Controlability and Makespan Issues with Robot Action Planning and Execution 1

Transcription

1 with Robot Action 1 Matthieu Gallien LAAS-CNRS IWPSS 2006 General 1 Part of this work has been supported by the European Social Fund (ESF).

2 For a planner, the plan execution raises new questions Will a correct plan be always executable? How to improve efficiency of the system? Autonomous robotics context Taking time into account (visibility windows, task durations,...) General Uncertain task durations and task effects

3 Solutions Three improvements of an existing system: Taking into account temporal uncertainties Optimization of the plan time makespan Improving the plan repair strategy General

4 Plan General General

5 of Plan space planner (POCL) Explicit representation of time Now embody a temporal executive Can partially repair a plan while executing the remaining of the plan General Consistency of the plan checked with two CSPs: one STN and a general CSP Flexible plans easy to execute and adapt

6 Typical Mission: Exploration Initially unknown environment: duration of navigations is uncertain Take pictures, communicate during visibility (visibility of an orbiter,...) The system makes its best to accomplish the mission New goals are added, tasks fails,... General validated using a real robot and its simulator

7 Temporal Planning State variables: piecewise constant functions of time PTU_POSITION() forward downward t1 t2 t3 event(ptu_position():(downward,forward),t1) hold(ptu_position():forward,(t2,t3)) Variable based representation (temporal and atemporal) General Able to monitor resource usage Task model partially instantiated Relevant approaches: EUROPA, IDEA, CASPER

8 Produced Plan A ]0, +oo[ MOVE_PTU ]10, +oo[ [12, 16] D E [10, +oo[ <C, 15> MOVE [10, 25] B C TAKE_PICTURE [2, 6] F G MOVE_PTU [12, 16] H I MOVE [15, 32.5] J K <K, 15> [10, +oo[ MOVE_PTU [12, 16] L M MOVE_PTU [12, 16] P Q Controllable link Precedence link Contingent link General R [8, 10] S TAKE_PICTURE [2, 6] N O MOVE T

9 Incremental plan execution An execution cycle: Sensing new events Plan repair if necessary Executing what is needed General Allows the plan repair to be distributed over several cycles Replanning from scratch if needed (failed plan repair) All running tasks are stopped

10 The Statement How to guarantee a correct execution when faced with temporal uncertainties? The dynamic controlability statement Some actions are controlable decides the start and the end time Others are not controlable General The system starts them It must wait the end of the task by observing it Their durations are not known precisely

11 Why and How [0, 50] ]0, +oo[ ]0, +oo[ [15, 20] [25, 40] ]0, +oo[ Start of the plan Start of tasks Upper or lower bounds propagation ]40, 50] End of tasks End of the plan Maximum task duration squeezed by propagation General ]0, 10[ [15, 20] ]0, 10[ [25, 35[ ]0, 10[ The durations are flexible constraints like: duration of a tasks anytime between 15 and 20s for example Consistency checking by propagation: May squeezed possible durations Squeezing an uncontrollable duration may lead to a failure

12 Definition Classically, temporal planning uses simple temporal network (STN) No uncertainty STNU [Vidal et al 97]: new framework with uncertainties Replace consistency by controlabilities General Weak controlability Dynamic controlability Strong controlability

13 Example Definition For the purpose of demonstration, we simulate a need for heating the pan&tilt unit for the camera before moving it The constraints are such than: moving the robot is compatible with moving the cameras For robustness, the heating will allways be done before the move Start and end of MOVE_PAN_TILT_UNIT General [12, 16] ]0, +oo[ [8, 10] A B C D ]0, +oo[ G ]0, +oo[ ]0, +oo[ ]0, +oo[ E [15, 38] F Start and end of MOVE Controllable link Precedence link Contingent link

14 Example of STNU [5.02, +oo[ B MOVE_PTU [12, 16] D [0.01, +oo[ General A [5.01, +oo[ [2.01, +oo[ G [0.01, +oo[ E MOVE [15, 38] F [2.02, +oo[

15 Strong Controlability [28.01, +oo[ B MOVE_PTU [12, 16] D [0.01, +oo[ General A [28.01, +oo[ [2.01, +oo[ G [0.01, +oo[ E MOVE [15, 38] F [2.02, +oo[

16 [15.01, +oo[ B MOVE_PTU [12, 16] D [0.01, +oo[ General A <F, 28.01> [15, +oo[ [2.01, +oo[ G [0.01, +oo[ E MOVE [15, 38] F [2.02, +oo[

17 Weak Controlability [18.02, +oo[ B MOVE_PTU [13, 13] D [0.01, +oo[ General A [18.01, +oo[ [3.01, +oo[ G [0.01, +oo[ E MOVE [28, 28] F [3.02, +oo[

18 Algorithm 3DC+ [Morris et al. 2001] Introduce waits" whose are conditional constraints Complete, polynomial and correct algorithm Analyze triangles of constraints Require more computations than path consistency of an STN Integration of an STNU in allows to make contingent plans General E [10, 25] F E [10, 25] F [8, +oo[ ]-oo, 10] [10, +oo[ <F, 15> ]-oo, 10] B B

19 an heuristic planner Depth first search Least commitment heuristic General Depend on a computed cost for each resolvant Theoretically the cost depends on the number of removed solutions In practice, it is computed with one formula by resolvant type

20 How The classical heuristic makes an equal repartition over the whole plan of all tasks: General The new one modify the temporal related cost functions to try to minimize the makespan

21 Plan General General

22 The LAAS Architecture General I has been integrated in the LAAS architecture I It works on a real robot and on its simulator

23 Result concerning the new heuristic Most of initial plans are shorter, some are not better Plan robustness: Not good if used with an STN General Good if used with an STNU Not a significant difference on planning duration

24 With an STN May work if you are lucky: statistically 50% of goals are abandonned May have very bad effect: May produce trivially not executable plans, instead of cancelling low priority goals and fails to execute the more priority goals General

25 Better with an STNU In all runs except one, all goals were achieved At execution, it takes 10ms for each timepoint, with an STN it takes 1ms General The planning duration with 8 goals is 3 times more than with an STN

26 Example of Plan Repair Initial Loc LOC 1 LOC 2 General LOC 5 LOC 3 LOC 4

27 Inefficiency of Actual Plan Repair Initial Loc LOC 1 Current position of the robot LOC 2 General LOC 5 LOC 3 LOC 6 New goal LOC 4

28 The New Plan Repair Initial Loc LOC 1 LOC 5 Current position of the robot LOC 2 LOC 3 General LOC 6 New goal LOC 4

29 a system for plan generation and execution New problematics due to plan execution Integrated a temporal framework with uncertainties Use a makespan minimizing heuristic General The simulator, a way to evaluate the system versus other versions Current work on upgrading the plan repair algorithm