"git@forgeb1.univ-lehavre.fr:khraimes/cours.git" n'existait pas sur "0f79903a10bcbad5d77bce13392f84b1caef40d8"
Newer
Older
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"# Planning\n",
"#### Chapters 10-11\n",
"----"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This notebook serves as supporting material for topics covered in **Chapter 10 - Classical Planning** and **Chapter 11 - Planning and Acting in the Real World** from the book *[Artificial Intelligence: A Modern Approach](http://aima.cs.berkeley.edu)*. \n",
"This notebook uses implementations from the [planning.py](https://github.com/aimacode/aima-python/blob/master/planning.py) module. \n",
"See the [intro notebook](https://github.com/aimacode/aima-python/blob/master/intro.ipynb) for instructions.\n",
"We'll start by looking at `PDDL` and `Action` data types for defining problems and actions. \n",
"Then, we will see how to use them by trying to plan a trip from *Sibiu* to *Bucharest* across the familiar map of Romania, from [search.ipynb](https://github.com/aimacode/aima-python/blob/master/search.ipynb) \n",
"followed by some common planning problems and methods of solving them.\n",
"Let's start by importing everything from the planning module."
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from planning import *\n",
"from notebook import psource"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## CONTENTS\n",
"\n",
"- PDDL\n",
"- Action\n",
"- Planning Problems\n",
" * Air cargo problem\n",
" * Spare tire problem\n",
" * Three block tower problem\n",
" * Shopping Problem\n",
" * Cake problem\n",
"- Solving Planning Problems\n",
" * GraphPlan"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## PDDL\n",
"\n",
"PDDL stands for Planning Domain Definition Language.\n",
"The `PDDL` class is used to represent planning problems in this module. The following attributes are essential to be able to define a problem:\n",
"* an initial state\n",
"* a set of goals\n",
"* a set of viable actions that can be executed in the search space of the problem\n",
"\n",
"View the source to see how the Python code tries to realise these."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<!DOCTYPE html PUBLIC \"-//W3C//DTD HTML 4.01//EN\"\n",
" \"http://www.w3.org/TR/html4/strict.dtd\">\n",
"\n",
"<html>\n",
"<head>\n",
" <title></title>\n",
" <meta http-equiv=\"content-type\" content=\"text/html; charset=None\">\n",
" <style type=\"text/css\">\n",
"td.linenos { background-color: #f0f0f0; padding-right: 10px; }\n",
"span.lineno { background-color: #f0f0f0; padding: 0 5px 0 5px; }\n",
"pre { line-height: 125%; }\n",
"body .hll { background-color: #ffffcc }\n",
"body { background: #f8f8f8; }\n",
"body .c { color: #408080; font-style: italic } /* Comment */\n",
"body .err { border: 1px solid #FF0000 } /* Error */\n",
"body .k { color: #008000; font-weight: bold } /* Keyword */\n",
"body .o { color: #666666 } /* Operator */\n",
"body .ch { color: #408080; font-style: italic } /* Comment.Hashbang */\n",
"body .cm { color: #408080; font-style: italic } /* Comment.Multiline */\n",
"body .cp { color: #BC7A00 } /* Comment.Preproc */\n",
"body .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */\n",
"body .c1 { color: #408080; font-style: italic } /* Comment.Single */\n",
"body .cs { color: #408080; font-style: italic } /* Comment.Special */\n",
"body .gd { color: #A00000 } /* Generic.Deleted */\n",
"body .ge { font-style: italic } /* Generic.Emph */\n",
"body .gr { color: #FF0000 } /* Generic.Error */\n",
"body .gh { color: #000080; font-weight: bold } /* Generic.Heading */\n",
"body .gi { color: #00A000 } /* Generic.Inserted */\n",
"body .go { color: #888888 } /* Generic.Output */\n",
"body .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n",
"body .gs { font-weight: bold } /* Generic.Strong */\n",
"body .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n",
"body .gt { color: #0044DD } /* Generic.Traceback */\n",
"body .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n",
"body .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n",
"body .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n",
"body .kp { color: #008000 } /* Keyword.Pseudo */\n",
"body .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n",
"body .kt { color: #B00040 } /* Keyword.Type */\n",
"body .m { color: #666666 } /* Literal.Number */\n",
"body .s { color: #BA2121 } /* Literal.String */\n",
"body .na { color: #7D9029 } /* Name.Attribute */\n",
"body .nb { color: #008000 } /* Name.Builtin */\n",
"body .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n",
"body .no { color: #880000 } /* Name.Constant */\n",
"body .nd { color: #AA22FF } /* Name.Decorator */\n",
"body .ni { color: #999999; font-weight: bold } /* Name.Entity */\n",
"body .ne { color: #D2413A; font-weight: bold } /* Name.Exception */\n",
"body .nf { color: #0000FF } /* Name.Function */\n",
"body .nl { color: #A0A000 } /* Name.Label */\n",
"body .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n",
"body .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
"body .nv { color: #19177C } /* Name.Variable */\n",
"body .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n",
"body .w { color: #bbbbbb } /* Text.Whitespace */\n",
"body .mb { color: #666666 } /* Literal.Number.Bin */\n",
"body .mf { color: #666666 } /* Literal.Number.Float */\n",
"body .mh { color: #666666 } /* Literal.Number.Hex */\n",
"body .mi { color: #666666 } /* Literal.Number.Integer */\n",
"body .mo { color: #666666 } /* Literal.Number.Oct */\n",
"body .sa { color: #BA2121 } /* Literal.String.Affix */\n",
"body .sb { color: #BA2121 } /* Literal.String.Backtick */\n",
"body .sc { color: #BA2121 } /* Literal.String.Char */\n",
"body .dl { color: #BA2121 } /* Literal.String.Delimiter */\n",
"body .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */\n",
"body .s2 { color: #BA2121 } /* Literal.String.Double */\n",
"body .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */\n",
"body .sh { color: #BA2121 } /* Literal.String.Heredoc */\n",
"body .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */\n",
