Download Modeling robot dynamics

Model-based Off-line Compensation of Path
Deviation for Industrial Robots in Milling
Applications
M. Friedmann
C. Reinl
O. von Stryk
E. Abele
J. Bauer
M. Pischan
Simulation,
Systems Optimization,
and Robotics
IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM) 2011
Presentation Outline
1. Introduction
2. Model of Robot Dynamics and Milling Force
3. Analysis and Model Calibration
4. Model-based Compensation of Deviation
5. Conlusion
Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 2
Potential Application Areas
Cutting
Volume
© EADS
© DELCAM
Milling and Drilling of
integral parts for the
aerospace industry
Milling Prototypingapplication
Area of milling
operation with IR
© Trimet
© Audi
© BMW
Milling and Drilling of
aluminum and steal parts
© Fehrer
Deburring, grinding and milling for the automotive industry
Trimming/ Milling of fibrealuminum and cast parts
reinforced plastics for
for foundry industry
aerospace und automotive
industries
© Röders
Milling and finishing of
molds for the mold and
die production industry
Accuracy
Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 3
Challenges during milling applications with robots
1. Static deflection:
 Reason:
High compliance of the robot structure
2. Low frequency oscillation:
 Reason:
Excitation of the system‘s eigen frequencies
3. High frequency oscillation:
 Reason:
Excitation of higher system‘s eigen frequencies (spindle, tool)
Static Offset
Low frequency oscillation
Work piece holder
Work
Werkst
piece
ücktisch
holder
IR
IR
y
yy
xx
statischer Versatz
1mm
Static offset
Desired
Path
Sollbahn
x
RealePath
Bahn
Real
Desired path
Desired
Path
Sollbahn
Real Path
yy
xx
Real path
yy
y
x
x
Cross section
z
x
 Adaption of the robot‘s tool path
Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 4
Interaction: Robot Structure  Milling Process
Structure
Interaction
Milling Process
Displacement Δx,y,z
Force FProcess
Multibody Robot Model
Process Force Model
Model coupling
Fx
Fy
Milling Force
Fz
M (q) q  C(q, q )  G(q)    J c' Fxyz ,tool
Frta, j ,e  K c h j ( , z )z  K e z
Offline
Compensation
Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 5
Ne N Z
Fxyz ,tool   T j ( )  Frta, j ,e
e 1 j 1
Presentation Outline
1. Introduction
2. Model of Robot Dynamics and Milling Force
3. Analysis and Model Calibration
4. Model-based Compensation of Deviation
5. Conlusion
Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 6
Modeling robot dynamics:
kinematic structure
• rigid link with rotational joint:
linkdh,i  Rot ( z; qi )·Trans(0, 0, di )·Trans(0, 0, ai )·Rot ( x; i )
qi joint position;
di, zi ai DH-parameter
• arbitrary positioning of joint axis along z-axis
by transition pi:
linkwrep,i  Trans(0,0, pi )·Rot ( z; qi )·Trans(0,0, di  pi )·
Trans(0,0, ai )·Rot ( x;i ).
• extension by virtual rotational axes by virtual
axes:
linkext ,i  Trans (0, 0, pi )·Rot ( z; qi )·Rot ( x; q x ,i )·
·Rot ( y; q y ,i )·Trans (0, 0, di  pi )
·Trans (0, 0, ai )·Rot ( x;  i )
qx,i qy,i : virtual joint positions
Covers arbitrary tilting effects at
actuated joints
Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 7
Modeling robot dynamics:
multi-body dynamics and drivetrain
• Prarametrization of dynamics for each rigid body i:
• mass mi
• intertia tensor Ii
• center of mass comi
• Newton-Euler algorithm for setting up
M(q): Inertia matrix
C ( q, q ) : Coriolis + centrifugal forces
G(q): Gravitational forces
: Joints Foces + Torques

  C (q, q )  G(q)    J c' Fxyz ,tool
M (q) q
i
• Torque in jonts: drivetrain an elasticity:
((qi  si )  qi ) , if (qi  qi )  si

