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Relaxed Planning Graph
(Tutorial)

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FACULTY OF NATURAL & MATHEMATICAL SCIENCES
DEPARTMENT OF INFORMATICS

The Satellite Domain
Planning and scheduling a collection of observation tasks between multiple satellites, each equipped in slightly different ways.

FACULTY OF NATURAL & MATHEMATICAL SCIENCES
DEPARTMENT OF INFORMATICS

The Satellite Domain
We consider the STRIPS version (no numbers, no temporal constraints)
Clearly a simplified model… but a very good starting point

Five Actions
turn_to (?s – satellite ?d_new – direction ?d_prev – direction)
switch_on(?i – instrument ?s – satellite)
switch_off(?i – instrument ?s – satellite)
calibrate(?s – satellite ?i – instrument ?d – direction)
take_image (?s – satellite ?d – direction ?i – instrument ?m – mode)

(:goal (and
(have_image Phenomenon4 thermograph0)
(have_image Star5 thermograph0)
(have_image Phenomenon6 thermograph0)

FACULTY OF NATURAL & MATHEMATICAL SCIENCES
DEPARTMENT OF INFORMATICS

The Satellite Domain
(:action turn_to
:parameters (?s – satellite ?d_new – direction ?d_prev – direction)
:precondition (and (pointing ?s ?d_prev) (not (= ?d_new ?d_prev)) )
:effect (and (pointing ?s ?d_new) (not (pointing ?s ?d_prev)))

TURN_TO SATELLITE0 GROUNDSTATION2 PHENOMENON6
TURN_TO SATELLITE0 PHENOMENON4 GROUNDSTATION2

FACULTY OF NATURAL & MATHEMATICAL SCIENCES
DEPARTMENT OF INFORMATICS

The Satellite Domain
(:action switch_on
:parameters (?i – instrument ?s – satellite)
:precondition (and (on_board ?i ?s) (power_avail ?s) )
:effect (and (power_on ?i) (not (calibrated ?i)) (not (power_avail ?s)) )

SWITCH_ON INSTRUMENT0 SATELLITE0

FACULTY OF NATURAL & MATHEMATICAL SCIENCES
DEPARTMENT OF INFORMATICS

The Satellite Domain
(:action switch_off
:parameters (?i – instrument ?s – satellite)
:precondition (and (on_board ?i ?s) (power_on ?i) )
:effect (and (not (power_on ?i)) (power_avail ?s) ) )

SWITCH_OFF INSTRUMENT0 SATELLITE0

FACULTY OF NATURAL & MATHEMATICAL SCIENCES
DEPARTMENT OF INFORMATICS

The Satellite Domain
(:action calibrate
:parameters (?s – satellite ?i – instrument ?d – direction)
:precondition (and (on_board ?i ?s) (calibration_target ?i ?d)
(pointing ?s ?d) (power_on ?i) )
:effect (calibrated ?i)

CALIBRATE SATELLITE0 INSTRUMENT0 GROUNDSTATION2

FACULTY OF NATURAL & MATHEMATICAL SCIENCES
DEPARTMENT OF INFORMATICS

The Satellite Domain
(:action take_image
:parameters (?s – satellite ?d – direction ?i – instrument
?m – mode)
:precondition (and (calibrated ?i) (on_board ?i ?s)
(supports ?i ?m) (power_on ?i) (pointing ?s ?d) (power_on ?i) )
:effect (have_image ?d ?m) )

TAKE_IMAGE SATELLITE0 PHENOMENON4 INSTRUMENT0 THERMOGRAPH0

FACULTY OF NATURAL & MATHEMATICAL SCIENCES
DEPARTMENT OF INFORMATICS

The Satellite Domain
(:goal (and
(have_image Phenomenon4 thermograph0)
(have_image Star5 thermograph0)
(have_image Phenomenon6 thermograph0)