"body .sx { color: #008000 } /* Literal.String.Other */\n",
"body .sr { color: #BB6688 } /* Literal.String.Regex */\n",
"body .s1 { color: #BA2121 } /* Literal.String.Single */\n",
"body .ss { color: #19177C } /* Literal.String.Symbol */\n",
"body .bp { color: #008000 } /* Name.Builtin.Pseudo */\n",
"body .fm { color: #0000FF } /* Name.Function.Magic */\n",
"body .vc { color: #19177C } /* Name.Variable.Class */\n",
"body .vg { color: #19177C } /* Name.Variable.Global */\n",
"body .vi { color: #19177C } /* Name.Variable.Instance */\n",
"body .vm { color: #19177C } /* Name.Variable.Magic */\n",
"body .il { color: #666666 } /* Literal.Number.Integer.Long */\n",
"\n",
" </style>\n",
"</head>\n",
"<body>\n",
"<h2></h2>\n",
"\n",
"<div class=\"highlight\"><pre><span></span><span class=\"k\">class</span> <span class=\"nc\">PDDL</span><span class=\"p\">:</span>\n",
" <span class=\"sd\">"""</span>\n",
"<span class=\"sd\"> Planning Domain Definition Language (PDDL) used to define a search problem.</span>\n",
"<span class=\"sd\"> It stores states in a knowledge base consisting of first order logic statements.</span>\n",
"<span class=\"sd\"> The conjunction of these logical statements completely defines a state.</span>\n",
"<span class=\"sd\"> """</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"fm\">__init__</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">init</span><span class=\"p\">,</span> <span class=\"n\">goals</span><span class=\"p\">,</span> <span class=\"n\">actions</span><span class=\"p\">):</span>\n",
" <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">init</span> <span class=\"o\">=</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">convert</span><span class=\"p\">(</span><span class=\"n\">init</span><span class=\"p\">)</span>\n",
" <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">goals</span> <span class=\"o\">=</span> <span class=\"n\">expr</span><span class=\"p\">(</span><span class=\"n\">goals</span><span class=\"p\">)</span>\n",
" <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">actions</span> <span class=\"o\">=</span> <span class=\"n\">actions</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">convert</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">init</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""Converts strings into exprs"""</span>\n",
" <span class=\"k\">try</span><span class=\"p\">:</span>\n",
" <span class=\"n\">init</span> <span class=\"o\">=</span> <span class=\"n\">conjuncts</span><span class=\"p\">(</span><span class=\"n\">expr</span><span class=\"p\">(</span><span class=\"n\">init</span><span class=\"p\">))</span>\n",
" <span class=\"k\">except</span> <span class=\"ne\">AttributeError</span><span class=\"p\">:</span>\n",
" <span class=\"n\">init</span> <span class=\"o\">=</span> <span class=\"n\">expr</span><span class=\"p\">(</span><span class=\"n\">init</span><span class=\"p\">)</span>\n",
" <span class=\"k\">return</span> <span class=\"n\">init</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">goal_test</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""Checks if the goals have been reached"""</span>\n",
" <span class=\"k\">return</span> <span class=\"nb\">all</span><span class=\"p\">(</span><span class=\"n\">goal</span> <span class=\"ow\">in</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">init</span> <span class=\"k\">for</span> <span class=\"n\">goal</span> <span class=\"ow\">in</span> <span class=\"n\">conjuncts</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">goals</span><span class=\"p\">))</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">act</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">action</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""</span>\n",
"<span class=\"sd\"> Performs the action given as argument.</span>\n",
"<span class=\"sd\"> Note that action is an Expr like expr('Remove(Glass, Table)') or expr('Eat(Sandwich)')</span>\n",
"<span class=\"sd\"> """</span> \n",
" <span class=\"n\">action_name</span> <span class=\"o\">=</span> <span class=\"n\">action</span><span class=\"o\">.</span><span class=\"n\">op</span>\n",
" <span class=\"n\">args</span> <span class=\"o\">=</span> <span class=\"n\">action</span><span class=\"o\">.</span><span class=\"n\">args</span>\n",
" <span class=\"n\">list_action</span> <span class=\"o\">=</span> <span class=\"n\">first</span><span class=\"p\">(</span><span class=\"n\">a</span> <span class=\"k\">for</span> <span class=\"n\">a</span> <span class=\"ow\">in</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">actions</span> <span class=\"k\">if</span> <span class=\"n\">a</span><span class=\"o\">.</span><span class=\"n\">name</span> <span class=\"o\">==</span> <span class=\"n\">action_name</span><span class=\"p\">)</span>\n",
" <span class=\"k\">if</span> <span class=\"n\">list_action</span> <span class=\"ow\">is</span> <span class=\"bp\">None</span><span class=\"p\">:</span>\n",
" <span class=\"k\">raise</span> <span class=\"ne\">Exception</span><span class=\"p\">(</span><span class=\"s2\">"Action '{}' not found"</span><span class=\"o\">.</span><span class=\"n\">format</span><span class=\"p\">(</span><span class=\"n\">action_name</span><span class=\"p\">))</span>\n",
" <span class=\"k\">if</span> <span class=\"ow\">not</span> <span class=\"n\">list_action</span><span class=\"o\">.</span><span class=\"n\">check_precond</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">init</span><span class=\"p\">,</span> <span class=\"n\">args</span><span class=\"p\">):</span>\n",
" <span class=\"k\">raise</span> <span class=\"ne\">Exception</span><span class=\"p\">(</span><span class=\"s2\">"Action '{}' pre-conditions not satisfied"</span><span class=\"o\">.</span><span class=\"n\">format</span><span class=\"p\">(</span><span class=\"n\">action</span><span class=\"p\">))</span>\n",
" <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">init</span> <span class=\"o\">=</span> <span class=\"n\">list_action</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">init</span><span class=\"p\">,</span> <span class=\"n\">args</span><span class=\"p\">)</span><span class=\"o\">.</span><span class=\"n\">clauses</span>\n",
