UNIVERSIDAD AUTONOMA DEL CARMEN Dependencia académica de Ingeniería I ngeniería y Tecnología Tecnología Facultad de Ingeniería
Diseño y construcción de un brazo brazo robótico de de dos grados grados de libertad (RR) Carlos A. Presuel Marrufo; Edgar A. Chulínes Domínguez; Luís A. May Rejón; Ma. Elena Meza Abreu
Robótica
Ingeniería Mecatrónica Dr. Rogelio de J. Portillo Vélez
Ciudad del Carmen, Campeche, México a 12 de Diciembre de 2013
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Contenido
1. INTRODUCCIÓN................................. ................ .................................. ................................... .................. ................................... ................. .................. .................. 2 2. DISEÑO MECÁNICO ..................................................................................................................
7
2.1. SOLIDWORKS ......................................................................................................................
7
2.2 GEOMETRÍA DEL ROBOT .................................................................................................
7
3. CINEMÁTICA DE ROBOTS MANIPULADORES ................................................................. 8 3.1. CONVENCIÓN DE DENAVIT-HARTENBERG ..............................................................
9
4. DINÁMICA DE ROBOTS MANIPULADORES ..................................................................... 18 4.1. MODELADO MEDIANTE LA FORMULACIÓN DE LAGRANGE-EULER. ............ ............ 1 9 4.2. ALGORITMO COMPUTACIONAL PARA EL MODELADO DINÁMICO POR LAGRANGE-EULER. ................................................................................................................
20
5. DISPOSITIVOS ELECTRÓNICOS APLICADO A ROBÓTICA ........................................ 23 5.1. MOTORREDUCTORES CC .............................................................................................. 23 5.2. ENCODER MAGNÉTICOS (EFECTO HALL) ............................................................... 23 5.3. PUENTE H L298N ...............................................................................................................
24
5.4. ARDUINO UNO ...................................................................................................................
26
6. DIAGRAMA DE CONFIGURACIÓN .....................................................................................
27
7. CONTROL DE ROBOTS ..........................................................................................................
28
7.1. CONTROL DE POSICIÓN DE ROBOTS MANIPULADORES.................................. ................. ................... .. 28 7.2. CONTROL DINÁMICO (PID) ........................................................................................... 30 8. RESULTADOS ............................................................................................................................
36
9. CONCLUSIONES .......................................................................................................................
38
10. BIBLIOGRAFÍA .......................................................................................................................
39
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Diseño y construcción de un robot manipulador de 2 GDL
Robótica
1. INTRODUCCIÓ I NTRODUCCIÓN N El hombre industrializado desde el siglo XX ha tenido la necesidad de aprender y adaptar términos globalizados tecnológicos, para Barrientos la palabra computadora quizás fue la más relevante y hasta hoy muchos cuentan con su propia computadora personal, pero un concepto recientemente relevante es la palabra robot . El término robot nació y creció de un mito: la creación por los humanos de un ser artificial que emulase en aspecto y capacidades cognitivas a su propio creador. Desde 1921, fecha de publicación por K. Capek de la obra de teatro «Robots Universales de Rossum», la literatura y el cine han alimentado este mito. [1]
Fig. 1. Robot industrial de seis grados con carga útil de 220 Kg
La palabra robot proviene proviene de la palabra checa robota que robota que significa trabajo. El diccionario Webster define a un robot como “dispositivo automático que efectúa funciones
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Diseño y construcción de un robot manipulador de 2 GDL
Robótica
reprogramable multifuncional diseñado para mover materiales, piezas o dispositivos industrializados, a través de movimientos programados variables para la realización de una diversidad de tareas. [2]
Para Fu se pueden clasificar los robots industriales en tres generaciones que se enlistan en la siguiente tabla:
GENERACIÓN a
1 Generación
a
2 Generación
a
3 Generación
DESCRIPCIÓN Repite la tarea programada secuencialmente. No toma en cuenta las posibles alteraciones de su entorno. Adquiere la información limitada en su entorno y actúa en consecuencia. Puede localizar, clasificar (visón) y detectar esfuerzos y adaptar sus movimientos en consecuencia. Su programación se realiza mediante el empleo de un lenguaje natural. Posee la capacidad de planificación automática Tabla 1. Generación en robótica
La International Federation of Robotic distingue cuatro tipos de robots:
Robot secuencial
Robot de trayectorias controlables
Robot Adaptivos
Robots Telemanipulado
Sin embargo, Reyes (2011) define que actualmente existen una gran cantidad de robots con diversas estructuras geométricas y mecánicas que definen su funcionalidad y aplicación. De manera general pueden clasificarse como muestra la tabla 2.
