Package Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components
Library of components of the robot

Information

This library contains the different components of the r3 robot. Usually, there is no need to use this library directly.

Extends from Modelica.Icons.Package (Icon for standard packages).

Package Contents

Name	Description
`AxisControlBus`	Data bus for one robot axis
`AxisType1`	Axis model of the r3 joints 1,2,3
`AxisType2`	Axis model of the r3 joints 4,5,6
`ControlBus`	Data bus for all axes of robot
`Controller`	P-PI cascade controller for one axis
`GearType1`	Motor inertia and gearbox model for r3 joints 1,2,3
`GearType2`	Motor inertia and gearbox model for r3 joints 4,5,6
`MechanicalStructure`	Model of the mechanical part of the r3 robot (without animation)
`Motor`	Motor model including current controller of r3 motors
`PathPlanning1`	Generate reference angles for fastest kinematic movement
`PathPlanning6`	Generate reference angles for fastest kinematic movement
`PathToAxisControlBus`	Map path planning to one axis control bus

Expandable Connector Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.AxisControlBus
Data bus for one robot axis

Information

Signal bus that is used to communicate all signals for one axis. This is an expandable connector which has a "default" set of signals. Note, the input/output causalities of the signals are determined from the connections to this bus.

Extends from Modelica.Icons.SignalSubBus (Icon for signal sub-bus).

Fields

Type	Name	Description
`Boolean`	`motion_ref`	= true, if reference motion is not in rest
`Angle`	`angle_ref`	Reference angle of axis flange
`Angle`	`angle`	Angle of axis flange
`AngularVelocity`	`speed_ref`	Reference speed of axis flange
`AngularVelocity`	`speed`	Speed of axis flange
`AngularAcceleration`	`acceleration_ref`	Reference acceleration of axis flange
`AngularAcceleration`	`acceleration`	Acceleration of axis flange
`Current`	`current_ref`	Reference current of motor
`Current`	`current`	Current of motor
`Angle`	`motorAngle`	Angle of motor flange
`AngularVelocity`	`motorSpeed`	Speed of motor flange

Expandable Connector Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.ControlBus
Data bus for all axes of robot

Information

Signal bus that is used to communicate all signals of the robot. This is an expandable connector which has a "default" set of signals. Note, the input/output causalities of the signals are determined from the connections to this bus.

Extends from Modelica.Icons.SignalBus (Icon for signal bus).

Fields

Type	Name	Description
`AxisControlBus`	`axisControlBus1`	Bus of axis 1
`AxisControlBus`	`axisControlBus2`	Bus of axis 2
`AxisControlBus`	`axisControlBus3`	Bus of axis 3
`AxisControlBus`	`axisControlBus4`	Bus of axis 4
`AxisControlBus`	`axisControlBus5`	Bus of axis 5
`AxisControlBus`	`axisControlBus6`	Bus of axis 6

Model Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.PathPlanning1
Generate reference angles for fastest kinematic movement

Information

Given

start and end angle of an axis
maximum speed of the axis
maximum acceleration of the axis

this component computes the fastest movement under the given constraints. This means, that:

The axis accelerates with the maximum acceleration until the maximum speed is reached.
Drives with the maximum speed as long as possible.
Decelerates with the negative of the maximum acceleration until rest.

The acceleration, constant velocity and deceleration phase are determined in such a way that the movement starts form the start angles and ends at the end angles. The output of this block are the computed angles, angular velocities and angular acceleration and this information is stored as reference motion on the controlBus of the r3 robot.

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block).

Parameters

Type	Name	Default	Description
`Real`	`angleBegDeg`	`0`	Start angle
`Real`	`angleEndDeg`	`1`	End angle
`AngularVelocity`	`speedMax`	`3`	Maximum axis speed
`AngularAcceleration`	`accMax`	`2.5`	Maximum axis acceleration
`Time`	`startTime`	`0`	Start time of movement
`Time`	`swingTime`	`0.5`	Additional time after reference motion is in rest before simulation is stopped
`final` `Angle`	`angleBeg`	`Cv.from_deg(angleBegDeg)`	Start angles
`final` `Angle`	`angleEnd`	`Cv.from_deg(angleEndDeg)`	End angles

Connectors

Type	Name	Description
`ControlBus`	`controlBus`

Model Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.PathPlanning6
Generate reference angles for fastest kinematic movement

Information

Given

start and end angles of every axis
maximum speed of every axis
maximum acceleration of every axis

this component computes the fastest movement under the given constraints. This means, that:

Every axis accelerates with the maximum acceleration until the maximum speed is reached.
Drives with the maximum speed as long as possible.
Decelerates with the negative of the maximum acceleration until rest.

