Towards improved performance for industrial robots
Mikael Norrlöf ISIS/Division of Automatic Control, Linköping University
[email protected] Special thanks to: Mattias Björkman, Torgny Brogårdh, Svante Gunnarsson, Rickard Karlsson, Stig Moberg and Erik Wernholt
Mikael Norrlöf 2004 ISIS Workshop
The robotics acivities within ISIS Iterative Learning Control Robot control Joint level control Robot trajectory generation Multivariable control and optimization Sensor fusion Robot modeling and Robot diagnosis identification
Common factor for all the activities:
Increased robot performance!
Mikael Norrlöf 2004 ISIS Workshop
1
The robot system and its components
Links Joints Motors Gears Bearings
Main Main problems: problems: Flexibilities Flexibilities Friction Friction Sensor Sensorand andactuator actuator uncertainties uncertainties Mikael Norrlöf 2004 ISIS Workshop
ISIS activities r(t)
+ +
-
FFf f FF
+
GG
y(t)
Control design
Modeling Identification Trajectory generation and optimization
Sensor fusion
Mikael Norrlöf 2004 ISIS Workshop
2
Robot modeling
Z
Kinematics Kinematics Elastostatic Elastostatic Rigid Rigid body bodydynamics dynamics Elastodynamic Elastodynamic
Z
Y
Y X
X
Compliance Offset Z
Z Y
Y
X
Z
Roll
Y
Z Y
X
Pitch
X
Yaw
X Mikael Norrlöf 2004 ISIS Workshop
Joint level modeling Linear system approximation.
Mikael Norrlöf 2004 ISIS Workshop
3
Robot modeling
q_a
1 Arm angle
q_m
Reference signal ref_in
tau_PID
tau_a
qd_a
2
ref_pos_a
Arm angular vel
PID Controller qdd_a
3 Arm angular acc
Manipulator (Robotics Toolbox)
4 x' = Ax+Bu y = Cx+Du
Motor angle
Demux
Motor and gear
5 mechanical system Non-linear Non-linear mechanical system Motor angular vel (manipulator) (manipulator) 6
Motor angular acc
Linear Linearspring springand anddamper damper(gear-box) (gear-box) Mikael Norrlöf 2004 ISIS Workshop
Non-linear joint model
Non-linear stiffness Measured output
Mikael Norrlöf 2004 ISIS Workshop
4
Non-linear joint model
Measured output
Mikael Norrlöf 2004 ISIS Workshop
ISIS activities r(t)
+ +
-
FFf f FF
+
GG
y(t)
Control design
Modeling Identification Trajectory generation and optimization
Sensor fusion
Mikael Norrlöf 2004 ISIS Workshop
5
Identification
Choice of excitation signal Measurements Stochastic disturbances Deterministic disturbances Transient and stationary behavior Non-linear system
Identification
Mikael Norrlöf 2004 ISIS Workshop
ISIS activities r(t)
+ +
-
FFf f FF
+
GG
y(t)
Control design
Modeling Identification Trajectory generation and optimization
Sensor fusion
Mikael Norrlöf 2004 ISIS Workshop
6
Non-linear joint model
Measured output
IP N HIP NSSH PPIIO O M A H M C A H N OPPEEN CONTTR HO OLL ISH RO DIS SSW C N WEED O T C O T B OBO IIN RO NR
Mikael Norrlöf 2004 ISIS Workshop
The iterative learning control technique
pk+1(t) = pk(t)+ Lek(t+1)
Mikael Norrlöf 2004 ISIS Workshop
7
The iterative learning control technique
pk+1(t) = pk(t)+ Lek(t+1)
Mikael Norrlöf 2004 ISIS Workshop
Iterative Learning Control
8
Iterative Learning Control
ISIS DCT Tower Automotive
Metalsa 650 ABB robots
80 ABB robots
ISIS activities r(t)
+ +
-
FFf f FF
+
GG
y(t)
Control design
Modeling Identification Trajectory generation and optimization
Sensor fusion
Mikael Norrlöf 2004 ISIS Workshop
9