CLASIFICACIÓN DE ROBOTS Móviles
Terrestres: ruedas patas
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Diseño y construcción de un robot manipulador de 2 GDL
Robótica
Un robot está formado por los siguientes elementos: estructura mecánica, trasmisiones, sistema de accionamiento, sistema sensorial, sistema de control y elementos terminales. La figura 2 muestra un ejemplo de los elementos en un robot.
Fig. 2. Ejemplo de una estructura mecánica y elementos consecutivos de un robot.
Cada uno de los movimientos independientes que puede realizar cada articulación con respecto a la anterior, se denomina grado de libertad (GDL). En la figura 3 se muestra el
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Diseño y construcción de un robot manipulador de 2 GDL
Robótica
Fig. 3. Distintos tipos de articulaciones para robots.
El empleo de diferentes combinaciones de articulaciones en un robot, da lugar a diferentes configuraciones, con características a en cuenta tanto el diseño y construcción del robot como en su aplicación. Las combinaciones más frecuentes son representadas en la figura 4 donde se atiende únicamente a las tres primeras articulaciones del robot, que son las más importantes a la hora de posicionar su extremo en un punto en el espacio.
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Diseño y construcción de un robot manipulador de 2 GDL
Robótica
Puesto que para posicionar y orientar un cuerpo de cualquier manera en el espacio son necesarios seis parámetros, tres para definir la orientación y tres para la posición, si se pretende que un robot posicione y oriente su extremo de cualquier modo en el espacio, esp acio, se precisarán al menos 6 GDL. En la práctica, a pesar de ser necesarios los seis GDL comentados para tener total libertad en el posicionamiento y orientación del extremo del robot, muchos robots industriales muchos robots industriales cuentan con sólo cuatro o cinco GDL , por ser éstos suficientes para llevar a cabo tareas que se les encomiendan.
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Diseño y construcción de un robot manipulador de 2 GDL
Robótica
2. DISEÑO MECÁNICO 2.1. SOLIDWORKS SolidWorks es un programa de diseño asistido por computadora para modelado mecánico desarrollado en la actualidad por SolidWorks Corp., una subsidiaria de Dassault de Dassault Systèmes (Suresnes, Francia), para el sistema operativo Microsoft Windows. Es un modelador de sólidos paramétrico. Fue introducido en el mercado en 1995 para competir con otros programas CAD como Pro/ENGINEER, NX, Pro/ENGINEER, NX, Solid Edge, CATIA, yAutodesk Mechanical Desktop. El programa permite modelar piezas y conjuntos y extraer de ellos tanto planos técnicos como otro tipo de información necesaria para la producción. Es un programa que funciona con base en las nuevas nu evas técnicas de modelado con sistemas CAD. El proceso consiste en trasvasar la idea mental del diseñador al sistema CAD, "construyendo virtualmente" la pieza o conjunto. Posteriormente todas las extracciones (planos y ficheros de intercambio) se realizan de manera bastante automatizada. La empresa SolidWorks Corp. fue fundada en 1993 por Jon Hirschtick con su sede en Concord, Massachusetts y lanzó su primer producto, SolidWorks 95, en 1995. En 1997 Dassault Systèmes, mejor conocida por su software CAD CATIA, adquirió la compañía. Actualmente posee el 100% de sus acciones y es liderada por Jeff Ray.
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Diseño y construcción de un robot manipulador de 2 GDL
Robótica
Nosotros realizaremos la segunda opción ya que no hay específicamente una tarea debido a que se trata de fines didácticos. En la figura 5 se muestra el diseño en 3D de nuestro prototipo ideado parta el proyecto.
Fig. 5. Diseño del nuestro proyecto de robótica con Solidworks 2013
3. CINEMÁTICA DE ROBOTS MANIPULADORES MANIPULADORES La cinemática del robot estudia el movimiento del mismo con respecto a un sistema de referencia. Así, la cinemática se interesa por la descripción analítica del movimiento
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Diseño y construcción de un robot manipulador de 2 GDL
Robótica
cinemática inverso resuelve la configuración que debe adoptar el robot para una posición y orientación del extremo conocidas. [9]
3.1. CONVENCIÓN DE DENAVIT-HARTENBER DENAVIT-HARTENBERG G Existen varios métodos para obtener el modelo de cinemática directa, se utiliza por lo general el álgebra vectorial y matricial para representar y describir la localización de un objeto en el espacio tridimensional con respecto a un sistema de referencia fijo. Dado que un robot se puede considerar una cadena cinemática formada por objetos rígidos o eslabones eslabones unidos entre sí mediante articulaciones, se puede establecer un sistema de referencia fijo situado en la base del robot y describir la localización de cada eslabón con respecto a la referencia fija. [11]
El estudio de los parámetros Denavit-Hartenberg (DH) forma parte de todo curso básico sobre robótica, ya que son un estándar a la hora de describir la geometría de un brazo o manipulador robótico. Se usan para resolver de forma trivial el problema de la cinemática directa, y como punto p unto inicial para plantear el más complejo de cinemática inversa. A continuación se describen los pasos necesarios para su desarrollo.