"</pre></div>\n",
"</body>\n",
"</html>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"psource(PDDL)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The `init` attribute is an expression that forms the initial knowledge base for the problem.\n",
"<br>\n",
"The `goals` attribute is an expression that indicates the goals to be reached by the problem.\n",
"<br>\n",
"Lastly, `actions` contains a list of `Action` objects that may be executed in the search space of the problem.\n",
"<br>\n",
"The `goal_test` method checks if the goal has been reached.\n",
"<br>\n",
"The `act` method acts out the given action and updates the current state.\n",
"<br>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## ACTION\n",
"\n",
"To be able to model a planning problem properly, it is essential to be able to represent an Action. Each action we model requires at least three things:\n",
"* preconditions that the action must meet\n",
"* the effects of executing the action\n",
"* some expression that represents the action"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The module models actions using the `Action` class"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<!DOCTYPE html PUBLIC \"-//W3C//DTD HTML 4.01//EN\"\n",
" \"http://www.w3.org/TR/html4/strict.dtd\">\n",
"\n",
"<html>\n",
"<head>\n",
" <title></title>\n",
" <meta http-equiv=\"content-type\" content=\"text/html; charset=None\">\n",
" <style type=\"text/css\">\n",
"td.linenos { background-color: #f0f0f0; padding-right: 10px; }\n",
"span.lineno { background-color: #f0f0f0; padding: 0 5px 0 5px; }\n",
"pre { line-height: 125%; }\n",
"body .hll { background-color: #ffffcc }\n",
"body { background: #f8f8f8; }\n",
"body .c { color: #408080; font-style: italic } /* Comment */\n",
"body .err { border: 1px solid #FF0000 } /* Error */\n",
"body .k { color: #008000; font-weight: bold } /* Keyword */\n",
"body .o { color: #666666 } /* Operator */\n",
"body .ch { color: #408080; font-style: italic } /* Comment.Hashbang */\n",
"body .cm { color: #408080; font-style: italic } /* Comment.Multiline */\n",
"body .cp { color: #BC7A00 } /* Comment.Preproc */\n",
"body .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */\n",
"body .c1 { color: #408080; font-style: italic } /* Comment.Single */\n",
"body .cs { color: #408080; font-style: italic } /* Comment.Special */\n",
"body .gd { color: #A00000 } /* Generic.Deleted */\n",
"body .ge { font-style: italic } /* Generic.Emph */\n",
"body .gr { color: #FF0000 } /* Generic.Error */\n",
"body .gh { color: #000080; font-weight: bold } /* Generic.Heading */\n",
"body .gi { color: #00A000 } /* Generic.Inserted */\n",
"body .go { color: #888888 } /* Generic.Output */\n",
"body .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n",
"body .gs { font-weight: bold } /* Generic.Strong */\n",
"body .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n",
"body .gt { color: #0044DD } /* Generic.Traceback */\n",
"body .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n",
"body .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n",
"body .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n",
"body .kp { color: #008000 } /* Keyword.Pseudo */\n",
"body .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n",
"body .kt { color: #B00040 } /* Keyword.Type */\n",
"body .m { color: #666666 } /* Literal.Number */\n",
"body .s { color: #BA2121 } /* Literal.String */\n",
"body .na { color: #7D9029 } /* Name.Attribute */\n",
"body .nb { color: #008000 } /* Name.Builtin */\n",
"body .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n",
"body .no { color: #880000 } /* Name.Constant */\n",
"body .nd { color: #AA22FF } /* Name.Decorator */\n",
"body .ni { color: #999999; font-weight: bold } /* Name.Entity */\n",
"body .ne { color: #D2413A; font-weight: bold } /* Name.Exception */\n",
"body .nf { color: #0000FF } /* Name.Function */\n",
"body .nl { color: #A0A000 } /* Name.Label */\n",
"body .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n",
"body .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
"body .nv { color: #19177C } /* Name.Variable */\n",
"body .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n",
"body .w { color: #bbbbbb } /* Text.Whitespace */\n",
"body .mb { color: #666666 } /* Literal.Number.Bin */\n",
"body .mf { color: #666666 } /* Literal.Number.Float */\n",
"body .mh { color: #666666 } /* Literal.Number.Hex */\n",
"body .mi { color: #666666 } /* Literal.Number.Integer */\n",
"body .mo { color: #666666 } /* Literal.Number.Oct */\n",
"body .sa { color: #BA2121 } /* Literal.String.Affix */\n",
"body .sb { color: #BA2121 } /* Literal.String.Backtick */\n",
"body .sc { color: #BA2121 } /* Literal.String.Char */\n",
"body .dl { color: #BA2121 } /* Literal.String.Delimiter */\n",
"body .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */\n",
"body .s2 { color: #BA2121 } /* Literal.String.Double */\n",
"body .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */\n",
"body .sh { color: #BA2121 } /* Literal.String.Heredoc */\n",
"body .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */\n",
"body .sx { color: #008000 } /* Literal.String.Other */\n",
"body .sr { color: #BB6688 } /* Literal.String.Regex */\n",
"body .s1 { color: #BA2121 } /* Literal.String.Single */\n",
"body .ss { color: #19177C } /* Literal.String.Symbol */\n",
"body .bp { color: #008000 } /* Name.Builtin.Pseudo */\n",
"body .fm { color: #0000FF } /* Name.Function.Magic */\n",
"body .vc { color: #19177C } /* Name.Variable.Class */\n",
"body .vg { color: #19177C } /* Name.Variable.Global */\n",
"body .vi { color: #19177C } /* Name.Variable.Instance */\n",
"body .vm { color: #19177C } /* Name.Variable.Magic */\n",
"body .il { color: #666666 } /* Literal.Number.Integer.Long */\n",
"\n",
" </style>\n",
"</head>\n",
"<body>\n",
"<h2></h2>\n",
"\n",
"<div class=\"highlight\"><pre><span></span><span class=\"k\">class</span> <span class=\"nc\">Action</span><span class=\"p\">:</span>\n",
