Anytime search in dynamic graphs

39 Pages·2013·0.88 MB·English

Anytime search in dynamic graphs
Max Likhachev, Dave Ferguson, Geoff Gordon, Anthony Stentz, Sebastian Thrun
(2008)
Presented by: Eric Andrews
Thu 3, October 2013
Outline of presentation
1 Motivation, anytime search, and incremental search
2 Generalization of A*
3 Anytime search algorithm: ARA*
4 Incremental search algorithm: LPA*
5 Anytime and incremental: Anytime D*
6 Example domains and results
Presentedby: EricAndrews Anytimesearchindynamicgraphs Thu3,October2013 2/39
Realistic planning problems
Agents planning and operating in real world. Two problems:
(cid:73) Limited time available for planning =⇒ producing optimal plans often
infeasible.
(cid:73) Model of world imperfect a priori, or world changes while executing
plan.
(cid:73) A* alone not good enough!
E.g. Autonomous car in traffic trying to get from A to B.
Presentedby: EricAndrews Anytimesearchindynamicgraphs Thu3,October2013 3/39
Anytime planners: a solution to time limitations
Quickly find an initial, highly suboptimal plan.
With left over time, try to (iteratively) improve plan.
Two desirable traits:
(cid:73) Ability to reuse work of previous iterations.
(cid:73) Controllable bound ((cid:15)) on the suboptimality of the produced plan.
One solution: Anytime Repairing A* (ARA*)
Presentedby: EricAndrews Anytimesearchindynamicgraphs Thu3,October2013 4/39
Incremental planners: a solution to dynamic graphs
While executing the plan, we may notice that our model (graph) of
the world is no longer in sync with reality.
Re-planning after each (minor) change is expensive!
Solution: try to reuse as much of previous search efforts as possible.
One approach: Lifelong Planning A* (LPA*)
Presentedby: EricAndrews Anytimesearchindynamicgraphs Thu3,October2013 5/39
Both have downsides...
Anytime planners:
(cid:73) Discrepancies in world model =⇒ new plan from scratch.
(cid:73) Interleaving planning and execution problematic.
Incremental planners:
(cid:73) Pre-configured to search for optimal or bounded suboptimal solution.
(cid:73) Can’t improve solution if time left.
Novelty of paper: combine both planner types to get Anytime D*
(ADA*).
(cid:73) Controllable suboptimality bound.
(cid:73) Allows interleaving.
Presentedby: EricAndrews Anytimesearchindynamicgraphs Thu3,October2013 6/39
Section 2
Generalization of A*
Presentedby: EricAndrews Anytimesearchindynamicgraphs Thu3,October2013 7/39
Algorithm 1 A* search ComputePath function.
1: Initialize:
g(s ) = 0 and for rest of nodes g(s) = ∞.
start
OPEN = {s }.
start
2: function ComputePath()
3: while sgoal is not expanded do
4: remove s with smallest f(s) from OPEN
5: for each successor s(cid:48) of s do
6: if g(s(cid:48)) > g(s)+c(s,s(cid:48)) then
7: g(s(cid:48)) = g(s)+c(s,s(cid:48))
8: insert/update s(cid:48) in OPEN with f(s(cid:48)) = g(s(cid:48))+h(s(cid:48)).
9: end if
10: end for
11: end while
12: end function
Presentedby: EricAndrews Anytimesearchindynamicgraphs Thu3,October2013 8/39
Naive anytime algorithm using Weighted A*
Use inflated heuristics, f(s) = g(s)+(cid:15)∗h(s), (cid:15) ≥ 1
=⇒ Bound on returned suboptimal solution is (cid:15)!
Series of ComputePath() calls, decrease (cid:15) in between each.
Good: anytime capability, controllable (cid:15)-suboptimality bound.
Bad: duplicate search effort, no reuse.
Presentedby: EricAndrews Anytimesearchindynamicgraphs Thu3,October2013 9/39
Generalizing A*: v-values
New bookkeeping variable along with f and g values.
No effect on operation of one-time A*.
Allows reuse of search results in subsequent A* runs.
Presentedby: EricAndrews Anytimesearchindynamicgraphs Thu3,October2013 10/39