodes with blue boundary are the ones in open set. The nodes of the graph are generated on the fly, and nodes falling inside the obstacle are discarded as inaccessible. The objective is to find the least cost path (restricted to the graph) from a given start to a given goal coordinate. The <a href="https://en.wikipedia.org/wiki/Consistent_heuristic" class="extiw" title="w:Consistent heuristic">heuristic (consistent)</a> used by a node is its <a href="https://en.wikipedia.org/wiki/Euclidean_distance" class="extiw" title="w:Euclidean distance">Euclidean distance</a> to goal. That is, <i>h</i><sub><i>a</i></sub>(<i>n</i>) = |<b>g</b> - <b>n</b>|<sub>2</sub>, where <b>n</b> represents the Euclidean coordinate of the node <i>n</i>, <i>g</i> is the goal node, and | . |<sub>2</sub> is the <a href="https://en.wikipedia.org/wiki/Norm_(mathematics)#Euclidean_norm" class="extiw" title="w:Norm (mathematics)">2-norm</a>. This is a typical example of <a href="https://en.wikipedia.org/wiki/motion_planning" class="extiw" title="w:motion planning">motion planning</a> in <a href="https://en.wikipedia.org/wiki/robotics" class="extiw" title="w:robotics">robotics</a> using A* search algorithm. Created using <a rel="nofollow" class="external text" href="http://code.google.com/p/yagsbpl/">YGSBPL graph-search library</a> and <a href="https://en.wikipedia.org/wiki/OpenCV" class="extiw" title="w:OpenCV">OpenCV</a>. |
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