Planning using Situation Calculus, Prolog and a - CEUR
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1. X is Y 1 X is Y 1 obstaculo X S poss eliminar_obstaculo X S robot Y S X is Y 1 X is Y 1 obstaculo X S successor state axioms for primitive fluents robot X do A S robot Y S A avanzar X is Y 1 A retroceder X is Y 1 yy robot X S A avanzar A retroceder obstaculo X do A S A agregar_obstaculo X obstaculo X S A eliminar_obstaculo X legal axioms legal s0 legal do A S legal S poss A S cambia_s2n s0 ACC ACC cambia_s2n do A S1 ACC X cambia_s2n S1 A ACC X translates convierte X C X avanzar gt C 1 X eliminar_obstaculo _ gt C 2 X retroceder gt C 3 X agregar_obstaculo _ gt C 4 The two first lines specify the initial state of the scenario in this case the robot is in position three and there is an initial obstacle in position five The next four clauses specify the preconditions associated with the four actions that the robot can execute avanzar retroceder elimina_obstaculo X and agrega_obstaculo X For example the first clause specifies that the robot can advance in situation S only if the robot is at the position X and there is not an obstacle Planning using Situation Calculus Prolog and a Mobile Robot 5 at the position X in the same situation S The rest of the preconditions have similar interpretations The next two clauses consider the successor state axioms regarding the position of the r2. be executed Actions typically have effects that is fluents that are changed as a result of performing the action Effect axioms are called positive if they describe when a fluent becomes true and negative otherwise 1 For any fluent p and situation s p s denotes the true value of p in s It is assumed that every change in the world is caused by an action The evolution of the fluents is represented by successor state axioms these axioms were introduced to solve the infamous frame problem 6 that is the problem of specifying exactly what features of a scenario are not affected by an action For a fluent p the successor state axiom is S p do a s lt 7 a s v p s A 7 a s 1 where Ve a s captures exactly the conditions under which p turns from false to true when a is performed in s and similarly y a s captures exactly the conditions under which p turns from true to false when a is performed in s Furthermore in order to solve the problem of specifying precisely the conditions under which an action is executable the action precondition axioms were introduced These are used with a special fluent Poss a s meaning it is possible to execute the action A in situation s The axioms are of the form P poss A s Tl s 2 Where A is a symbol of an action and II s is a formula that defines the preconditions for the possibility of executing action A in s 2 1 Planning The planning is one of the m
3. the consultation represented by a query identifier The Prolog queries can then be executed with the help of the PrologNextSolution function this obtains a solution of the open query represented by the identifier of the query given as a parameter returning 1 when there is success 0 when there is a fault and 1 in the case of an error 6 Pilar Pozos Edgardo Yescas Jacob Vasquez After the successful return of PrologNextSolution the values assigned to the variables of the query can be obtained by the specific functions of the interface There are separate functions to obtain the value of the variables in a string PrologGetString or as an integer PrologGetLong The PrologGetString function obtains the value of a variable given within a query as a string where as PrologGetLong the value of the given variable is turned into a whole number returning 1 when there is a success In this way the most important lines of the program in VB are the following ones The string Expr is taken from the text box of the application which asks the user to write a query Q Expr Form the query qid PrologOpenQuery Q Open the query If qid 1 Then GoTo Err Verify the identifier of query gret PrologNextSolution qid Get a solution If gret lt gt 1 Then GoTo Err failed or error gret PrologGetString qid SS result Take the output in form of string Given the previous scenario if the robot has as a goal to arrive at pos
4. Avanzar 3 0 0 1 080 avanzar eliminar_obstaculo 3 avanzar 4 0 02 0 03 51 615 avanzar eliminar_obstaculo 3 avanzar eliminar_obstaculo 4 avanzar 5 0 13 0 22 338 240 avanzar eliminar_obstaculo 3 avanzar eliminar_obstaculo 4 avanzar avanzar 6 0 89 1 54 2 205 341 avanzar eliminar_obstaculo 3 avanzar eliminar_obstaculo 4 avanzar avanzar avanzar 10 Pilar Pozos Edgardo Yescas Jacob Vasquez 7 5 76 9 28 14 351 333 avanzar eliminar_obstaculo 3 avanzar eliminar_obstaculo 4 avanzar avanzar avanzar avanzar 8 40 48 60 33 93 454 303 avanzar eliminar_obstaculo 3 avanzar eliminar_obstaculo 4 avanzar avanzar avanzar avanzar avanzar 9 290 22 392 85 608 973 879 avanzar eliminar_obstaculo 3 avanzar eliminar_obstaculo 4 avanzar avanzar avanzar avanzar avanzar avanzar 400 T T T T T T p t 350 H i I 300 F dell I 250 toshiba 4 Time sec Position Fig 4 Position to reach vs time to obtain the answer for the query 2 Note that the time grows in an exponential fashion as the position increments On the other hand once the program in VB with the help of Prolog finds outs which actions to make the commands are sent to the robot in a serial form The time for delay that must exist between two consecutive commands is approximately 1 5 seconds Planning using Situation Calculus Prolog and a Mob
