we need fast, flexible, and reliable planning

1

Massachusetts Institute of Technology

“Enabling Fast Flexible Planning through Incremental Temporal Reasoning with

Conflict Extraction”

I’shiang Shu, Robert Effinger, Prof. Brian Williams

Model-Based Embedded and Robotic Systems GroupMassachusetts Institute of Technology

ICAPS 2005

We Need Fast, Flexible, and Reliable Planning

ATRV Rover Testbed Robonaut Simulator

Kirk Planner

TemporallyFlexible Planning

• Redundant Methods

• Conflict-directed Plan Repair

• Flexible Execution Times

• Incremental Reasoning

• Conflict Extraction

TPN (Kim, Williams, Abrahmson 01)

STN ( Dechter, Meiri, Pearl, 91 )

( Shu, Effinger, Williams 05 )

( Cesta, Oddi 96 ) and many others

combines:

ContingencyPlanning

Dynamic Backtracking (Ginsberg 96)

Kirk Plannercombines:

ContingencyPlanning






• Conflict-directed Plan RepairTPN (Kim, Williams, Abrahmson 01)

STN ( Dechter, Meiri, Pearl, 91 )

( Shu, Effinger, Williams 05 )

( Cesta, Oddi 96 ) and many others

Kirk Planner

Dynamic Backtracking (Ginsberg 96)

Kirk Plannercombines:

ContingencyPlanning


{ITC Algorithm

Kirk Planner






Flexible Execution Times

Simple Temporal Network (STN):

Equivalent Distance Graph Representation:

(Dechter, Meiri, Pearl 91)

[ ] lTTuTTulTT jiijij −≤−∩≤−⇒∈− ,

[ ] 5 , 1 ∈− ij TTBegin-engine-start

[1,5] End-engine-start

A B[l,u]

A B

u

-lSTN Distance Graph

2

Flexible Execution Times (Dechter, Meiri, Pearl 91)

A B[1,5]

A B

5

-1

A Simple STN:

d = 0 d = 5

Consistent !

Determine STN consistency:

- Calculate the Single Source Shortest Path (polynomial-time algorithm)

Flexible Execution Times

Determine STN consistency:

- Calculate the Single Source Shortest Path (polynomial-time algorithm)

- A continually looping negative cycle indicates an inconsistency in STN

(Dechter, Meiri, Pearl 91)

d = 0 d = 1d = - 4 d = - 3d = - 8

Inconsistent STN !

Two methods to detect a continually looping negative cycle1.) Check for any d-value to drop below –nC.2.) Keep an acyclic spanning tree of support, and terminate

when a self-loop is formed. (Cesta, Oddi 96)

(most space efficient)

(most time efficient)

A Simple STN:

A B[5,1]

A B

1

-5

Kirk Planner: Overviewcombines:

ContingencyPlanning


Kirk Planner






{ITC Algorithm

ITC Algorithm

• Basic Idea:

1.) Keep dependency information for each shortest-path value in the distance graph (Cesta, Oddi 96)

2.) Use incremental update rules to localize necessary changes to the distance graph.

a.) 3 Update Rules to change a consistent distance graph.b.) 3 Update Rules to repair an inconsistent distance graph.

• ITC’s Novel Claims:

1.) A conflict extraction mechanism to guide plan repair2.) Allow multiple arc-changes3.) Can repair inconsistent distance graphs incrementally

• Given a consistent STN, changing Arc(i,j)’s cost can have three possible effects on the shortest path.

1. Arc(i,j) change does not affect the shortest path to node j.2. Arc(i,j) change improves the shortest path to node j.3. Arc(i,j) change invalidates the shortest path to node j.

3 Update Rules to Change a Consistent Distance Graph

ji

g

h

EDistance graph d = 7d=6

d=5

d=5

2

2

3

10 d = 17

d = shortest path valuep = supporting node

p = g p = j

• Keep track of the support for each shortest path value(Cesta & Oddi 96)

p = s

p = s

p = s

CASE 1

3 jid=6

g

h

2

2

3d=5

d=5

Distance graph

1.) Arc(i,j) change does not affect shortest path

• The cost from node i to node j increases from 2 to 3.

E10d = 7 d = 17p = g p = j

d = shortest path valuep = supporting node

• No changes are needed.

p = s

p = s

p = s

3

3

CASE 2

0 ji

g

h

Distance graph

• The cost from node i to node j decreases from 3 to 0.

• Propagate the improved shortest path.

6i

E

2.) Arc(i,j) change improves shortest path to j

d=6

2

3d=5

d=5

10d = 7 d = 17p = g p = j

16

p = s

p = s

p = s

∞?

40

CASE 3

ji

g

h

2

3

Distance graph

• Increasing Arc(i,j) now invalidates node j’s shortest path.

E

• Reset node j• Recursively reset nodes dependent upon node j. • Insert node j’s parents into the queue so that a new path to node j can be

found for node j and all other invalidated nodes.

3.) Arc(i,j) change invalidates shortest path to j

d=6

d=5

d=5

d = 6p = i

d = 16p = j

∞?

7g

17

j10

p = s

p = s

p = s

3 Update Rules to repair an Inconsistent distance graph

• ITC discovers an inconsistency (a negative cycle) by detecting cyclically dependent backpointers.

D

B

2 3-1

3 8

-2

-2

-8

d=-3p=B

d=-1p=A

d=-10p=D

S2d=0

p=none-1

d=2p=CA

CThis must be a negative cycle

cycle:(A,B,D,C,A)


• Now ITC must incrementally repair the inconsistency.

