Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components

Information

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

Package Content

Name	Description
AxisControlBus	Data bus for one robot axis
ControlBus	Data bus for all axes of robot
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
GearType1	Motor inertia and gearbox model for r3 joints 1,2,3
GearType2	Motor inertia and gearbox model for r3 joints 4,5,6
Motor	Motor model including current controller of r3 motors
Controller	P-PI cascade controller for one axis
AxisType1	Axis model of the r3 joints 1,2,3
AxisType2	Axis model of the r3 joints 4,5,6
MechanicalStructure	Model of the mechanical part of the r3 robot (without animation)

Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.AxisControlBus

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.

Contents

Name	Description
motion_ref	= true, if reference motion is not in rest
angle_ref	Reference angle of axis flange [rad]
angle	Angle of axis flange [rad]
speed_ref	Reference speed of axis flange [rad/s]
speed	Speed of axis flange [rad/s]
acceleration_ref	Reference acceleration of axis flange [rad/s2]
acceleration	Acceleration of axis flange [rad/s2]
current_ref	Reference current of motor [A]
current	Current of motor [A]
motorAngle	Angle of motor flange [rad]
motorSpeed	Speed of motor flange [rad/s]

Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.ControlBus

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.

Contents

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

Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.PathPlanning1

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:

1. The axis accelerates with the maximum acceleration until the maximum speed is reached.
2. Drives with the maximum speed as long as possible.
3. 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.

Parameters

Name	Description
angleBegDeg	Start angle [deg]
angleEndDeg	End angle [deg]
speedMax	Maximum axis speed [rad/s]
accMax	Maximum axis acceleration [rad/s2]
startTime	Start time of movement [s]
swingTime	Additional time after reference motion is in rest before simulation is stopped [s]

Connectors

Name	Description
controlBus

Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.PathPlanning6

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:

1. Every axis accelerates with the maximum acceleration until the maximum speed is reached.
2. Drives with the maximum speed as long as possible.
3. 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.

Parameters

Name	Description
naxis	number of driven axis
angleBegDeg[naxis]	Start angles [deg]
angleEndDeg[naxis]	End angles [deg]
speedMax[naxis]	Maximum axis speed [rad/s]
accMax[naxis]	Maximum axis acceleration [rad/s2]
startTime	Start time of movement [s]
swingTime	Additional time after reference motion is in rest before simulation is stopped [s]

Connectors

Name	Description
controlBus

Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.PathToAxisControlBus

Information

Parameters

Name	Description
nAxis	Number of driven axis
axisUsed	Map path planning of axisUsed to axisControlBus

Connectors

Name	Description
q[nAxis]
qd[nAxis]
qdd[nAxis]
axisControlBus
moving[nAxis]

Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.GearType1

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.

Parameters

Name	Description
i	gear ratio
c	Spring constant [N.m/rad]
d	Damper constant [N.m.s/rad]
Rv0	Viscous friction torque at zero velocity [N.m]
Rv1	Viscous friction coefficient (R=Rv0+Rv1*abs(qd)) [N.m.s/rad]
peak	Maximum static friction torque is peak*Rv0 (peak >= 1)

Connectors

Name	Description
flange_a	Flange of left shaft
flange_b	Flange of right shaft

Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.GearType2

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

Name	Description
i	Gear ratio
Rv0	Viscous friction torque at zero velocity [N.m]
Rv1	Viscous friction coefficient in [Nms/rad] (R=Rv0+Rv1*abs(qd))
peak	Maximum static friction torque is peak*Rv0 (peak >= 1)

Connectors

Name	Description
flange_a	Flange of left shaft
flange_b	Flange of right shaft

Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.Motor

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).

Parameters

Name	Description
J	Moment of inertia of motor [kg.m2]
k	Gain of motor
w	Time constant of motor
D	Damping constant of motor
w_max	Maximum speed of motor [rad/s]
i_max	Maximum current of motor [A]

Connectors

Name	Description
flange_motor
axisControlBus

Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.Controller

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".

Parameters

Name	Description
kp	Gain of position controller
ks	Gain of speed controller
Ts	Time constant of integrator of speed controller [s]
ratio	Gear ratio of gearbox

Connectors

Name	Description
axisControlBus

Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.AxisType1

Information

Parameters

Name	Description
Controller
kp	Gain of position controller
ks	Gain of speed controller
Ts	Time constant of integrator of speed controller [s]
Motor
k	Gain of motor
w	Time constant of motor
D	Damping constant of motor
J	Moment of inertia of motor [kg.m2]
Gear
ratio	Gear ratio
Rv0	Viscous friction torque at zero velocity in [Nm] [N.m]
Rv1	Viscous friction coefficient in [Nms/rad] [N.m.s/rad]
peak	Maximum static friction torque is peak*Rv0 (peak >= 1)
c	Spring constant [N.m/rad]
cd	Damper constant [N.m.s/rad]

Connectors

Name	Description
flange
axisControlBus

Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.AxisType2

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

Name	Description
gear
Controller
kp	Gain of position controller
ks	Gain of speed controller
Ts	Time constant of integrator of speed controller [s]
Motor
k	Gain of motor
w	Time constant of motor
D	Damping constant of motor
J	Moment of inertia of motor [kg.m2]
Gear
ratio	Gear ratio
Rv0	Viscous friction torque at zero velocity in [Nm] [N.m]
Rv1	Viscous friction coefficient in [Nms/rad] [N.m.s/rad]
peak	Maximum static friction torque is peak*Rv0 (peak >= 1)

Connectors

Name	Description
flange
axisControlBus

Modelica.Mechanics.MultiBody.Examples.Systems.RobotR3.Components.MechanicalStructure

Information

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

Parameters

Name	Description
animation	= true, if animation shall be enabled
mLoad	Mass of load [kg]
rLoad[3]	Distance from last flange to load mass> [m]
g	Gravity acceleration [m/s2]

Connectors

Name	Description
axis1
axis2
axis3
axis4
axis5
axis6