" <span class=\"sd\">"""</span>\n",
"<span class=\"sd\"> Defines an action schema using preconditions and effects.</span>\n",
"<span class=\"sd\"> Use this to describe actions in PDDL.</span>\n",
"<span class=\"sd\"> action is an Expr where variables are given as arguments(args).</span>\n",
"<span class=\"sd\"> Precondition and effect are both lists with positive and negative literals.</span>\n",
"<span class=\"sd\"> Negative preconditions and effects are defined by adding a 'Not' before the name of the clause</span>\n",
"<span class=\"sd\"> Example:</span>\n",
"<span class=\"sd\"> precond = [expr("Human(person)"), expr("Hungry(Person)"), expr("NotEaten(food)")]</span>\n",
"<span class=\"sd\"> effect = [expr("Eaten(food)"), expr("Hungry(person)")]</span>\n",
"<span class=\"sd\"> eat = Action(expr("Eat(person, food)"), precond, effect)</span>\n",
"<span class=\"sd\"> """</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"fm\">__init__</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">action</span><span class=\"p\">,</span> <span class=\"n\">precond</span><span class=\"p\">,</span> <span class=\"n\">effect</span><span class=\"p\">):</span>\n",
" <span class=\"n\">action</span> <span class=\"o\">=</span> <span class=\"n\">expr</span><span class=\"p\">(</span><span class=\"n\">action</span><span class=\"p\">)</span>\n",
" <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">name</span> <span class=\"o\">=</span> <span class=\"n\">action</span><span class=\"o\">.</span><span class=\"n\">op</span>\n",
" <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">args</span> <span class=\"o\">=</span> <span class=\"n\">action</span><span class=\"o\">.</span><span class=\"n\">args</span>\n",
" <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">precond</span><span class=\"p\">,</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">effect</span> <span class=\"o\">=</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">convert</span><span class=\"p\">(</span><span class=\"n\">precond</span><span class=\"p\">,</span> <span class=\"n\">effect</span><span class=\"p\">)</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"fm\">__call__</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">kb</span><span class=\"p\">,</span> <span class=\"n\">args</span><span class=\"p\">):</span>\n",
" <span class=\"k\">return</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">act</span><span class=\"p\">(</span><span class=\"n\">kb</span><span class=\"p\">,</span> <span class=\"n\">args</span><span class=\"p\">)</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">convert</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">precond</span><span class=\"p\">,</span> <span class=\"n\">effect</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""Converts strings into Exprs"""</span>\n",
"\n",
" <span class=\"n\">precond</span> <span class=\"o\">=</span> <span class=\"n\">precond</span><span class=\"o\">.</span><span class=\"n\">replace</span><span class=\"p\">(</span><span class=\"s1\">'~'</span><span class=\"p\">,</span> <span class=\"s1\">'Not'</span><span class=\"p\">)</span>\n",
" <span class=\"k\">if</span> <span class=\"nb\">len</span><span class=\"p\">(</span><span class=\"n\">precond</span><span class=\"p\">)</span> <span class=\"o\">></span> <span class=\"mi\">0</span><span class=\"p\">:</span>\n",
" <span class=\"n\">precond</span> <span class=\"o\">=</span> <span class=\"n\">expr</span><span class=\"p\">(</span><span class=\"n\">precond</span><span class=\"p\">)</span>\n",
" <span class=\"n\">effect</span> <span class=\"o\">=</span> <span class=\"n\">effect</span><span class=\"o\">.</span><span class=\"n\">replace</span><span class=\"p\">(</span><span class=\"s1\">'~'</span><span class=\"p\">,</span> <span class=\"s1\">'Not'</span><span class=\"p\">)</span>\n",
" <span class=\"k\">if</span> <span class=\"nb\">len</span><span class=\"p\">(</span><span class=\"n\">effect</span><span class=\"p\">)</span> <span class=\"o\">></span> <span class=\"mi\">0</span><span class=\"p\">:</span>\n",
" <span class=\"n\">effect</span> <span class=\"o\">=</span> <span class=\"n\">expr</span><span class=\"p\">(</span><span class=\"n\">effect</span><span class=\"p\">)</span>\n",
"\n",
" <span class=\"k\">try</span><span class=\"p\">:</span>\n",
" <span class=\"n\">precond</span> <span class=\"o\">=</span> <span class=\"n\">conjuncts</span><span class=\"p\">(</span><span class=\"n\">precond</span><span class=\"p\">)</span>\n",
" <span class=\"k\">except</span> <span class=\"ne\">AttributeError</span><span class=\"p\">:</span>\n",
" <span class=\"k\">pass</span>\n",
" <span class=\"k\">try</span><span class=\"p\">:</span>\n",
" <span class=\"n\">effect</span> <span class=\"o\">=</span> <span class=\"n\">conjuncts</span><span class=\"p\">(</span><span class=\"n\">effect</span><span class=\"p\">)</span>\n",
" <span class=\"k\">except</span> <span class=\"ne\">AttributeError</span><span class=\"p\">:</span>\n",
" <span class=\"k\">pass</span>\n",
"\n",
" <span class=\"k\">return</span> <span class=\"n\">precond</span><span class=\"p\">,</span> <span class=\"n\">effect</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">substitute</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">e</span><span class=\"p\">,</span> <span class=\"n\">args</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""Replaces variables in expression with their respective Propositional symbol"""</span>\n",
"\n",
" <span class=\"n\">new_args</span> <span class=\"o\">=</span> <span class=\"nb\">list</span><span class=\"p\">(</span><span class=\"n\">e</span><span class=\"o\">.</span><span class=\"n\">args</span><span class=\"p\">)</span>\n",
" <span class=\"k\">for</span> <span class=\"n\">num</span><span class=\"p\">,</span> <span class=\"n\">x</span> <span class=\"ow\">in</span> <span class=\"nb\">enumerate</span><span class=\"p\">(</span><span class=\"n\">e</span><span class=\"o\">.</span><span class=\"n\">args</span><span class=\"p\">):</span>\n",