DH1. Numerar los eslabones comenzando con 1 (primer eslabón móvil de la cadena) y acabando con n (último eslabón móvil). Se numerara como eslabón 0 a la base fija del robot.
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Diseño y construcción de un robot manipulador de 2 GDL
Robótica
DH5. Situar el origen del sistema de la base (S0) en cualquier punto del eje Z0. Los ejes X0 e Y0 se situaran dé modo que formen un sistema dextrógiro con Z0.
DH6. Para i de 1 a n-1, situar el sistema (Si) (solidario al eslabón i) en la intersección del eje Zi con la línea normal no rmal común a Zi-1 y Zi. Si ambos ejes se cortasen se situaría (Si) en el punto de corte. Si fuesen paralelos (Si) se situaría en la articulación i+1.
DH7. Situar Xi en la línea normal común a Zi-1 y Zi.
DH8.Situar DH8.Situar Yi de modo que forme un sistema dextrógiro con Xi y Zi.
DH9. DH9. Situar el sistema (Sn) en el extremo del robot de modo que Zn coincida con la dirección de Zn-1 y Xn sea normal a Zn-1 y Zn.
DH10. Obtener Øi como el ángulo que hay que girar en torno a Zi-1 para que Xi-1 y Xi queden paralelos.
DH11. Obtener Di como la distancia, medida a lo largo de Zi-1, que habría que desplazar (Si-1) para que Xi y Xi-1 quedasen alineados.
DH12. Obtener Ai como la distancia medida a lo largo de Xi (que ahora coincidiría con Xi1) que habría que desplazar el nuevo (Si-1) para que su origen coincidiese con (Si).
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Diseño y construcción de un robot manipulador de 2 GDL
Robótica
DH16. La DH16. La matriz T define la orientación (submatriz de rotación) y posición (submatriz de traslación) del extremo referido a la base en función de las n coordenadas articulares. Aplicando los puntos anteriores a nuestro diseño en la figura 6, obtendremos la siguiente tabla 3.
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Diseño y construcción de un robot manipulador de 2 GDL
Robótica
Las relaciones entre eslabones no consecutivos vienen dadas por las matrices T que se obtienen como producto de un conjunto de matrices A. Obtenida la matriz T, esta expresara la orientación (submatriz (3x3) de rotación) y posición (submatriz (3x1) de traslación) del extremo del robot en función de sus coordenadas articulares, con lo que quedara resuelto el p roblema cinemático directo. [2]
Matrices de transformación
i-1
i-1
0
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Diseño y construcción de un robot manipulador de 2 GDL
Robótica
Para corroborar los parámetros y el modelo cinemático, nos apoyamos de MATLAB y con el siguiente código:
clc clear syms q1 q2 L1 L2 L3 pi M real %pi=3.14159; %Denavith - Hatenberg A_01=dena(q1+pi/2, L1, L2, pi/2) A_12=dena(q2-pi/2 , 0, L3, 0) % Matrices de transformacion parciales T_01=A_01 T_02=A_01*A_12 P1=T_01*[0 0 0 1]' P2=T_02*[0 0 0 1]' %%% Valores de las articulaciones i=1; L1=0.30;
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Diseño y construcción de un robot manipulador de 2 GDL
Se puede observa el resultado del código en la figura 7. Modelo Cinemático
0.3
0.25
0.2
Z
0.15
0.1
0.05
0 0.2 0.15
0.15 0.1
0.1
0.05 0.05
0 -0.05
0 -0.05
-0.1
Fig. 7. Respuesta del modelo cinemático en MATLAB
Robótica
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Diseño y construcción de un robot manipulador de 2 GDL
Robótica
Al contrario de lo que ocurría en el problema cinematico directo, con cierta
frecuencia la solución del problema cinematico inverso no es única; existiendo diferentes n-uplas
que posicionan y orientan el extremo del
robot de mismo modo. En estos casos una solución cerrada permite incluir determinadas reglas o restricciones que aseguren que la solución obtenida sea la más adecuada posible.
No obstante, a pesar de las dificultades comentadas, la mayor parte de los robots poseen cinemáticas relativamente simples que facilitan en cierta medida la resolución de su problema cinemático inverso.
