Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3

Library to demonstrate robot system models based on the Manutec r3 robot

Information

This package contains models of the robot r3 of the company Manutec. These models are used to demonstrate in which way complex robot models might be built up by testing first the component models individually before composing them together. Furthermore, it is shown how CAD data can be used for animation.

The following models are available:

   oneAxis   Test one axis (controller, motor, gearbox).
   fullRobot Test complete robot model.

The r3 robot is no longer manufactured. In fact the company Manutec does no longer exist. The parameters of this robot have been determined by measurements in the laboratory of DLR. The measurement procedure is described in:

   Tuerk S. (1990): Zur Modellierung der Dynamik von Robotern mit
       rotatorischen Gelenken. Fortschrittberichte VDI, Reihe 8, Nr. 211,
       VDI-Verlag 1990.

The robot model is described in detail in

   Otter M. (1995): Objektorientierte Modellierung mechatronischer
       Systeme am Beispiel geregelter Roboter. Dissertation,
       Fortschrittberichte VDI, Reihe 20, Nr. 147, VDI-Verlag 1995.
       This report can be downloaded as compressed postscript file
       from: http://www.robotic.dlr.de/Martin.Otter.

The path planning is performed in a simple way by using essentially the Modelica.Mechanics.Rotational.KinematicPTP block. A user defines a path by start and end angle of every axis. A path is planned such that all axes are moving as fast as possible under the given restrictions of maximum joint speeds and maximum joint accelerations. The actual r3 robot from Manutec had a different path planning strategy. Todays path planning algorithms from robot companies are much more involved.

In order to get a nice animation, CAD data from a KUKA robot is used, since CAD data of the original r3 robot was not available. The KUKA CAD data was derived from public data of KUKA available at: http://www.kuka-roboter.de/english/produkte/cad/low_payloads.html. Since dimensions of the corresponding KUKA robot are similar but not identical to the r3 robot, the data of the r3 robot (such as arm lengths) have been modified, such that it matches the CAD data.

In this model, a simplified P-PI cascade controller for every axes is used. The parameters have been manually adjusted by simulations. The original r3 controllers are more complicated. The reason to use simplified controllers is to have a simpler demo.

Extends from Modelica.Icons.ExamplesPackage (Icon for packages containing runnable examples).

Package Content

Name Description

oneAxis Model of one axis of robot (controller, motor, gearbox) with simple load

fullRobot 6 degree of freedom robot with path planning, controllers, motors, brakes, gears and mechanics

Components Library of components of the robot

Name	Description
oneAxis	Model of one axis of robot (controller, motor, gearbox) with simple load
fullRobot	6 degree of freedom robot with path planning, controllers, motors, brakes, gears and mechanics
Components	Library of components of the robot

Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.oneAxis

Model of one axis of robot (controller, motor, gearbox) with simple load

Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.oneAxis

Information

With this model one axis of the r3 robot is checked. The mechanical structure is replaced by a simple load inertia.

Extends from Modelica.Icons.Example (Icon for runnable examples).

Parameters

Type Name Default Description

Mass mLoad 15 Mass of load [kg]

Real kp 5 Gain of position controller of axis 2

Real ks 0.5 Gain of speed controller of axis 2

Time Ts 0.05 Time constant of integrator of speed controller of axis 2 [s]

Real startAngle 0 Start angle of axis 2 [deg]

Real endAngle 120 End angle of axis 2 [deg]

Time swingTime 0.5 Additional time after reference motion is in rest before simulation is stopped [s]

AngularVelocity refSpeedMax 3 Maximum reference speed [rad/s]

AngularAcceleration refAccMax 10 Maximum reference acceleration [rad/s2]

Type	Name	Default	Description
Mass	mLoad	15	Mass of load [kg]
Real	kp	5	Gain of position controller of axis 2
Real	ks	0.5	Gain of speed controller of axis 2
Time	Ts	0.05	Time constant of integrator of speed controller of axis 2 [s]
Real	startAngle	0	Start angle of axis 2 [deg]
Real	endAngle	120	End angle of axis 2 [deg]
Time	swingTime	0.5	Additional time after reference motion is in rest before simulation is stopped [s]
AngularVelocity	refSpeedMax	3	Maximum reference speed [rad/s]
AngularAcceleration	refAccMax	10	Maximum reference acceleration [rad/s2]