0: SWITCH_ON INSTRUMENT0 SATELLITE0
1: TURN_TO SATELLITE0 GROUNDSTATION2 PHENOMENON6
2: CALIBRATE SATELLITE0 INSTRUMENT0 GROUNDSTATION2
3: TURN_TO SATELLITE0 PHENOMENON4 GROUNDSTATION2
4: TAKE_IMAGE SATELLITE0 PHENOMENON4 INSTRUMENT0 THERMOGRAPH0
5: TURN_TO SATELLITE0 STAR5 PHENOMENON4
6: TAKE_IMAGE SATELLITE0 STAR5 INSTRUMENT0 THERMOGRAPH0
7: TURN_TO SATELLITE0 PHENOMENON6 STAR5
8: TAKE_IMAGE SATELLITE0 PHENOMENON6 INSTRUMENT0 THERMOGRAPH0

FACULTY OF NATURAL & MATHEMATICAL SCIENCES
DEPARTMENT OF INFORMATICS

The Satellite Domain: how would FF find a solution ?
(define (problem strips-sat-x-1)
(:domain satellite)
satellite1- satellite
instrument1 – instrument
thermograph1 – mode
GroundStation1 – direction
Phenomenon1 – direction
Phenomenon2 – direction
(supports instrument1 thermograph1)
(calibration_target instrument1 GroundStation1)
(on_board instrument1 satellite1)
(power_avail satellite1)
(pointing satellite1 Phenomenon1)
(:goal (and (have_image Phenomenon2 thermograph1)

FACULTY OF NATURAL & MATHEMATICAL SCIENCES
DEPARTMENT OF INFORMATICS

The Satellite Domain: How would FF find a solution ?
Build the RPG for the initial state.
Extract a solution from the RPG.
Compute the h value for the initial state
i.e. the number of actions in the relaxed plan

FACULTY OF NATURAL & MATHEMATICAL SCIENCES
DEPARTMENT OF INFORMATICS

The Rovers Domain
Rovershave to navigate a planet surface, finding samples and communicating them back to a lander.

Inspired by planetary rovers problems

FACULTY OF NATURAL & MATHEMATICAL SCIENCES
DEPARTMENT OF INFORMATICS

The Rovers Domain
We consider the STRIPS version (no numbers, no temporal constraints)

Six actions
navigate (?x – rover ?y – waypoint ?z – waypoint)
sample_soil(?x – rover ?s – store ?p – waypoint)
calibrate(?r – rover ?i – camera ?t – objective ?w – waypoint)
take_image (?r – rover ?p – waypoint ?o – objective ?i – camera ?m – mode)
communicate_soil_data(?r – rover ?l – lander ?p – waypoint ?x – waypoint ?y – waypoint)
communicate_image_data(?r – rover ?l – lander
?o – objective ?m – mode ?x – waypoint ?y – waypoint)

(:goal (and
(communicated_soil_data waypoint2)
(communicated_image_data objective1 high_res))

FACULTY OF NATURAL & MATHEMATICAL SCIENCES
DEPARTMENT OF INFORMATICS

The Rovers Domain
(:action navigate
:parameters (?x – rover ?y – waypoint ?z – waypoint)
:precondition (and (can_traverse ?x ?y ?z) (available ?x) (at ?x ?y)
(visible ?y ?z))
:effect (and (not (at ?x ?y)) (at ?x ?z))

NAVIGATE ROVER0 WAYPOINT2 WAYPOINT1

FACULTY OF NATURAL & MATHEMATICAL SCIENCES
DEPARTMENT OF INFORMATICS

The Rovers Domain
(:action sample_soil
:parameters (?x – rover ?s – store ?p – waypoint)
:precondition (and (at ?x ?p) (at_soil_sample ?p)(equipped_for_soil_analysis ?x) )
:effect (and (have_soil_analysis ?x ?p) (not (at_soil_sample ?p)))

SAMPLE_SOIL ROVER0 ROVER0STORE WAYPOINT2

FACULTY OF NATURAL & MATHEMATICAL SCIENCES
DEPARTMENT OF INFORMATICS

The Rovers Domain
(:action calibrate
:parameters (?r – rover ?i – camera ?t – objective ?w – waypoint)
:precondition(and (equipped_for_imaging ?r) (calibration_target ?i ?t)
(at ?r ?w) (visible_from ?t ?w)(on_board ?i ?r))
:effect (calibrated ?i ?r)