Por ejemplo si se consideran solo tres primeros grados de libertad de muchos robots, estos tienen una estructura planar, esto es, los tres primeros elementos quedan contenidos en un plano. Esta circunstancia facilita la resolución del problema. Asimismo, en muchos robots se da la circunstancia de que los tres grados de libertad últimos, dedicados
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Diseño y construcción de un robot manipulador de 2 GDL
P1=T_01*[0 0 0 1]' P2=T_02*[0 0 0 1]' %%% Valores de las articulaciones i=1; L1=0.30; L2=0.16; L3=0.12; q1=1.0*(i-1)*15*(pi/180); q2=1.0*(i-1)*15*(pi/180); P_0=[0 0 0]'; P_1=eval(P1(1:3)); P_2=eval(P2(1:3));
Robótica
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Diseño y construcción de un robot manipulador de 2 GDL
Robótica
El modelado cinemático de un robot busca las relaciones entre las variables articulares y la posición (expresada normalmente en forma de coordenadas cartesianas) y orientación del extremo del robot. En esta relación no se tienen en cuenta las fuerzas o pares que actúan sobre el robot (actuadores, cargas, fricciones, etc.) y que pueden originar el movimiento del mismo. Sin embargo, sí que debe permitir conocer, además de la relación entre las coordenadas articulares y del extremo, la relación entre sus respectivas derivadas. Así, el sistema de control del robot debe establecer que velocidades debe imprimir a cada articulación (a través de sus respectivos actuadores) para conseguir que el extremo desarrolle una
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Diseño y construcción de un robot manipulador de 2 GDL
Robótica
J32=diff(f3,'q2' J32=diff(f3,'q2'); ); J=[J11 J12; J21 J22; J31 J32]; Jinv=pinv(J) OK=J*Jinv
Con esto comprobamos que nuestro Jacobiano se realizo correctamente. Podemos seguir avanzando.
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Diseño y construcción de un robot manipulador de 2 GDL
Robótica
Para un par motor t determinado, la integración de la ecuación anterior, daría lugar a la expresión de q(t) y de sus derivadas dq(t) y d²q(t), con lo que sería posible conocer la evolución de la coordenada articular del robot y de su velocidad y aceleración.
De forma inversa, si se pretende que q(t) evolucione según una determinada función del tiempo, sustituyendo en la ecuación anterior, podría obtenerse el par t(t) que sería necesario aplicar. Si el robot tuviese que ejercer alguna fuerza en su extremo, ya sea al manipular una carga o por ejemplo, realizar un proceso sobre alguna pieza, bastaría con incluir esta condición en la mencionada ecuación y proceder del mismo modo. [12]
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Diseño y construcción de un robot manipulador de 2 GDL
Robótica
Este planteamiento utiliza, por tanto, las matrices i-1Ai que relacionan el sistema de coordenadas de referencia del elemento i con el elemento i-1. Se realizan en este caso operaciones de producto y suma innecesarias. Se trata de un procedimiento ineficiente desde el punto de vista computacional. Puede comprobarse que el algoritmo es de un orden de complejidad computacional O(n²²), es decir, el número de operaciones a realizar crece con la potencia 4 del numero de grados de libertad. Sin embargo, conduce a unas ecuaciones finales bien estructuradas donde aparecen de manera clara los diversos pares y fuerzas que intervienen en el movimiento.
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Diseño y construcción de un robot manipulador de 2 GDL
Ji= X² dm YiXi dm ZiXi dm Xi dm
XiYi dm Yi² dm ZiYi dm Yi dm
XiZi dm YiZi dm Zi² dm Zi dm
Xi dm Yi dm Zi dm dm
Robótica
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Diseño y construcción de un robot manipulador de 2 GDL
Robótica
irj : Es el vector de coordenadas homogéneas del centro de masas del elemento j expresado en el sistema de referencia del elemento i. L-E 10. La ecuación dinámica del sistema será:
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Diseño y construcción de un robot manipulador de 2 GDL
5. DISPOSITIVOS ELECTRÓNICOS APLICADO A ROBÓTICA 5.1. MOTORREDUCTORES CC
Robótica
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Diseño y construcción de un robot manipulador de 2 GDL
Robótica
A diferencia de las foto barreras (encoders ópticos), los sensores Hall al ser magnéticos pueden trabajar en entornos extremos (temperatura) y polvorientos, no hará falta mantenimiento de limpieza. Por otra parte, prácticamente (si sabes buscar) no existe mucha
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Diseño y construcción de un robot manipulador de 2 GDL
Conversor CC-CA
Amplificadores clase D
Entre otras
Robótica
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Trusted by over 1 million members
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Trusted by over 1 million members
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Trusted by over 1 million members
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Trusted by over 1 million members
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Trusted by over 1 million members
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Trusted by over 1 million members
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Trusted by over 1 million members
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Trusted by over 1 million members
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Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.
Trusted by over 1 million members
Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.