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block).

Parameters

Type	Name	Default	Description
`Integer`	`naxis`	`6`	Number of driven axis
`Real`	`angleBegDeg[naxis]`	`zeros(naxis)`	Start angles
`Real`	`angleEndDeg[naxis]`	`ones(naxis)`	End angles
`AngularVelocity`	`speedMax[naxis]`	`fill(3, naxis)`	Maximum axis speed
`AngularAcceleration`	`accMax[naxis]`	`fill(2.5, naxis)`	Maximum axis acceleration
`Time`	`startTime`	`0`	Start time of movement
`Time`	`swingTime`	`0.5`	Additional time after reference motion is in rest before simulation is stopped
`final` `Angle`	`angleBeg[:]`	`Cv.from_deg(angleBegDeg)`	Start angles
`final` `Angle`	`angleEnd[:]`	`Cv.from_deg(angleEndDeg)`	End angles

Connectors

Type	Name	Description
`ControlBus`	`controlBus`

Model Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.PathToAxisControlBus
Map path planning to one axis control bus

Information

This model stores the 4 reference variables q, qd, qdd, moving from the path planning on the axis control bus.

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block).

Parameters

Type	Name	Default	Description
`Integer`	`nAxis`	`6`	Number of driven axis
`Integer`	`axisUsed`	`1`	Map path planning of axisUsed to axisControlBus

Connectors

Type	Name	Description
`input` `RealInput`	`q[nAxis]`
`input` `RealInput`	`qd[nAxis]`
`input` `RealInput`	`qdd[nAxis]`
`AxisControlBus`	`axisControlBus`
`input` `BooleanInput`	`moving[nAxis]`

Model Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.GearType1
Motor inertia and gearbox model for r3 joints 1,2,3

Information

Models the gearbox used in the first three joints with all its effects, like elasticity and friction. Coulomb friction is approximated by a friction element acting at the "motor"-side. In reality, bearing friction should be also incorporated at the driven side of the gearbox. However, this would require considerable more effort for the measurement of the friction parameters. Default values for all parameters are given for joint 1. Model relativeStates is used to define the relative angle and relative angular velocity across the spring (=gear elasticity) as state variables. The reason is, that a default initial value of zero of these states makes always sense. If the absolute angle and the absolute angular velocity of model Jmotor would be used as states, and the load angle (= joint angle of robot) is NOT zero, one has always to ensure that the initial values of the motor angle and of the joint angle are modified correspondingly. Otherwise, the spring has an unrealistic deflection at initial time. Since relative quantities are used as state variables, this simplifies the definition of initial values considerably.

Extends from Modelica.Mechanics.Rotational.Icons.Gearbox (Icon of a gear box) and Modelica.Mechanics.Rotational.Interfaces.PartialTwoFlanges (Partial model for a component with two rotational 1-dim. shaft flanges).

Parameters

Type	Name	Default	Description
`Real`	`i`	`-105`	Gear ratio
`Real`	`c`	`43`	Spring constant
`Real`	`d`	`0.005`	Damper constant
`Torque`	`Rv0`	`0.4`	Viscous friction torque at zero velocity
`Real`	`Rv1`	`8.125e-4`	Viscous friction coefficient (R=Rv0+Rv1*abs(qd))
`Real`	`peak`	`1`	Maximum static friction torque is peak*Rv0 (peak >= 1)

Connectors

Type	Name	Description
`Flange_a`	`flange_a`	Flange of left shaft
`Flange_b`	`flange_b`	Flange of right shaft

Model Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.GearType2
Motor inertia and gearbox model for r3 joints 4,5,6

Information

The elasticity and damping in the gearboxes of the outermost three joints of the robot is neglected. Default values for all parameters are given for joint 4.

Parameters

Type	Name	Default	Description
`Real`	`i`	`-99`	Gear ratio
`Torque`	`Rv0`	`21.8`	Viscous friction torque at zero velocity
`Real`	`Rv1`	`9.8`	Viscous friction coefficient in [Nms/rad] (R=Rv0+Rv1*abs(qd))
`Real`	`peak`	`1.224770642201835`	Maximum static friction torque is peak*Rv0 (peak >= 1)

Connectors

Type	Name	Description
`Flange_a`	`flange_a`	Flange of left shaft
`Flange_b`	`flange_b`	Flange of right shaft

Model Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.Motor
Motor model including current controller of r3 motors

Information

Default values are given for the motor of joint 1. The input of the motor is the desired current (the actual current is proportional to the torque produced by the motor).