Sensor fusion
The basic idea:
”Use measurements from a sensor mounted at the tool to get better estimates of the position, velocity, and on ed acceleration.” bas es on fusi chniqu r o s te Sen esian y a B
Mikael Norrlöf 2004 ISIS Workshop
Using additional sensors
What can be achieved? Increased robustness Higher accuracy Increased stiffness
Mikael Norrlöf 2004 ISIS Workshop
10
The “true” system
q_a
1 Arm angle
q_m tau_PID
Reference signal
tau_a
ref_in
qd_a
2
ref_pos_a
Arm angular vel
PID Controller qdd_a
3 Arm angular acc
Manipulator (Robotics Toolbox)
4 x' = Ax+Bu y = Cx+Du
Motor angle
Demux
5 mechanical system Non-linear Non-linear mechanical system Motor angular vel (manipulator) (manipulator)
Motor and gear
6
Motor angular acc
Linear Linearspring springand anddamper damper(gear-box) (gear-box) Mikael Norrlöf 2004 ISIS Workshop
Evaluation of arm position estimation 5
x 10
EKF RMSE with/without accelerometer and CRLB
-5
4.5
4
3.5
3
2.5
2
1.5
0
100
200
300
400
500
600
700
800
Mikael Norrlöf 2004 ISIS Workshop
11
Other possible sensors
Mikael Norrlöf 2004 ISIS Workshop
ISIS activities r(t)
+ +
-
FFf f FF
+
GG
y(t)
Control design
Modeling Identification Trajectory generation and optimization
Sensor fusion
Mikael Norrlöf 2004 ISIS Workshop
12
The trajectory generation problem
Cart. path P(lc) Geo. correct path φ(lc) Dyn. plan. +optimization
p1
lc(t)
p0
Mikael Norrlöf 2004 ISIS Workshop
Path generation Toolbox in Matlab p1 = [0.4,0.3,0.9]; p2 = [0.1,0.45,1.1]; p3 = [0.3,0.60,1.1]; p4 = [0.2,0.8,1.1]; zone1 = 0.1; zonemethod = 1; v1 = 0.25; v2 = 0.25; esec = emptysec(p1); lsec = moveline(esec,p2,zone1,[],v1); csec = movecirc(lsec,p3,p4,0,1,v2); rpath = makepath(lsec,csec) 1.15 1.1
z
1.05 1 0.95 0.4
0.9 1
0.3 0.8
0.2
0.6
0.1
0.4 y
0.2
0
x
Mikael Norrlöf 2004 ISIS Workshop
13
Path generation Toolbox in Matlab
Orientation Orientationinformation informationwill will be added in be added in PGT PGT v0.3 v0.3 1.45
1.4
z
1.35
1.3
1.25 0
0.02
0.94 0.92 0.9
0.04
y
x
Mikael Norrlöf 2004 ISIS Workshop
Dynamic optimization Path: P(lc), φ(lc) Path speed and acceleration:
dP dl c v= , dl c dt
apath
dP d 2l c = dl c dt 2
dφ dl c d 2φ dl c dφ d 2 l c & & & φ= , φ= 2 + dl c dt dl c dt dl c dt 2 2
Mikael Norrlöf 2004 ISIS Workshop
14
Dynamic optimization
Let
A (sub) optimal minimum time trajectory is found by solving the following LP problem
Mikael Norrlöf 2004 ISIS Workshop
Dynamic optimization
O P T I M I Z E R
dx dt d2x dt2 d3x dt3 d dt d2 dt2 d3 dt3
xx xx xx xx
xx xx
xx xx
dec .
xx xx
dis t
! m! eem l l b pprroob C PC M MP
Mikael Norrlöf 2004 ISIS Workshop
15
Conclusions Impact on current and future products Auto tune Control design
Modeling
Identification
Mikael Norrlöf 2004 ISIS Workshop
Conclusions Impact on current and future products Iterative Learning Control More flexible mechanical design
r(t)
+ +
-
Ff Ff FF
+
GG
y(t)
Control design
Sensor fusion Mikael Norrlöf 2004 ISIS Workshop
16
Conclusions Impact on current and future products Make better use of the robot performance Reduced price
Trajectory generation and optimization
Mikael Norrlöf 2004 ISIS Workshop
Conclusions
“ISIS has activities in areas central for the future developments in industrial robotics”
Mikael Norrlöf 2004 ISIS Workshop
17