CALIBRATE ROVER0 CAMERA0 OBJECTIVE1 WAYPOINT3

FACULTY OF NATURAL & MATHEMATICAL SCIENCES
DEPARTMENT OF INFORMATICS

The Rovers Domain
(:action take_image
:parameters (?r – rover ?p – waypoint ?o – objective ?i – camera
?m – mode)
:precondition (and (calibrated ?i ?r) (on_board ?i ?r)
(equipped_for_imaging ?r) (supports ?i ?m)
(visible_from ?o ?p) (at ?r ?p))
:effect (and (have_image ?r ?o ?m)(not (calibrated ?i ?r)))

TAKE_IMAGE ROVER0 WAYPOINT3 OBJECTIVE1 CAMERA0 HIGH_RES

FACULTY OF NATURAL & MATHEMATICAL SCIENCES
DEPARTMENT OF INFORMATICS

The Rovers Domain
(:action communicate_image_data
:parameters (?r – rover ?l – lander ?o – objective ?m – mode
?x – waypoint?y – waypoint)
:precondition(and (at ?r ?x)(at_lander ?l ?y)(have_image ?r ?o ?m)
(visible ?x ?y)(available ?r)(channel_free ?l))
:effect(and (not (available ?r))(not (channel_free ?l))
(channel_free ?l)(communicated_image_data ?o ?m)(available ?r))

COMMUNICATE_IMAGE_DATA ROVER0 GENERAL OBJECTIVE1 HIGH_RES WAYPOINT3 WAYPOINT0

FACULTY OF NATURAL & MATHEMATICAL SCIENCES
DEPARTMENT OF INFORMATICS

The Rovers Domain
(:action communicate_soil_data
:parameters (?r – rover ?l – lander ?p – waypoint ?x – waypoint
?y -waypoint)
:precondition (and (at ?r ?x)(at_lander ?l ?y)(have_soil_analysis ?r ?p)
(visible ?x ?y)(available ?r)(channel_free ?l))
:effect (and (not (available ?r))(not (channel_free ?l))(channel_free ?l)
(communicated_soil_data ?p)(available ?r))

COMMUNICATE_SOIL_DATA ROVER0 GENERAL WAYPOINT2 WAYPOINT3 WAYPOINT0

FACULTY OF NATURAL & MATHEMATICAL SCIENCES
DEPARTMENT OF INFORMATICS

The Rovers Domain
(:goal (and
(communicated_soil_data waypoint2)
(communicated_image_data objective1 high_res)

0: SAMPLE_SOIL ROVER0 ROVER0STORE WAYPOINT2
1: NAVIGATE ROVER0 WAYPOINT2 WAYPOINT1
2: CALIBRATE ROVER0 CAMERA0 OBJECTIVE1 WAYPOINT1
3: TAKE_IMAGE ROVER0 WAYPOINT1 OBJECTIVE1 CAMERA0 HIGH_RES
4: COMMUNICATE_SOIL_DATA ROVER0 GENERAL WAYPOINT2 WAYPOINT1 WAYPOINT0
5: COMMUNICATE_IMAGE_DATA ROVER0 GENERAL OBJECTIVE1 HIGH_RES WAYPOINT1 WAYPOINT0

FACULTY OF NATURAL & MATHEMATICAL SCIENCES
DEPARTMENT OF INFORMATICS

The Rovers Domain: how would FF find a solution ?
(visible waypoint2 waypoint0)
(visible waypoint0 waypoint2)
(visible waypoint2 waypoint1)
(visible waypoint1 waypoint2)
(can_traverse rover waypoint1 waypoint2)
(can_traverse rover waypoint2 waypoint1)
(visible_from objective1 waypoint1)

(at_lander general waypoint0)
(channel_free general)
(at rover waypoint2)
(available rover)
(equipped_for_imaging rover)
(on_board camera rover)
(calibration_target camera objective1)
(supports camera high_res)

(:goal (and(communicated_image_data objective1 high_res))

FACULTY OF NATURAL & MATHEMATICAL SCIENCES
DEPARTMENT OF INFORMATICS

The Rovers Domain: how would FF find a solution ?
Build the RPG for the initial state.
Extract a solution from the RPG.
Compute the h value for the initial state
i.e the number of actions in the relaxed plan

FACULTY OF NATURAL & MATHEMATICAL SCIENCES
DEPARTMENT OF INFORMATICS

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