Extends from Modelica.Electrical.Machines.Icons.Machine (Generic icon of an electric machine).

Parameters

Type	Name	Default	Description
`Inertia`	`J`	`0.0013`	Moment of inertia of motor
`Real`	`k`	`1.1616`	Gain of motor
`Real`	`w`	`4590`	Time constant of motor
`Real`	`D`	`0.6`	Damping constant of motor
`AngularVelocity`	`w_max`	`315`	Maximum speed of motor
`Current`	`i_max`	`9`	Maximum current of motor

Connectors

Type	Name	Description
`Flange_b`	`flange_motor`
`AxisControlBus`	`axisControlBus`

Model Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.Controller
P-PI cascade controller for one axis

Information

This controller has an inner PI-controller to control the motor speed, and an outer P-controller to control the motor position of one axis. The reference signals are with respect to the gear-output, and the gear ratio is used in the controller to determine the motor reference signals. All signals are communicated via the "axisControlBus".

Extends from Modelica.Blocks.Icons.Block (Basic graphical layout of input/output block).

Parameters

Type	Name	Default	Description
`Real`	`kp`	`10`	Gain of position controller
`Real`	`ks`	`1`	Gain of speed controller
`Time`	`Ts`	`0.01`	Time constant of integrator of speed controller
`Real`	`ratio`	`1`	Gear ratio of gearbox

Connectors

Type	Name	Description
`AxisControlBus`	`axisControlBus`

Model Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.AxisType1
Axis model of the r3 joints 1,2,3

Information

Model of axis 1, 2, 3 of the robot r3. An axis consists of a gearbox with modelled gear elasticity and bearing friction, a model of the electrical motor and a continuous-time cascade controller.

Extends from Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.AxisType2 (Axis model of the r3 joints 4,5,6).

Parameters

Type	Name	Default	Description
`Real`	`kp`	`10`	Gain of position controller
`Real`	`ks`	`1`	Gain of speed controller
`Time`	`Ts`	`0.01`	Time constant of integrator of speed controller
`Real`	`k`	`1.1616`	Gain of motor
`Real`	`w`	`4590`	Time constant of motor
`Real`	`D`	`0.6`	Damping constant of motor
`Inertia`	`J`	`0.0013`	Moment of inertia of motor
`Real`	`ratio`	`-105`	Gear ratio
`Torque`	`Rv0`	`0.4`	Viscous friction torque at zero velocity in [Nm]
`Real`	`Rv1`	`8.125e-4`	Viscous friction coefficient in [Nms/rad]
`Real`	`peak`	`1`	Maximum static friction torque is peak*Rv0 (peak >= 1)
`Real`	`c`	`43`	Spring constant
`Real`	`cd`	`0.005`	Damper constant

Connectors

Type	Name	Description
`Flange_b`	`flange`
`AxisControlBus`	`axisControlBus`

Model Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.AxisType2
Axis model of the r3 joints 4,5,6

Information

The axis model consists of the controller, the motor including current controller and the gearbox including gear elasticity and bearing friction. The only difference to the axis model of joints 4,5,6 (= model axisType2) is that elasticity and damping in the gear boxes are not neglected.

The input signals of this component are the desired angle and desired angular velocity of the joint. The reference signals have to be "smooth" (position has to be differentiable at least 2 times). Otherwise, the gear elasticity leads to significant oscillations.

Default values of the parameters are given for the axis of joint 1.

Parameters

Type	Name	Default	Description
`Real`	`kp`	`10`	Gain of position controller
`Real`	`ks`	`1`	Gain of speed controller
`Time`	`Ts`	`0.01`	Time constant of integrator of speed controller
`Real`	`k`	`1.1616`	Gain of motor
`Real`	`w`	`4590`	Time constant of motor
`Real`	`D`	`0.6`	Damping constant of motor
`Inertia`	`J`	`0.0013`	Moment of inertia of motor
`Real`	`ratio`	`-105`	Gear ratio
`Torque`	`Rv0`	`0.4`	Viscous friction torque at zero velocity in [Nm]
`Real`	`Rv1`	`8.125e-4`	Viscous friction coefficient in [Nms/rad]
`Real`	`peak`	`1`	Maximum static friction torque is peak*Rv0 (peak >= 1)

Connectors

Type	Name	Description
`Flange_b`	`flange`
`AxisControlBus`	`axisControlBus`

Model Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.MechanicalStructure
Model of the mechanical part of the r3 robot (without animation)

Information

This model contains the mechanical components of the r3 robot (multibody system).