" <span class=\"k\">for</span> <span class=\"n\">i</span><span class=\"p\">,</span> <span class=\"n\">_</span> <span class=\"ow\">in</span> <span class=\"nb\">enumerate</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">args</span><span class=\"p\">):</span>\n",
" <span class=\"k\">if</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">args</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">]</span> <span class=\"o\">==</span> <span class=\"n\">x</span><span class=\"p\">:</span>\n",
" <span class=\"n\">new_args</span><span class=\"p\">[</span><span class=\"n\">num</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"n\">args</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">]</span>\n",
" <span class=\"k\">return</span> <span class=\"n\">Expr</span><span class=\"p\">(</span><span class=\"n\">e</span><span class=\"o\">.</span><span class=\"n\">op</span><span class=\"p\">,</span> <span class=\"o\">*</span><span class=\"n\">new_args</span><span class=\"p\">)</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">check_precond</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">kb</span><span class=\"p\">,</span> <span class=\"n\">args</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""Checks if the precondition is satisfied in the current state"""</span>\n",
"\n",
" <span class=\"k\">if</span> <span class=\"nb\">isinstance</span><span class=\"p\">(</span><span class=\"n\">kb</span><span class=\"p\">,</span> <span class=\"nb\">list</span><span class=\"p\">):</span>\n",
" <span class=\"n\">kb</span> <span class=\"o\">=</span> <span class=\"n\">FolKB</span><span class=\"p\">(</span><span class=\"n\">kb</span><span class=\"p\">)</span>\n",
"\n",
" <span class=\"k\">for</span> <span class=\"n\">clause</span> <span class=\"ow\">in</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">precond</span><span class=\"p\">:</span>\n",
" <span class=\"k\">if</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">substitute</span><span class=\"p\">(</span><span class=\"n\">clause</span><span class=\"p\">,</span> <span class=\"n\">args</span><span class=\"p\">)</span> <span class=\"ow\">not</span> <span class=\"ow\">in</span> <span class=\"n\">kb</span><span class=\"o\">.</span><span class=\"n\">clauses</span><span class=\"p\">:</span>\n",
" <span class=\"k\">return</span> <span class=\"bp\">False</span>\n",
" <span class=\"k\">return</span> <span class=\"bp\">True</span>\n",
"\n",
" <span class=\"k\">def</span> <span class=\"nf\">act</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"p\">,</span> <span class=\"n\">kb</span><span class=\"p\">,</span> <span class=\"n\">args</span><span class=\"p\">):</span>\n",
" <span class=\"sd\">"""Executes the action on the state's knowledge base"""</span>\n",
"\n",
" <span class=\"k\">if</span> <span class=\"nb\">isinstance</span><span class=\"p\">(</span><span class=\"n\">kb</span><span class=\"p\">,</span> <span class=\"nb\">list</span><span class=\"p\">):</span>\n",
" <span class=\"n\">kb</span> <span class=\"o\">=</span> <span class=\"n\">FolKB</span><span class=\"p\">(</span><span class=\"n\">kb</span><span class=\"p\">)</span>\n",
"\n",
" <span class=\"k\">if</span> <span class=\"ow\">not</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">check_precond</span><span class=\"p\">(</span><span class=\"n\">kb</span><span class=\"p\">,</span> <span class=\"n\">args</span><span class=\"p\">):</span>\n",
" <span class=\"k\">raise</span> <span class=\"ne\">Exception</span><span class=\"p\">(</span><span class=\"s1\">'Action pre-conditions not satisfied'</span><span class=\"p\">)</span>\n",
" <span class=\"k\">for</span> <span class=\"n\">clause</span> <span class=\"ow\">in</span> <span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">effect</span><span class=\"p\">:</span>\n",
" <span class=\"n\">kb</span><span class=\"o\">.</span><span class=\"n\">tell</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">substitute</span><span class=\"p\">(</span><span class=\"n\">clause</span><span class=\"p\">,</span> <span class=\"n\">args</span><span class=\"p\">))</span>\n",
" <span class=\"k\">if</span> <span class=\"n\">clause</span><span class=\"o\">.</span><span class=\"n\">op</span><span class=\"p\">[:</span><span class=\"mi\">3</span><span class=\"p\">]</span> <span class=\"o\">==</span> <span class=\"s1\">'Not'</span><span class=\"p\">:</span>\n",
" <span class=\"n\">new_clause</span> <span class=\"o\">=</span> <span class=\"n\">Expr</span><span class=\"p\">(</span><span class=\"n\">clause</span><span class=\"o\">.</span><span class=\"n\">op</span><span class=\"p\">[</span><span class=\"mi\">3</span><span class=\"p\">:],</span> <span class=\"o\">*</span><span class=\"n\">clause</span><span class=\"o\">.</span><span class=\"n\">args</span><span class=\"p\">)</span>\n",
"\n",
" <span class=\"k\">if</span> <span class=\"n\">kb</span><span class=\"o\">.</span><span class=\"n\">ask</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">substitute</span><span class=\"p\">(</span><span class=\"n\">new_clause</span><span class=\"p\">,</span> <span class=\"n\">args</span><span class=\"p\">))</span> <span class=\"ow\">is</span> <span class=\"ow\">not</span> <span class=\"bp\">False</span><span class=\"p\">:</span>\n",
" <span class=\"n\">kb</span><span class=\"o\">.</span><span class=\"n\">retract</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">substitute</span><span class=\"p\">(</span><span class=\"n\">new_clause</span><span class=\"p\">,</span> <span class=\"n\">args</span><span class=\"p\">))</span>\n",
" <span class=\"k\">else</span><span class=\"p\">:</span>\n",
" <span class=\"n\">new_clause</span> <span class=\"o\">=</span> <span class=\"n\">Expr</span><span class=\"p\">(</span><span class=\"s1\">'Not'</span> <span class=\"o\">+</span> <span class=\"n\">clause</span><span class=\"o\">.</span><span class=\"n\">op</span><span class=\"p\">,</span> <span class=\"o\">*</span><span class=\"n\">clause</span><span class=\"o\">.</span><span class=\"n\">args</span><span class=\"p\">)</span>\n",
"\n",