Modelica definition

model oneAxis 
  "Model of one axis of robot (controller, motor, gearbox) with simple load"

  import SI = Modelica.SIunits;
  extends Modelica.Icons.Example;
  parameter SI.Mass mLoad(min=0)=15 "Mass of load";
  parameter Real kp=5 "Gain of position controller of axis 2";
  parameter Real ks=0.5 "Gain of speed controller of axis 2";
  parameter SI.Time Ts=0.05 
    "Time constant of integrator of speed controller of axis 2";
  parameter Real startAngle(unit="deg") = 0 "Start angle of axis 2";
  parameter Real endAngle(unit="deg") = 120 "End angle of axis 2";

  parameter SI.Time swingTime=0.5 
    "Additional time after reference motion is in rest before simulation is stopped";
  parameter SI.AngularVelocity refSpeedMax=3 "Maximum reference speed";
  parameter SI.AngularAcceleration refAccMax=10 
    "Maximum reference acceleration";

  Components.AxisType1 axis(
    w=5500,
    ratio=210,
    c=8,
    cd=0.01,
    Rv0=0.5,
    Rv1=(0.1/130),
    kp=kp,
    ks=ks,
    Ts=Ts);
  Modelica.Mechanics.Rotational.Components.Inertia load(
                                             J=1.3*mLoad);
  Components.PathPlanning1 pathPlanning(
    swingTime=swingTime,
    angleBegDeg=startAngle,
    angleEndDeg=endAngle,
    speedMax=refSpeedMax,
    accMax=refAccMax);
protected 
  Components.ControlBus controlBus;
equation 
  connect(axis.flange, load.flange_a);
  connect(pathPlanning.controlBus, controlBus);
  connect(controlBus.axisControlBus1, axis.axisControlBus);
end oneAxis;

Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.fullRobot

6 degree of freedom robot with path planning, controllers, motors, brakes, gears and mechanics

Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.fullRobot

Information

This is a detailed model of the robot. For animation CAD data is used. Translate and simulate with the default settings (default simulation time = 3 s). Use command script "modelica://Modelica/Resources/Scripts/Dymola/Mechanics/MultiBody/Examples/Systems/fullRobotPlot.mos" to plot variables.

model Examples.Loops.Systems.RobotR3.fullRobot

Extends from Modelica.Icons.Example (Icon for runnable examples).

Parameters

Type Name Default Description

Mass mLoad 15 Mass of load [kg]

Position rLoad[3] {0.1,0.25,0.1} Distance from last flange to load mass [m]

Acceleration g 9.81 Gravity acceleration [m/s2]

Time refStartTime 0 Start time of reference motion [s]

Time refSwingTime 0.5 Additional time after reference motion is in rest before simulation is stopped [s]

Reference

startAngles

Real startAngle1 -60 Start angle of axis 1 [deg]

Real startAngle2 20 Start angle of axis 2 [deg]

Real startAngle3 90 Start angle of axis 3 [deg]

Real startAngle4 0 Start angle of axis 4 [deg]

Real startAngle5 -110 Start angle of axis 5 [deg]

Real startAngle6 0 Start angle of axis 6 [deg]

endAngles

Real endAngle1 60 End angle of axis 1 [deg]

Real endAngle2 -70 End angle of axis 2 [deg]

Real endAngle3 -35 End angle of axis 3 [deg]

Real endAngle4 45 End angle of axis 4 [deg]

Real endAngle5 110 End angle of axis 5 [deg]

Real endAngle6 45 End angle of axis 6 [deg]

Limits

AngularVelocity refSpeedMax[6] {3,1.5,5,3.1,3.1,4.1} Maximum reference speeds of all joints [rad/s]

AngularAcceleration refAccMax[6] {15,15,15,60,60,60} Maximum reference accelerations of all joints [rad/s2]

Controller

Axis 1

Real kp1 5 Gain of position controller

Real ks1 0.5 Gain of speed controller

Time Ts1 0.05 Time constant of integrator of speed controller [s]

Axis 2

Real kp2 5 Gain of position controller

Real ks2 0.5 Gain of speed controller

Time Ts2 0.05 Time constant of integrator of speed controller [s]

Axis 3

Real kp3 5 Gain of position controller

Real ks3 0.5 Gain of speed controller

Time Ts3 0.05 Time constant of integrator of speed controller [s]

Axis 4

Real kp4 5 Gain of position controller

Real ks4 0.5 Gain of speed controller

Time Ts4 0.05 Time constant of integrator of speed controller [s]

Axis 5

Real kp5 5 Gain of position controller

Real ks5 0.5 Gain of speed controller

Time Ts5 0.05 Time constant of integrator of speed controller [s]

Axis 6

Real kp6 5 Gain of position controller

Real ks6 0.5 Gain of speed controller

Time Ts6 0.05 Time constant of integrator of speed controller [s]