Parameters

Type	Name	Default	Description
`Boolean`	`animation`	`true`	= true, if animation shall be enabled
`Mass`	`mLoad`	`15`	Mass of load
`Position`	`rLoad[3]`	`{0, 0.25, 0}`	Distance from last flange to load mass>
`Acceleration`	`g`	`9.81`	Gravity acceleration

Connectors

Type	Name	Description
`Flange_a`	`axis1`
`Flange_a`	`axis2`
`Flange_a`	`axis3`
`Flange_a`	`axis4`
`Flange_a`	`axis5`
`Flange_a`	`axis6`

Package Modelica.​Mechanics.​MultiBody.​Examples.​Systems.​RobotR3.​ComponentsLibrary of components of the robot

Information

Package Contents

Expandable Connector Modelica.​Mechanics.​MultiBody.​Examples.​Systems.​RobotR3.​Components.​AxisControlBusData bus for one robot axis

Information

Fields

Expandable Connector Modelica.​Mechanics.​MultiBody.​Examples.​Systems.​RobotR3.​Components.​ControlBusData bus for all axes of robot

Information

Fields

Model Modelica.​Mechanics.​MultiBody.​Examples.​Systems.​RobotR3.​Components.​PathPlanning1Generate reference angles for fastest kinematic movement

Information

Parameters

Connectors

Model Modelica.​Mechanics.​MultiBody.​Examples.​Systems.​RobotR3.​Components.​PathPlanning6Generate reference angles for fastest kinematic movement

Information

Parameters

Connectors

Model Modelica.​Mechanics.​MultiBody.​Examples.​Systems.​RobotR3.​Components.​PathToAxisControlBusMap path planning to one axis control bus

Information

Parameters

Connectors

Model Modelica.​Mechanics.​MultiBody.​Examples.​Systems.​RobotR3.​Components.​GearType1Motor inertia and gearbox model for r3 joints 1,2,3

Information

Parameters

Connectors

Model Modelica.​Mechanics.​MultiBody.​Examples.​Systems.​RobotR3.​Components.​GearType2Motor inertia and gearbox model for r3 joints 4,5,6

Information

Parameters

Connectors

Model Modelica.​Mechanics.​MultiBody.​Examples.​Systems.​RobotR3.​Components.​MotorMotor model including current controller of r3 motors

Information

Parameters

Connectors

Model Modelica.​Mechanics.​MultiBody.​Examples.​Systems.​RobotR3.​Components.​ControllerP-PI cascade controller for one axis

Information

Parameters

Connectors

Model Modelica.​Mechanics.​MultiBody.​Examples.​Systems.​RobotR3.​Components.​AxisType1Axis model of the r3 joints 1,2,3

Information

Parameters

Connectors

Model Modelica.​Mechanics.​MultiBody.​Examples.​Systems.​RobotR3.​Components.​AxisType2Axis model of the r3 joints 4,5,6

Information

Parameters

Connectors

Model Modelica.​Mechanics.​MultiBody.​Examples.​Systems.​RobotR3.​Components.​MechanicalStructureModel of the mechanical part of the r3 robot (without animation)

Information

Parameters

Connectors

Package Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components
Library of components of the robot

Expandable Connector Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.AxisControlBus
Data bus for one robot axis

Expandable Connector Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.ControlBus
Data bus for all axes of robot

Model Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.PathPlanning1
Generate reference angles for fastest kinematic movement

Model Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.PathPlanning6
Generate reference angles for fastest kinematic movement

Model Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.PathToAxisControlBus
Map path planning to one axis control bus

Model Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.GearType1
Motor inertia and gearbox model for r3 joints 1,2,3

Model Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.GearType2
Motor inertia and gearbox model for r3 joints 4,5,6

Model Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.Motor
Motor model including current controller of r3 motors

Model Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.Controller
P-PI cascade controller for one axis

Model Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.AxisType1
Axis model of the r3 joints 1,2,3

Model Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.AxisType2
Axis model of the r3 joints 4,5,6

Model Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.MechanicalStructure
Model of the mechanical part of the r3 robot (without animation)