" <span class=\"k\">if</span> <span class=\"n\">kb</span><span class=\"o\">.</span><span class=\"n\">ask</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">substitute</span><span class=\"p\">(</span><span class=\"n\">new_clause</span><span class=\"p\">,</span> <span class=\"n\">args</span><span class=\"p\">))</span> <span class=\"ow\">is</span> <span class=\"ow\">not</span> <span class=\"bp\">False</span><span class=\"p\">:</span> \n",
" <span class=\"n\">kb</span><span class=\"o\">.</span><span class=\"n\">retract</span><span class=\"p\">(</span><span class=\"bp\">self</span><span class=\"o\">.</span><span class=\"n\">substitute</span><span class=\"p\">(</span><span class=\"n\">new_clause</span><span class=\"p\">,</span> <span class=\"n\">args</span><span class=\"p\">))</span>\n",
"\n",
" <span class=\"k\">return</span> <span class=\"n\">kb</span>\n",
"</pre></div>\n",
"</body>\n",
"</html>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"psource(Action)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This class represents an action given the expression, the preconditions and its effects. \n",
"A list `precond` stores the preconditions of the action and a list `effect` stores its effects.\n",
"Negative preconditions and effects are input using a `~` symbol before the clause, which are internally prefixed with a `Not` to make it easier to work with.\n",
"For example, the negation of `At(obj, loc)` will be input as `~At(obj, loc)` and internally represented as `NotAt(obj, loc)`. \n",
"This equivalently creates a new clause for each negative literal, removing the hassle of maintaining two separate knowledge bases.\n",
"This greatly simplifies algorithms like `GraphPlan` as we will see later.\n",
"The `convert` method takes an input string, parses it, removes conjunctions if any and returns a list of `Expr` objects.\n",
"The `check_precond` method checks if the preconditions for that action are valid, given a `kb`.\n",
"The `act` method carries out the action on the given knowledge base."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now lets try to define a planning problem using these tools. Since we already know about the map of Romania, lets see if we can plan a trip across a simplified map of Romania.\n",
"\n",
"Here is our simplified map definition:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from utils import *\n",
"# this imports the required expr so we can create our knowledge base\n",
"\n",
"knowledge_base = [\n",
" expr(\"Connected(Bucharest,Pitesti)\"),\n",
" expr(\"Connected(Pitesti,Rimnicu)\"),\n",
" expr(\"Connected(Rimnicu,Sibiu)\"),\n",
" expr(\"Connected(Sibiu,Fagaras)\"),\n",
" expr(\"Connected(Fagaras,Bucharest)\"),\n",
" expr(\"Connected(Pitesti,Craiova)\"),\n",
" expr(\"Connected(Craiova,Rimnicu)\")\n",
" ]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us add some logic propositions to complete our knowledge about travelling around the map. These are the typical symmetry and transitivity properties of connections on a map. We can now be sure that our `knowledge_base` understands what it truly means for two locations to be connected in the sense usually meant by humans when we use the term.\n",
"\n",
"Let's also add our starting location - *Sibiu* to the map."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"knowledge_base.extend([\n",
" expr(\"Connected(x,y) ==> Connected(y,x)\"),\n",
" expr(\"Connected(x,y) & Connected(y,z) ==> Connected(x,z)\"),\n",
" expr(\"At(Sibiu)\")\n",
" ])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now have a complete knowledge base, which can be seen like this:"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[Connected(Bucharest, Pitesti),\n",
" Connected(Pitesti, Rimnicu),\n",
" Connected(Rimnicu, Sibiu),\n",
" Connected(Sibiu, Fagaras),\n",
" Connected(Fagaras, Bucharest),\n",
" Connected(Pitesti, Craiova),\n",
" Connected(Craiova, Rimnicu),\n",
" (Connected(x, y) ==> Connected(y, x)),\n",
" ((Connected(x, y) & Connected(y, z)) ==> Connected(x, z)),\n",
" At(Sibiu)]"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"knowledge_base"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now define possible actions to our problem. We know that we can drive between any connected places. But, as is evident from [this](https://en.wikipedia.org/wiki/List_of_airports_in_Romania) list of Romanian airports, we can also fly directly between Sibiu, Bucharest, and Craiova.\n",
"\n",
"We can define these flight actions like this:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"#Sibiu to Bucharest\n",
"precond = 'At(Sibiu)'\n",
"effect = 'At(Bucharest) & ~At(Sibiu)'\n",
"fly_s_b = Action('Fly(Sibiu, Bucharest)', precond, effect)\n",
"\n",
"#Bucharest to Sibiu\n",
"precond = 'At(Bucharest)'\n",
"effect = 'At(Sibiu) & ~At(Bucharest)'\n",
"fly_b_s = Action('Fly(Bucharest, Sibiu)', precond, effect)\n",
"\n",
"#Sibiu to Craiova\n",
"precond = 'At(Sibiu)'\n",
"effect = 'At(Craiova) & ~At(Sibiu)'\n",
"fly_s_c = Action('Fly(Sibiu, Craiova)', precond, effect)\n",
"\n",
"#Craiova to Sibiu\n",
"precond = 'At(Craiova)'\n",
"effect = 'At(Sibiu) & ~At(Craiova)'\n",
"fly_c_s = Action('Fly(Craiova, Sibiu)', precond, effect)\n",
"\n",
"#Bucharest to Craiova\n",
"precond = 'At(Bucharest)'\n",
"effect = 'At(Craiova) & ~At(Bucharest)'\n",
"fly_b_c = Action('Fly(Bucharest, Craiova)', precond, effect)\n",
"\n",
"#Craiova to Bucharest\n",
"precond = 'At(Craiova)'\n",
"effect = 'At(Bucharest) & ~At(Craiova)'\n",
"fly_c_b = Action('Fly(Craiova, Bucharest)', precond, effect)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"And the drive actions like this."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"#Drive\n",
"precond = 'At(x)'\n",
"effect = 'At(y) & ~At(x)'\n",
"drive = Action('Drive(x, y)', precond, effect)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Our goal is defined as"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"goals = 'At(Bucharest)'"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Finally, we can define a a function that will tell us when we have reached our destination, Bucharest."