D

B

2 3-1

3 8

-2

-2

-8

d=-3p=B

d=-1p=A

d=-10p=D

S2d=0

p=none-1

d=2p=CA

C

• Three repair steps:1.) Reset all nodes in negative cycle.2.) Recursively reset all nodes that depend on the negative cycle nodes.3.) Put any parent of a reset node that was not also reset on the Q.

Negative cycle:(A,B,D,C,A)

∞

∞

∞

∞

?

?

?

?


• Now ITC must incrementally repair the inconsistency.

D

B

2 3-1

3 8

-2

-2

-8

d= ∞p = ?

d= ∞p= ?

d=-10p=D

S2d=0

p=none-1

d= ∞p= ?

A

C

• Change arc cost CD to 10.

• Propagate the new shortest path values

Consistent !

5

13

4

2

A

B

A

S 10

Kirk Planner: Overviewcombines:

ContingencyPlanning


Kirk Planner






{ITC Algorithm

4

Temporal Plan Network ( Kim, Williams, Abrahmson 01 )

p1

p2 p3

pL

pR

1

Temporal Plan Network ( Kim, Williams, Abrahmson 01 )

p1

p2 p3

pL

pR

Redundant Methods

Start EndbeHomeBeforeDark()

imageTargets( ) driveTo(p3)

[0,30]

[5,10] [5,10]

driveTo(pL) driveTo(p2)

driveTo(pR) driveTo(p2)

[3,6] [2,5]

[20,30] [20,30]

[0,0][0,0]

1

Conflict-Directed Plan Repair

p1

p2 p3

pL

pR



[0,30]

[5,10] [5,10]



[3,6] [2,5]

[20,30] [20,30]

[0,0][0,0]

1

Generate NewCandidate Plan

Test Candidate PlanFor Temporal Consistency

Inconsistency

Incremental Updates

Conflict-Directed Plan Repair

p1

p2 p3

pL

pR



[0,30]

[5,10] [5,10]



[3,6] [2,5]

[20,30] [20,30]

[0,0][0,0]

1

Consistent !

Generate NewCandidate Plan

Test Candidate PlanFor Temporal Consistency

Inconsistency

Incremental Updates

Performance ImprovementsUAV Scenarios

Randomly Generated Plans

Water UAVNFZ1

NFZ2

WaterA

WaterB

Fire1

Fire2

Seeker UAV

No-Fly Zone

Legend:

FireWaterUAV Base

UAV Base

Plan Goal: Extinguish All FiresVehicles: Two Seeker UAVs

One Water UAV Resources: Fuel & Water

Comparison of Algorithm Runtime

0

2

4

6

8

10

12

1 10 19 28 37 46 55 64 73 82 91

Number of Activities

Alg

orith

m R

untim

e (s

ec)

Non-incrementalAlgorithm

IncrementalAlgorithm

Comparison of Algorithm Runtime

0

2

4

6

8

10

12

1 10 19 28 37 46 55 64 73 82 91

Number of Activities

Algo

rithm

Run

time

(sec

)

Non - incrementalAlgorithmIncrementalAlgorithm

Conclusions

• ITC is an incremental shortest path algorithm that can repair distance graphs incrementally as the plan changes

• ITC’s Novel Claims:1.) A conflict extraction mechanism2.) Allow multiple arc-changes at once3.) Can incrementally repair inconsistent distance graphs

• Shows an order of magnitude improvement over non -incremental planning

• Applicable to any plan representation that uses disjunctions of simple temporal constraints.

5

Any Questions?

References

Ahuja, R.; Magnanti T.; Orlin J, 1958. Network Flows: Theory, Algorithms, and Applications. Prentice Hall.

Cesta, A. and Oddi, A., 1996. Gaining Efficiency and Flexibility in the Simple Temporal Problem, 3rd Workshop on Temporal Representation and Reasoning.

Dechter, R.; Meiri, I.; Pearl, J., 1991. Temporal Constraint Networks. Artificial Intelligence, 49:61-95.

Estlin, T.; et al., 2000. Using Continuous Planning Techniques to Coordinate Multiple Rovers. Electronic Transactions on Artificial Inttligence, 4:45-57.

Gelle, E. and Sabin M., 2003. Solving Methods for Conditional Constraint Satisfaction. In IJCAI-2003.

Gerevini, A., et al., 1996. Incremental Algorithms for Managing Temporal Constraints. 8th International Conference of Tools with Artificial Intelligence.

Ginsberg, M.L., 1993. Dynamic backtracking. Journal of AI Research, 1:25-46.

Kim, P.; Williams, B.; and Abrahmson, M, 2001. Executing Reactive, Model-based Programs through Graph-based Temporal Planning. IJCAI-2001.

Koenig, S. and Likhachev. M., 2001. Incremental A*. In Adv. in Neural Information Processing Systems 14.

McAllester, D., 1991. Truth Maintenance. In Proceedings of AAAI-90, 1109-1116.

Muscettola N., et al., 1998. Issues in temporal reasoning for autonomous control systems. In Autonomous Agents

Prosser, P., 1993. Hybrid algorithms for the constraint satisfaction problem, Comp. Intelligence. 3 268-299.

References (continued)

Rabideau, G., et.al., 1999. Iterative Repair Planning for Spacecraft Operations in the ASPEN System. ISAIRAS.

Stergiou, K, and Koubarakis, M., 1998. Backtracking Algorithms for Disjunctions of Temporal Constraints.15th Nat. Conference of Artificial Intelligence, 81-117.

Tsamardinos, I., Vidal T., Pollack, M., 2003. CTP: A new constraint-based formalism for conditional, temporalplanning. Constraints., vol. 8, no. 4, pp. 365-388.

Williams, B. and Ragno, J., 2002. Conflict-directed A* and its role in model-based embedded systems. Journalof Discrete Applied Math.

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