5. Planning using Situation Calculus Prolog and a Mobile Robot Pilar Pozos Edgardo Yescas Jacob Vasquez Divisi n de Estudios de Postgrado Universidad Tecnol gica de la Mixteca Carretera a Acatlima Km 2 5 Huajuapan de Le n Oaxaca Divisi n Acad mica de Informatica y Sistemas Universidad Ju rez Aut noma de Tabasco Carretera Cunduacan Km 1 Cunduacan Tabasco maripozos gmail com yescas mixteco utm mx jvasquez mixteco utm mx Abstract This paper presents a system that controls the behavior of a mobile robot The system is based on situation calculus the initial state is described and a goal is given Prolog produces an answer to this goal and we use an interface in Visual Basic to interpret the answer given by it After of interpreting the given actions in response we send commands to the mobile robot through a serial port from a computer This is a tool aimed at researchers and instructors in cognitive robotic 1 Introduction Generally a course in Artificial Intelligence AI can be considered interesting from a theoretical point of view However a practical side of this area is not commonly presented This work tries to show a way of bringing together theory and practice This paper presents a system which controls a mobile robot The central part of the system uses a planner that is based on situation calculus which has been implemented in Prolog The resulting plan is used by a program written in Visual B
6. acional de Informatica y Computaci n de la ANIEI Zacatecas 2003 4 Reiter R Knowledge in Action Logical Foundations for Specifying and Implementing Dynamical Systems MIT Press 2001 5 Intelligent System Laboratory SICStus Prolog User s Manual release 3 12 7 Swedish Institute of Computer Science October 2006 6 Reiter R The frame Problem in the situation calculus a simple solution sometimes and a completeness result for goal regression In Lifschitz V ed Artificial Intelligence and Mathematical Theory of Computation Papers in Honor of John McCarthy Academic Press 1991 359 380 7 User Manual Khepera II ftp k team com khepera documentation KheperaUserManual pdf
7. ar puero Puerto en uso COMI Velocidad Soluci n eranzar erninar_obstaculo nranzae sranzar sranzar wanzar wanzar Fig 1 Interface of user in VB To the left it is possible to see the robot s actions appear and to the right it shows the commands sent to the serial port 5 Test and results It is possible to verify that the plan created was executed as a series of action by the robot The following figure shows the robot and the obstacle Fig 2 Mobile robot follows the trajectory to the goal if an obstacle is in its way it removes it using the gripper 8 Pilar Pozos Edgardo Yescas Jacob Vasquez The test was applied to satisfy diverse goals with different obstacle s location and the results were satisfactory We tested our proposal with the following query legal S robot X S cambia_s2n S SS where X is the position that the robot must reach In order to compare the results obtained different computers were used e Dell Desktop Pentium IV 1 99 GHz 768 MB XP e Toshiba Laptop Celeron 1GHz 512 MB XP Consider as query 1 the following initial situation the robot is in position 1 and an object is in position 3 Table 1 shows different desired positions the time required to obtain the answer from Prolog and the inferences necessary for satisfying the goal Table 1 Values for the query 1 position to reach time required to obtain the answer and number of inferences Posi Time
8. asic VB that interprets the plan and sends the commands via the serial port to a mobile robot so that it carries out the actions needed to achieve the goal This paper is organized in the following way the second section begins with a brief revision of situation calculus and its use in the representation of the evolution of the world The third section shows the design of the system The fourth section describes the implementation followed by the tests and results in the fifth section Finally we conclude in the sixth section 2 The Situation Calculus The situation calculus is a dialect of first order logic in which situation and actions are explicitly taken to be objects in the domain In particular two types of first order terms are distinguished actions and situations Actions every change requires actions The constant and function symbols for actions are completely dependent on the application Situations denote possible world histories A distinguished constant 2 Pilar Pozos Edgardo Yescas Jacob Vasquez sO and function symbol do are used s0 denotes the initial situation before any action has been performed do a s denotes the new situation that results from the performing action a in situation s Predicates and functions whose values may vary from situation to situation are called fluents The last argument of a fluent is a situation Actions typically have preconditions that is conditions that need to be true for the action to
