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Incremental
Path Planning
Continuous Planning and Dynamic A*
Prof. Brian Williams
(help from Ihsiang Shu)
16.412/6.834 Cognitive Robotics
March 16
th
, 2004
Outline
Optimal Path Planning in
Partially Known Environments.
Continuous Optimal Path Planning
±
Dynamic A*
±
Incremental A* (LRTA*) [Appendix]
[
1.
Generate global path plan from initial map.
2.
Repeat until goal reached or failure:
±
Execute next step in current global path plan
±
Update map based on sensors.
±
If map changed generate new global path
from map.
Compute Optimal Path
F
C
A
S
K
H
D
B
G
L
I
E
O
N
M
J
Zellinsky, 92]
Begin Executing Optimal Path
F
C
A
S
K
H
D
B
G
L
I
E
O
N
M
J
h = 5
h = 4
h = 3
h = 4
h = 4
h = 3
h = 2
h = 3
h = 3
h = 2
h = 1
h = 2
h = 2
h = 1
h = 0
h = 1
Uses sensors to detect discrepancies along way.
Obstacle Encountered!
F
C
A
S
K
H
D
B
G
L
I
E
O
N
M
J
h = 5
h = 4
h = 3
h = 4
h = 4
h = 3
h = 2
h = 3
h = 3
h = 2
h = 1
h = 1
h = 2
h = 1
h = 0
h = 1
Robot moves along backpointers towards goal.
At state A, robot discovers edge from D to H is blocked (cost 5,000 units).
Update map and reinvoke planner.
1
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F
C
A
S
K
H
D
B
G
L
I
E
O
N
M
J
h = 5
h = 4
h = 3
h = 4
h = 4
h = 3
h = 2
h = 3
h = 3
h = 2
h = 1
h = 1
h = 2
h = 1
h = 0
h = 1
A’s previous path is still optimal.
Continue moving robot along back pointers.
F
C
A
S
K
H
D
B
G
L
I
E
O
N
M
J
h = 5
h = 4
h = 3
h = 4
h = 4
h = 3
h = 2
h = 3
h = 3
h = 2
h = 1
h = 1
h = 2
h = 1
h = 0
h = 1
Second Obstacle, Replan!
At C robot discovers blocked edges from C to F and H (cost 5,000 units).
Update map and reinvoke planner.
h = 5
Path Execution Achieves Goal
F
C
A
S
K
H
D
B
G
L
I
E
O
N
M
J
h = 5
h = 4
h = 3
h = 4
h = 4
h = 3
h = 2
h = 3
h = 2
h = 1
h = 1
h = 2
h = 1
h = 0
h = 1
Follow back pointers to goal.
No further discrepancies detected; goal achieved!
Outline
Optimal Path Planning in
Partially Known Environments.
Continuous Optimal Path Planning
±
Dynamic A*
±
Incremental A* (LRTA*) [Appendix]
What is Continuous
Optimal Path Planning?
Supports search as a repetitive online process.
Exploits similarities between a series of
searches to solve much faster than
solving each search starting from scratch.
Reuses the identical parts of the previous search
tree, while updating differences.
Solutions guaranteed to be optimal.
On the first search, behaves like traditional
algorithms.
±
±
Incremental A* A* behaves exactly like A*.
[
1.
Generate global path plan from initial map.
2.
Repeat until Goal reached, or failure.
±
Execute next step of current global path plan.
±
Update map based on sensor information.
±
²
1 to 3 orders of magnitude speedup
D* behaves exactly like Dijkstra’s .
Dynamic A* (aka D*)
Stenz, 94]
Incrementally update global path plan from map
changes .
relative to a nonincremental path planner.
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This note was uploaded on 11/07/2011 for the course AERO 16.410 taught by Professor Brianwilliams during the Fall '05 term at MIT.
 Fall '05
 BrianWilliams

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