 i  Di ·(qi  qi )  Ki ·((qi  si )  qi ) , if (qi  qi )  si

, else
0
qi: desired joint position
Ki: stiffness
Di: damping
si: backlash
si
Coverd effects:
Backlash of gears
Friction in joints
Dyanmic tilting at actuated and virtual axes
Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 8
si
qi  qi
Modeling robot dynamics:
Implementation „MBSLIB“
 Efficient, object-oriented, modular Implementation in C++
• Modeling entities used here: base, rigid body, variable/fixed rotation
• Further available: variable translations ( prismatic joints), forks ( tree-shaped
structures beyond the kinematic chain)
 Equations of motion
  C(q, q )  G(q)    J c' Fxyz ,tool
•General form: M (q) q
• Is obtained by recursive method evaluating robot structure during runtime
 MBS can be changed without changing program:
• Invers dynamics: recursive Newton-Euler-algorithm
• Forward dynamics: Composite Rigid Body Algorithm, Articulated Body Algorithm
 Optional: Calculation of derivatives
• Automated derivation based on ADOL-C-library [Walther‘06]
• Precise derivatives of equations of motion with respect to any state variable and
modeling parameter
 interface to numerical sensitivity analysis, parameter estimation and trajectory
optimization
Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 9
Process Force Calculation
1. Representation of the work piece
- Multi dexel discretisation
- Dexel representation as a line segment 
p  dt  s
- To receive a sufficient accuracy the discretisation should be:
x y z
kd 
; ;
 0.05
R R R
z
2. Calculation of the chip geometry
- Tool moves in discrete time steps
y
ap
∆z
- Chip subdivided into disks of the height ∆z, ∆φ
x
- Calculation of the chip thickness h for each section
3. Process force calculation
- Calculation of the force per tooth Frta for each
disk
- Summation over all teeth and disks
- Transformation into the tool coordinate system
Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 10
T(φ)
Presentation Outline
1. Introduction
2. Model of Robot Dynamics and Milling Force
3. Analysis and Model Calibration
4. Model-based Compensation of Deviation
5. Conlusion
Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 12
Prediction of Path Deviation by Coupled Simulation
Simulation loop
1. Calculate pose and velocity of
TCP depending on current state
of robot
2. Calculate external forces
resulting from process force
model
3. Calculate forces in joints
resulting from drives
4. Solve equations of motion for
acceleration of joints
5. Integrate for next time-step
6. For each time-step: go to 1.
Fx
Fy
Fz
+
Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 13
Optimal Design of Experiment and Sensitivity-Analysis
Example 1):
Find optimal position to determine a certain
parameter ( e.g. mass m6) by measurements.
Example 2):
Calculation of sensitivities simulataneously
to simulation
• consider bounded working volume
• solve constraint non-linear problem
• automated derivative calculation of
integration step
n
min 
q
 i (q; m6 )
m6
j 1
M

i 1
subject to
robot path
forward _ kinematics(q) Vxyz
sensitivities in actuated joints
qi (q (t ); m6 )
m6
• Derivatives w.r.t. q and m6 are
•
available with ADOL-C
Solution by interior-pointmethod IPOPT
[Wächter‘06]
Key feature to deepest possible
understanding of interaction between
parameters dynamics
Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 15
Presentation Outline
1. Introduction
2. Model of Robot Dynamics and Milling Force
3. Analysis and Model Calibration
4. Model-based Offline Compensation of Deviation
5. Conlusion
Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 16
Compensation of the TCP displacement
(1) Reference solution
Simulation run with an ideal robot and reference trajectory:
• Recording of joint positions
• Calculation external forces at TCP  Low pass filtering
Simulation of ideal robot
Filtered ideal forces
tool path
work piece
Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 17
Compensation of the TCP displacement
(2) Determination of compensating trajectories
Reference: forces and joint position
from first simulation run
• filtering
Ideal trajectories
qideal (t ), qideal (t ), qideal (t ), Fext (t )
• select interpolating points
• invers dynamics calculation
Torques at interpolating points ideal.
• assume qcomp  qideal
Model-based approach considers milling
forces and robot dynamics
Off-line method does not require
access to internal robot control
Efficient calulation of compensational
path
Compensational points qcomp :
 Ki1 ( iideal (tl )  si ) , if  iideal  0

qicomp (tl )  qiideal (tl )   Ki1 ( iideal (tl )  si ) , if  iideal  0
ideal
0
,
i
f

0
i

Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 18
Compensation of the TCP displacement
(3) Experimental Validation
Experimantal set-up:
1. First run with low feed rate 1.5 mm/s and milling depth 0.5 mm
 process forces neglectable  no deviation
2. Milling with feed rate 50 mm/s and milling depth 1.5 mm
a) without compensation
b) with compensation
Result:
 Signifikant error reduction: root mean square error from erms,1=0.7 mm to erms,2=0.57 mm
Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 19
Presentation Outline
1. Introduction
2. Model of Robot Dynamics and Milling Force
3. Analysis and Model Calibration
4. Model-based Compensation of Deviation
5. Conlusion
Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 20
Conclusion
•
•
•
•
High speed cutting in hard materials with industrial robots: strong interaction of
mechanical robot structure and removal process
Prediction of static and dynamic TCP-deviations by coupled efficient simulation of milling
process and of robot motion dynamics:
Modular implementation for multi-body-system dynamics
• Covers causal effects for path deviation: tilting, elasticities and backlash of gears
• Applicable to any robot with tree structure
• Automated precise calculation of derivatives with respect to any model parameter.
efficient model-based off-line compensation strategy
 Significant improvements to the processing accuracy
 Neither a modification of the robot nor access to the robot’s internal control is necessary:

the users standard access possibilities are met
Enabling advanced analysis, design of experiments, numerical parameter estimation and
trajectory optimization
Cost-saving expansion the scope of machining applications of industrial robots
Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 21
Thank you for your
attention!
M. Friedmann
C. Reinl
O. von Stryk
E. Abele
J. Bauer
M. Pischan
Simulation,
Systems Optimization,
and Robotics
{friedmann, reinl, stryk}@sim.tu-darmstadt.de
{abele, bauer, pischan}@ptw.tu-darmstadt.de
Mechanical Engineering | Institute of Production Management, Technology and Machine Tools | 22