Type	Name	Default	Description
Mass	mLoad	15	Mass of load [kg]
Position	rLoad[3]	{0.1,0.25,0.1}	Distance from last flange to load mass [m]
Acceleration	g	9.81	Gravity acceleration [m/s2]
Time	refStartTime	0	Start time of reference motion [s]
Time	refSwingTime	0.5	Additional time after reference motion is in rest before simulation is stopped [s]
Reference
startAngles
Real	startAngle1	-60	Start angle of axis 1 [deg]
Real	startAngle2	20	Start angle of axis 2 [deg]
Real	startAngle3	90	Start angle of axis 3 [deg]
Real	startAngle4	0	Start angle of axis 4 [deg]
Real	startAngle5	-110	Start angle of axis 5 [deg]
Real	startAngle6	0	Start angle of axis 6 [deg]
endAngles
Real	endAngle1	60	End angle of axis 1 [deg]
Real	endAngle2	-70	End angle of axis 2 [deg]
Real	endAngle3	-35	End angle of axis 3 [deg]
Real	endAngle4	45	End angle of axis 4 [deg]
Real	endAngle5	110	End angle of axis 5 [deg]
Real	endAngle6	45	End angle of axis 6 [deg]
Limits
AngularVelocity	refSpeedMax[6]	{3,1.5,5,3.1,3.1,4.1}	Maximum reference speeds of all joints [rad/s]
AngularAcceleration	refAccMax[6]	{15,15,15,60,60,60}	Maximum reference accelerations of all joints [rad/s2]
Controller
Axis 1
Real	kp1	5	Gain of position controller
Real	ks1	0.5	Gain of speed controller
Time	Ts1	0.05	Time constant of integrator of speed controller [s]
Axis 2
Real	kp2	5	Gain of position controller
Real	ks2	0.5	Gain of speed controller
Time	Ts2	0.05	Time constant of integrator of speed controller [s]
Axis 3
Real	kp3	5	Gain of position controller
Real	ks3	0.5	Gain of speed controller
Time	Ts3	0.05	Time constant of integrator of speed controller [s]
Axis 4
Real	kp4	5	Gain of position controller
Real	ks4	0.5	Gain of speed controller
Time	Ts4	0.05	Time constant of integrator of speed controller [s]
Axis 5
Real	kp5	5	Gain of position controller
Real	ks5	0.5	Gain of speed controller
Time	Ts5	0.05	Time constant of integrator of speed controller [s]
Axis 6
Real	kp6	5	Gain of position controller
Real	ks6	0.5	Gain of speed controller
Time	Ts6	0.05	Time constant of integrator of speed controller [s]

Modelica definition

model fullRobot 
  "6 degree of freedom robot with path planning, controllers, motors, brakes, gears and mechanics"
  extends Modelica.Icons.Example;

  import SI = Modelica.SIunits;

  parameter SI.Mass mLoad(min=0) = 15 "Mass of load";
  parameter SI.Position rLoad[3]={0.1,0.25,0.1} 
    "Distance from last flange to load mass";
  parameter SI.Acceleration g=9.81 "Gravity acceleration";
  parameter SI.Time refStartTime=0 "Start time of reference motion";
  parameter SI.Time refSwingTime=0.5 
    "Additional time after reference motion is in rest before simulation is stopped";

  parameter Real startAngle1(unit="deg") = -60 "Start angle of axis 1";
  parameter Real startAngle2(unit="deg") = 20 "Start angle of axis 2";
  parameter Real startAngle3(unit="deg") = 90 "Start angle of axis 3";
  parameter Real startAngle4(unit="deg") = 0 "Start angle of axis 4";
  parameter Real startAngle5(unit="deg") = -110 "Start angle of axis 5";
  parameter Real startAngle6(unit="deg") = 0 "Start angle of axis 6";

  parameter Real endAngle1(unit="deg") = 60 "End angle of axis 1";
  parameter Real endAngle2(unit="deg") = -70 "End angle of axis 2";
  parameter Real endAngle3(unit="deg") = -35 "End angle of axis 3";
  parameter Real endAngle4(unit="deg") = 45 "End angle of axis 4";
  parameter Real endAngle5(unit="deg") = 110 "End angle of axis 5";
  parameter Real endAngle6(unit="deg") = 45 "End angle of axis 6";

  parameter SI.AngularVelocity refSpeedMax[6]={3,1.5,5,3.1,3.1,4.1} 
    "Maximum reference speeds of all joints";
  parameter SI.AngularAcceleration refAccMax[6]={15,15,15,60,60,60} 
    "Maximum reference accelerations of all joints";

