Application of Dijkstra Algorithm in Robot path planning
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This document discusses using Dijkstra's algorithm for robot path planning to find the shortest collision-free path between a starting and ending point. It introduces path planning and modeling the robot and obstacles. It then explains how to determine obstacles using line intersection and describes applying Dijkstra's algorithm to build a graph of nodes and find the shortest path. An example application is shown and it is concluded that Dijkstra's algorithm can effectively find the optimal path for robot navigation.
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algorithm Dijkstra(Graph, source):
dist[source] := 0 // Distance from source to source
for each vertex v in Graph: // Initializations
if v ≠ source
dist[v] := infinity // Unknown distance function from source to v
previous[v] := undefined // Previous node in optimal path from source
end if
add v to Q // All nodes initially in Q (unvisited nodes)
end for
while Q is not empty: // The main loop
u := vertex in Q with min dist[u] // Source node in first case
remove u from Q
for each neighbor v of u: // where v has not yet been removed from Q.
alt := dist[u] + length(u, v)
if alt < dist[v]: // A shorter path to v has been found
dist[v] := alt
previous[v] := u end if
end for
end while
return dist[], previous[]
end algorithm Dijkstra](https://image.slidesharecdn.com/ds-170131144916/85/Application-of-Dijkstra-Algorithm-in-Robot-path-planning-5-320.jpg)
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Application of Dijkstra Algorithm in Robot path planning
- 1. Application of Dijkstra algorithm in Robot path-planning (Huijuan Wang, Yuan Yu, Yuan Q) Presented by D. Darling Jemima.
- 2. Introduction • Path planning is a collision free path that the mobile robot could reach the goal state from the initial state. • The robot’s working space is two-dimensional structure of space. • The robot is simplified as a point and the obstacle as straight line.
- 3. Robot map
- 4. Determining the current obstacles • The intersection method is used to find the obstacles. • Draw a line l from source O to the goal G. • Determine whether there are intersections between the line l and the obstacles. • If so, identify the obstacles that intersected with l first, connect the two endpoints as two vertices. • If l has no intersection with the obstacles, the robot will draw a straight line from the target point.
- 5. Contd.., algorithm Dijkstra(Graph, source): dist[source] := 0 // Distance from source to source for each vertex v in Graph: // Initializations if v ≠ source dist[v] := infinity // Unknown distance function from source to v previous[v] := undefined // Previous node in optimal path from source end if add v to Q // All nodes initially in Q (unvisited nodes) end for while Q is not empty: // The main loop u := vertex in Q with min dist[u] // Source node in first case remove u from Q for each neighbor v of u: // where v has not yet been removed from Q. alt := dist[u] + length(u, v) if alt < dist[v]: // A shorter path to v has been found dist[v] := alt previous[v] := u end if end for end while return dist[], previous[] end algorithm Dijkstra
- 6. Example
- 7. Conclusion •O is the Starting point and G is the Ending point.(using Dijkstra’s Algorithm) •The coarse straight lines are obstacles, and the fine lines is obtained path with the simulation of the final path. •Thus Dijkstra algorithm is used to find the shortest path in the robot path planning .
- 8. Dijkstra’s Algorithm to find the shortest path
- 9. References • Application of Dijkstra’s algorithm in robot path-planning published in IEEE conference on Mechanical Automation and Control Engineering. • Introduction to robotics Jiang Xinsong. • Artificial Intelligence Elaine Rich, Kevin Knight.
- 10. Thank you