9. er remove_obstacle elimina_obstaculo and add_obstacle agrega_obstaculo If the robot carries out the action of advance the result is that the robot is in x if it was in x 1 if the robot carries out the action of reverse the result is that the robot is in x if it was in x 1 Moreover if it executes advance or reverse the result is that the robot is not in x anymore if it was in x we formally express these facts in the following successor state axiom robot x do a 8 lt gt robot x 1 s A a avanzar v 3 robot x I s a retroceder v robot x s a avanzar v a retroceder Observe that the translation of this axiom to Prolog language has the same structure robot X do A S robot Y S A avanzar X is Y 1 A retroceder X is Y 1 Jia robot X S A avanzar A retroceder ye 4 Implementation Considering the preconditions of actions the axioms of successor state the axioms of legality and finally the necessary conversions for VB the next program in Prolog works as the planner for the proposal in order to determine plans for the specified scenario Some comments are given below 4 Pilar Pozos Edgardo Yescas Jacob Vasquez initial conditions robot 3 s0 obstaculo 5 s0 preconditions for primitive actions poss avanzar S robot X S Y is X 1 obstaculo Y S poss retroceder S robot X S Y is X 1 obstaculo Y S poss agregar_obstaculo X S robot Y S
10. ile Robot 11 6 Conclusions We present the implementation of an interface that allows interpretation and transfer to a mobile robot of the results provided by a planner implemented in Prolog The planner was implemented in a declarative language giving the advantage of fast and easy modification of the representation of the initial situations and evolution of the scenes Handling of dynamical scenes is given through the axioms of successor states This is one of our first stages towards the creation of a cognitive robot It makes a compromise between the theory and practice and there are many issues that have been considered on both sides Future work will try to provide feedback to the planner based on environmental information This will be sensed by the robot and transferred via the serial port thus making it possible to revise the plan in the light of any changes to the situation In addition the development of two dimensions scenarios will be pursued to increase the degree of complexity of the planning task with the intention of giving the robot more realistic tasks References 1 Brachman R Levesque H Knowledge Representation And Reasoning Morgan Faufmann 2004 285 297 2 Demolombe R Pozos P Theories Of Intentions In The Framework Of Situation Calculus Springer Verlag Berlin Heidelberg 2005 3 Demolombe R Pozos P Implementaci n de la arquitectura BDI basada en el c lculo de situaciones In Proc 2ndo Congreso Intern
11. ition 7 the query would be Jegal S robot 7 S and the answer would be SS _ avancar eliminar_obstaculo 5 avanzar avanzar avanzar With this solution VB interprets the code as avanzar 1 eliminar_obstaculo X 2 retrocede 3 y agrega_obstaculo X 4 in order to create the string 1 2 1 1 1 This corresponds to a code in the VB program which translates orders which are sent to the serial port The orders sent to the robot are G 0 0 initialize the coordinates for the position of the robot C 600 600 indicate that the robot must be advance a distance of 4 8 cm if the command C 0 0 is sent the robot would be back to the initial position To control the arm we use the orders T 1 E 161 to lift the arm to the required position T 1 D 100 lowers the arm to the required position in order to remove an obstacle finally T 1 D 1 and T 1 D 0 is used to open and close the gripper respectively The next figure shows the user interface of the application in which it is possible to write a query and to get the solution It also allows the user to set the speed of communication for the serial port Planning using Situation Calculus Prolog and a Mobile Robot 7 Trayectoria del robot Khepera It Sauene sol obstaculo 3 Enviar lncluir saito de carro y avance de linea al ermar Rosultado dol intento de emio Se end terio SS Contiol de los puertos seriales Texto tesbeds Puoro COMI Velocidad 9600 bauds Co