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def goal_test(kb):\n",
" return kb.ask(expr('At(Bucharest)'))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Thus, with all the components in place, we can define the planning problem."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"prob = PDDL(knowledge_base, goals, [fly_s_b, fly_b_s, fly_s_c, fly_c_s, fly_b_c, fly_c_b, drive])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## PLANNING PROBLEMS\n",
"---\n",
"\n",
"## Air Cargo Problem"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the Air Cargo problem, we start with cargo at two airports, SFO and JFK. Our goal is to send each cargo to the other airport. We have two airplanes to help us accomplish the task. \n",
"The problem can be defined with three actions: Load, Unload and Fly. \n",
"Let us look how the `air_cargo` problem has been defined in the module. "
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<!DOCTYPE html PUBLIC \"-//W3C//DTD HTML 4.01//EN\"\n",
" \"http://www.w3.org/TR/html4/strict.dtd\">\n",
"\n",
"<html>\n",
"<head>\n",
" <title></title>\n",
" <meta http-equiv=\"content-type\" content=\"text/html; charset=None\">\n",
" <style type=\"text/css\">\n",
"td.linenos { background-color: #f0f0f0; padding-right: 10px; }\n",
"span.lineno { background-color: #f0f0f0; padding: 0 5px 0 5px; }\n",
"pre { line-height: 125%; }\n",
"body .hll { background-color: #ffffcc }\n",
"body { background: #f8f8f8; }\n",
"body .c { color: #408080; font-style: italic } /* Comment */\n",
"body .err { border: 1px solid #FF0000 } /* Error */\n",
"body .k { color: #008000; font-weight: bold } /* Keyword */\n",
"body .o { color: #666666 } /* Operator */\n",
"body .ch { color: #408080; font-style: italic } /* Comment.Hashbang */\n",
"body .cm { color: #408080; font-style: italic } /* Comment.Multiline */\n",
"body .cp { color: #BC7A00 } /* Comment.Preproc */\n",
"body .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */\n",
"body .c1 { color: #408080; font-style: italic } /* Comment.Single */\n",
"body .cs { color: #408080; font-style: italic } /* Comment.Special */\n",
"body .gd { color: #A00000 } /* Generic.Deleted */\n",
"body .ge { font-style: italic } /* Generic.Emph */\n",
"body .gr { color: #FF0000 } /* Generic.Error */\n",
"body .gh { color: #000080; font-weight: bold } /* Generic.Heading */\n",
"body .gi { color: #00A000 } /* Generic.Inserted */\n",
"body .go { color: #888888 } /* Generic.Output */\n",
"body .gp { color: #000080; font-weight: bold } /* Generic.Prompt */\n",
"body .gs { font-weight: bold } /* Generic.Strong */\n",
"body .gu { color: #800080; font-weight: bold } /* Generic.Subheading */\n",
"body .gt { color: #0044DD } /* Generic.Traceback */\n",
"body .kc { color: #008000; font-weight: bold } /* Keyword.Constant */\n",
"body .kd { color: #008000; font-weight: bold } /* Keyword.Declaration */\n",
"body .kn { color: #008000; font-weight: bold } /* Keyword.Namespace */\n",
"body .kp { color: #008000 } /* Keyword.Pseudo */\n",
"body .kr { color: #008000; font-weight: bold } /* Keyword.Reserved */\n",
"body .kt { color: #B00040 } /* Keyword.Type */\n",
"body .m { color: #666666 } /* Literal.Number */\n",
"body .s { color: #BA2121 } /* Literal.String */\n",
"body .na { color: #7D9029 } /* Name.Attribute */\n",
"body .nb { color: #008000 } /* Name.Builtin */\n",
"body .nc { color: #0000FF; font-weight: bold } /* Name.Class */\n",
"body .no { color: #880000 } /* Name.Constant */\n",
"body .nd { color: #AA22FF } /* Name.Decorator */\n",
"body .ni { color: #999999; font-weight: bold } /* Name.Entity */\n",
"body .ne { color: #D2413A; font-weight: bold } /* Name.Exception */\n",
"body .nf { color: #0000FF } /* Name.Function */\n",
"body .nl { color: #A0A000 } /* Name.Label */\n",
"body .nn { color: #0000FF; font-weight: bold } /* Name.Namespace */\n",
"body .nt { color: #008000; font-weight: bold } /* Name.Tag */\n",
"body .nv { color: #19177C } /* Name.Variable */\n",
"body .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */\n",
"body .w { color: #bbbbbb } /* Text.Whitespace */\n",
"body .mb { color: #666666 } /* Literal.Number.Bin */\n",
"body .mf { color: #666666 } /* Literal.Number.Float */\n",
"body .mh { color: #666666 } /* Literal.Number.Hex */\n",
"body .mi { color: #666666 } /* Literal.Number.Integer */\n",
"body .mo { color: #666666 } /* Literal.Number.Oct */\n",
"body .sa { color: #BA2121 } /* Literal.String.Affix */\n",
"body .sb { color: #BA2121 } /* Literal.String.Backtick */\n",
"body .sc { color: #BA2121 } /* Literal.String.Char */\n",
"body .dl { color: #BA2121 } /* Literal.String.Delimiter */\n",
"body .sd { color: #BA2121; font-style: italic } /* Literal.String.Doc */\n",
"body .s2 { color: #BA2121 } /* Literal.String.Double */\n",
"body .se { color: #BB6622; font-weight: bold } /* Literal.String.Escape */\n",
"body .sh { color: #BA2121 } /* Literal.String.Heredoc */\n",
"body .si { color: #BB6688; font-weight: bold } /* Literal.String.Interpol */\n",
"body .sx { color: #008000 } /* Literal.String.Other */\n",
"body .sr { color: #BB6688 } /* Literal.String.Regex */\n",
"body .s1 { color: #BA2121 } /* Literal.String.Single */\n",
"body .ss { color: #19177C } /* Literal.String.Symbol */\n",
"body .bp { color: #008000 } /* Name.Builtin.Pseudo */\n",
"body .fm { color: #0000FF } /* Name.Function.Magic */\n",
"body .vc { color: #19177C } /* Name.Variable.Class */\n",
"body .vg { color: #19177C } /* Name.Variable.Global */\n",
"body .vi { color: #19177C } /* Name.Variable.Instance */\n",
"body .vm { color: #19177C } /* Name.Variable.Magic */\n",
"body .il { color: #666666 } /* Literal.Number.Integer.Long */\n",
"\n",
" </style>\n",
"</head>\n",
"<body>\n",
"<h2></h2>\n",
"\n",
"<div class=\"highlight\"><pre><span></span><span class=\"k\">def</span> <span class=\"nf\">air_cargo</span><span class=\"p\">():</span>\n",
" <span class=\"sd\">"""Air cargo problem"""</span>\n",
"\n",