  parameter Real kp1=5 "Gain of position controller";
  parameter Real ks1=0.5 "Gain of speed controller";
  parameter SI.Time Ts1=0.05 "Time constant of integrator of speed controller";
  parameter Real kp2=5 "Gain of position controller";
  parameter Real ks2=0.5 "Gain of speed controller";
  parameter SI.Time Ts2=0.05 "Time constant of integrator of speed controller";
  parameter Real kp3=5 "Gain of position controller";
  parameter Real ks3=0.5 "Gain of speed controller";
  parameter SI.Time Ts3=0.05 "Time constant of integrator of speed controller";
  parameter Real kp4=5 "Gain of position controller";
  parameter Real ks4=0.5 "Gain of speed controller";
  parameter SI.Time Ts4=0.05 "Time constant of integrator of speed controller";
  parameter Real kp5=5 "Gain of position controller";
  parameter Real ks5=0.5 "Gain of speed controller";
  parameter SI.Time Ts5=0.05 "Time constant of integrator of speed controller";
  parameter Real kp6=5 "Gain of position controller";
  parameter Real ks6=0.5 "Gain of speed controller";
  parameter SI.Time Ts6=0.05 "Time constant of integrator of speed controller";
  Components.MechanicalStructure mechanics(
    mLoad=mLoad,
    rLoad=rLoad,
    g=g);
  Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.PathPlanning6
    pathPlanning(
    naxis=6,
    angleBegDeg={startAngle1,startAngle2,startAngle3,startAngle4,startAngle5,
        startAngle6},
    angleEndDeg={endAngle1,endAngle2,endAngle3,endAngle4,endAngle5,endAngle6},
    speedMax=refSpeedMax,
    accMax=refAccMax,
    startTime=refStartTime,
    swingTime=refSwingTime);

  RobotR3.Components.AxisType1 axis1(
    w=4590,
    ratio=-105,
    c=43,
    cd=0.005,
    Rv0=0.4,
    Rv1=(0.13/160),
    kp=kp1,
    ks=ks1,
    Ts=Ts1);
  RobotR3.Components.AxisType1 axis2(
    w=5500,
    ratio=210,
    c=8,
    cd=0.01,
    Rv1=(0.1/130),
    Rv0=0.5,
    kp=kp2,
    ks=ks2,
    Ts=Ts2);

  RobotR3.Components.AxisType1 axis3(
    w=5500,
    ratio=60,
    c=58,
    cd=0.04,
    Rv0=0.7,
    Rv1=(0.2/130),
    kp=kp3,
    ks=ks3,
    Ts=Ts3);
  RobotR3.Components.AxisType2 axis4(
    k=0.2365,
    w=6250,
    D=0.55,
    J=1.6e-4,
    ratio=-99,
    Rv0=21.8,
    Rv1=9.8,
    peak=26.7/21.8,
    kp=kp4,
    ks=ks4,
    Ts=Ts4);
  RobotR3.Components.AxisType2 axis5(
    k=0.2608,
    w=6250,
    D=0.55,
    J=1.8e-4,
    ratio=79.2,
    Rv0=30.1,
    Rv1=0.03,
    peak=39.6/30.1,
    kp=kp5,
    ks=ks5,
    Ts=Ts5);
  RobotR3.Components.AxisType2 axis6(
    k=0.0842,
    w=7400,
    D=0.27,
    J=4.3e-5,
    ratio=-99,
    Rv0=10.9,
    Rv1=3.92,
    peak=16.8/10.9,
    kp=kp6,
    ks=ks6,
    Ts=Ts6);
protected 
  Components.ControlBus controlBus;
equation 
  connect(axis2.flange, mechanics.axis2);
  connect(axis1.flange, mechanics.axis1);
  connect(axis3.flange, mechanics.axis3);
  connect(axis4.flange, mechanics.axis4);
  connect(axis5.flange, mechanics.axis5);
  connect(axis6.flange, mechanics.axis6);
  connect(controlBus, pathPlanning.controlBus);
  connect(controlBus.axisControlBus1, axis1.axisControlBus);

  connect(controlBus.axisControlBus2, axis2.axisControlBus);

  connect(controlBus.axisControlBus3, axis3.axisControlBus);

  connect(controlBus.axisControlBus4, axis4.axisControlBus);
  connect(controlBus.axisControlBus5, axis5.axisControlBus);
  connect(controlBus.axisControlBus6, axis6.axisControlBus);
end fullRobot;

Automatically generated Fri Nov 12 16:30:20 2010.