12. obot fluent robot and the positions of the obstacles fluent obstaculo For example there is an obstacle in position X in situation do A S only if action A considers the introduction of an obstacle in position X A agrega_obstacle X or if in the previous situation i e in situation S there is already an obstacle in position X and the action does not consider the elimination of this obstacle not A remove_obstacle X The Prolog program considers the clause legal with only one parameter of type situation this clause allows the calculation of a situation that satisfies all the preconditions of actions appearing in the situation i e the legal clause verifies that the preconditions of the sequence of actions appearing in a situation are satisfied The function cambia_s2n is used to convert the form in which the answer appears so as to simplify its use in VB by removing the term do and ordering the actions to be executed by the robot We will say that the length of an optimal plan is less or equal to any other plan Notice that the program obtains an optimal plan as its first answer Given that in the search of the solution the planner builds using the legal clause situations which have the possibility of being executed and given that legal provides as the first situation the initial situation if it does not satisfy the goal then legal provides the situations with one action if these kinds of situations do not satisfy the goal then legal
13. ost useful ways that an intelligent agent can take advantage of the knowledge it has and its ability to reason about actions and their consequences The planning produces intelligent behavior and in particular the use of what is known to find a course of action that will achieve some goal Given its properties of representing dynamically changing worlds the situation calculus is a candidate to support planning 1 The planning task can be formulated in the language of the situation calculus as follows Given the knowledge base KB and a formula Goal s of the situation calculus with a single free variable s find a sequence of actions Ay 5 5 A such that KB Goal do s0 Legal do s0 3 Planning using Situation Calculus Prolog and a Mobile Robot 3 Where do s0 means do a do a _ do a 50 and Legal do a s0 is equal to A _ Poss a do d _ 50 where do da s0 s0 In others words given a goal formula we hope to find a sequence of actions beginning in the known initial situation so that e the goal formula will hold in the situation that results from executing the actions in sequence starting in the initial state and e itis possible to execute each action in the appropriate situation that is each action s precondition is satisfied 3 Design Take as an example the robot presented in 3 It considers four possible actions advance avanzar reverse retroced
14. provides the situations with two actions and so on We could be confident that the plan will contain the minimum number of actions possible The objective of this work is to use these results to control the movements of a mobile Khepera II robot its arm and its gripper The robot can be controlled through a serial port by issuing a sequence of instructions 7 Thanks to the research oriented nature of the robot s design its central processing unit CPU or microcontroller does not required any task specific programming and it responds to a set of commands To achieve this transmission of a series of commands to the robot it was necessary to use a program that served as a connection between Prolog and the robot This program should be developed in a language capable of sending data via the computer s serial port After some research it was determined that the SICStus Prolog program v3 12 7 provides a simple interface for unidirectional use which allows the loading and to calling of Prolog programs from VB As SICStus is executed under Windows XP in order to make a query in SICStus from VB the following considerations must be taken into account VB must explicitly be initialized calling the PrologInit function before calling others In order to execute a query it must be explicitly opened via the PrologOpenQuery function which returns a query identifier that can be used for recovery of the next solutions 5 The PrologCloseQuery will close
15. sec Time sec Inferences tion Dell Toshiba 1 0 0 51 agregar_obstaculo 0 2 0 0 22 Avanzar 3 0 0 1 080 avanzar eliminar_obstaculo 3 avanzar 4 0 0 01 7 361 avanzar eliminar_obstaculo 3 avanzar avanzar 5 0 01 0 03 49 645 avanzar eliminar_obstaculo 3 avanzar avanzar avanzar 6 0 13 0 22 330 033 avanzar eliminar_obstaculo 3 avanzar avanzar avanzar avanzar 7 0 89 1 43 2 179 704 avanzar eliminar_obstaculo 3 avanzar avanzar avanzar avanzar avanzar 8 5 74 9 47 14 356 233 avanzar eliminar_obstaculo 3 avanzar avanzar avanzar avanzar avanzar avanzar 9 37 7 66 12 94 532 951 avanzar eliminar_obstaculo 3 avanzar avanzar avanzar avanzar avanzar avanzar avanzar Planning using Situation Calculus Prolog and a Mobile Robot 9 70 T T T T T T T 6860F 50F e dell 40 F toshiba Time sec Position Fig 3 Graph position to reach vs time to obtained the answer for query 1 As query 2 we consider two obstacles and the initial position of the robot is 1 The initial situation of the planner was loaded as follows robot 1 s0 obstaculo 3 s0 obstaculo 4 s0 The obtained results are shown in Table 2 Table 2 Values for the query 2 position to reach time for calculating the answer number of inferences and plans Posi Time sec Time sec Inferences tion Dell Toshiba 1 0 0 51 agregar_obstaculo 0 2 0 0 22
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