" <span class=\"k\">return</span> <span class=\"n\">PDDL</span><span class=\"p\">(</span><span class=\"n\">init</span><span class=\"o\">=</span><span class=\"s1\">'At(C1, SFO) & At(C2, JFK) & At(P1, SFO) & At(P2, JFK) & Cargo(C1) & Cargo(C2) & Plane(P1) & Plane(P2) & Airport(SFO) & Airport(JFK)'</span><span class=\"p\">,</span>\n",
" <span class=\"n\">goals</span><span class=\"o\">=</span><span class=\"s1\">'At(C1, JFK) & At(C2, SFO)'</span><span class=\"p\">,</span> \n",
" <span class=\"n\">actions</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"n\">Action</span><span class=\"p\">(</span><span class=\"s1\">'Load(c, p, a)'</span><span class=\"p\">,</span> \n",
" <span class=\"n\">precond</span><span class=\"o\">=</span><span class=\"s1\">'At(c, a) & At(p, a) & Cargo(c) & Plane(p) & Airport(a)'</span><span class=\"p\">,</span> \n",
" <span class=\"n\">effect</span><span class=\"o\">=</span><span class=\"s1\">'In(c, p) & ~At(c, a)'</span><span class=\"p\">),</span>\n",
" <span class=\"n\">Action</span><span class=\"p\">(</span><span class=\"s1\">'Unload(c, p, a)'</span><span class=\"p\">,</span>\n",
" <span class=\"n\">precond</span><span class=\"o\">=</span><span class=\"s1\">'In(c, p) & At(p, a) & Cargo(c) & Plane(p) & Airport(a)'</span><span class=\"p\">,</span>\n",
" <span class=\"n\">effect</span><span class=\"o\">=</span><span class=\"s1\">'At(c, a) & ~In(c, p)'</span><span class=\"p\">),</span>\n",
" <span class=\"n\">Action</span><span class=\"p\">(</span><span class=\"s1\">'Fly(p, f, to)'</span><span class=\"p\">,</span>\n",
" <span class=\"n\">precond</span><span class=\"o\">=</span><span class=\"s1\">'At(p, f) & Plane(p) & Airport(f) & Airport(to)'</span><span class=\"p\">,</span>\n",
" <span class=\"n\">effect</span><span class=\"o\">=</span><span class=\"s1\">'At(p, to) & ~At(p, f)'</span><span class=\"p\">)])</span>\n",
"</pre></div>\n",
"</body>\n",
"</html>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"psource(air_cargo)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**At(c, a):** The cargo **'c'** is at airport **'a'**.\n",
"\n",
"**~At(c, a):** The cargo **'c'** is _not_ at airport **'a'**.\n",
"\n",
"**In(c, p):** Cargo **'c'** is in plane **'p'**.\n",
"\n",
"**~In(c, p):** Cargo **'c'** is _not_ in plane **'p'**.\n",
"\n",
"**Cargo(c):** Declare **'c'** as cargo.\n",
"\n",
"**Plane(p):** Declare **'p'** as plane.\n",
"\n",
"**Airport(a):** Declare **'a'** as airport.\n",
"\n",
"\n",
"\n",
"In the `initial_state`, we have cargo C1, plane P1 at airport SFO and cargo C2, plane P2 at airport JFK. \n",
"Our goal state is to have cargo C1 at airport JFK and cargo C2 at airport SFO. We will discuss on how to achieve this. Let us now define an object of the `air_cargo` problem:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"airCargo = air_cargo()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Before taking any actions, we will check if `airCargo` has reached its goal:"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"False\n"
]
}
],
"source": [
"print(airCargo.goal_test())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It returns False because the goal state is not yet reached. Now, we define the sequence of actions that it should take in order to achieve the goal.\n",
"The actions are then carried out on the `airCargo` PDDL.\n",
"\n",
"The actions available to us are the following: Load, Unload, Fly\n",
"\n",
"**Load(c, p, a):** Load cargo **'c'** into plane **'p'** from airport **'a'**.\n",
"\n",
"**Fly(p, f, t):** Fly the plane **'p'** from airport **'f'** to airport **'t'**.\n",
"\n",
"**Unload(c, p, a):** Unload cargo **'c'** from plane **'p'** to airport **'a'**.\n",
"\n",
"This problem can have multiple valid solutions.\n",
"One such solution is shown below."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"solution = [expr(\"Load(C1 , P1, SFO)\"),\n",
" expr(\"Fly(P1, SFO, JFK)\"),\n",
" expr(\"Unload(C1, P1, JFK)\"),\n",
" expr(\"Load(C2, P2, JFK)\"),\n",
" expr(\"Fly(P2, JFK, SFO)\"),\n",
" expr(\"Unload (C2, P2, SFO)\")] \n",
"\n",
"for action in solution:\n",
" airCargo.act(action)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As the `airCargo` has taken all the steps it needed in order to achieve the goal, we can now check if it has acheived its goal:"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"True\n"
]
}
],
"source": [
"print(airCargo.goal_test())"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It has now achieved its goal."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## The Spare Tire Problem"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's consider the problem of changing a flat tire of a car. \n",
"The goal is to mount a spare tire onto the car's axle, given that we have a flat tire on the axle and a spare tire in the trunk. "
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<!DOCTYPE html PUBLIC \"-//W3C//DTD HTML 4.01//EN\"\n",
" \"http://www.w3.org/TR/html4/strict.dtd\">\n",
"\n",
"<html>\n",
"<head>\n",
" <title></title>\n",
" <meta http-equiv=\"content-type\" content=\"text/html; charset=None\">\n",
" <style type=\"text/css\">\n",
"td.linenos { background-color: #f0f0f0; padding-right: 10px; }\n",
"span.lineno { background-color: #f0f0f0; padding: 0 5px 0 5px; }\n",
"pre { line-height: 125%; }\n",
"body .hll { background-color: #ffffcc }\n",
"body { background: #f8f8f8; }\n",
"body .c { color: #408080; font-style: italic } /* Comment */\n",
"body .err { border: 1px solid #FF0000 } /* Error */\n",
"body .k { color: #008000; font-weight: bold } /* Keyword */\n",
"body .o { color: #666666 } /* Operator */\n",
"body .ch { color: #408080; font-style: italic } /* Comment.Hashbang */\n",
"body .cm { color: #408080; font-style: italic } /* Comment.Multiline */\n",
"body .cp { color: #BC7A00 } /* Comment.Preproc */\n",
"body .cpf { color: #408080; font-style: italic } /* Comment.PreprocFile */\n",
"body .c1 { color: #408080; font-style: italic } /* Comment.Single */\n",
"body .cs { color: #408080; font-style: italic } /* Comment.Special */\n",
"body .gd { color: #A00000 } /* Generic.Deleted */\n",
"body .ge { font-style: italic } /* Generic.Emph */\n",