Tool Position Estimation of a Flexible Industrial Robot using Recursive Bayesian Methods Patrik Axelsson, Rickard Karlsson, and Mikael Norrlöf Division of Automatic Control Department of Electrical Engineering Linköping University, Sweden Patrik Axelsson, Rickard Karlsson, and Mikael Norrlöf Tool Position Estimation of a Flexible Industrial Robot using Recursive Bayesian Methods AUTOMATIC CONTROL REGLERTEKNIK LINKÖPINGS UNIVERSITET
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Tool Position Estimation of a Flexible IndustrialRobot using Recursive Bayesian Methods
Division of Automatic ControlDepartment of Electrical EngineeringLinköping University, Sweden
Patrik Axelsson, Rickard Karlsson, and Mikael Norrlöf
Tool Position Estimation of a Flexible Industrial Robot using Recursive Bayesian Methods
AUTOMATIC CONTROLREGLERTEKNIK
LINKÖPINGS UNIVERSITET
Outline 2(12)
1. Introduction• Problem Formulation• Bayesian Estimation
2. Modelling• Robot Model• Accelerometer Model• Estimation Model
3. Experimental Results
4. Conclusions and Future Work
Patrik Axelsson, Rickard Karlsson, and Mikael Norrlöf
Tool Position Estimation of a Flexible Industrial Robot using Recursive Bayesian Methods
AUTOMATIC CONTROLREGLERTEKNIK
LINKÖPINGS UNIVERSITET
Problem Formulation 3(12)
Controller Robot
Observer
qrefm u
d
X
qmXref
Can control
Want to measure
Want to control the TCP. Can only measure the motor angles qm.
Feedback of qm does not work sufficiently due to flexible joints.
If the TCP can be measured it is natural to feedback it.
What can we do instead of measuring the TCP?
Patrik Axelsson, Rickard Karlsson, and Mikael Norrlöf
Tool Position Estimation of a Flexible Industrial Robot using Recursive Bayesian Methods
AUTOMATIC CONTROLREGLERTEKNIK
LINKÖPINGS UNIVERSITET
Problem Formulation 3(12)
Controller Robot
Observer
qrefm u
d
X
qmXref
Want to control
Can measure
Want to control the TCP. Can only measure the motor angles qm.
Feedback of qm does not work sufficiently due to flexible joints.
If the TCP can be measured it is natural to feedback it.
What can we do instead of measuring the TCP?
Patrik Axelsson, Rickard Karlsson, and Mikael Norrlöf
Tool Position Estimation of a Flexible Industrial Robot using Recursive Bayesian Methods
AUTOMATIC CONTROLREGLERTEKNIK
LINKÖPINGS UNIVERSITET
Problem Formulation 3(12)
Controller Robot
Observer
qrefm u
d
X
qmXref
Want to control
Can measure
Want to control the TCP. Can only measure the motor angles qm.
Feedback of qm does not work sufficiently due to flexible joints.
If the TCP can be measured it is natural to feedback it.
What can we do instead of measuring the TCP?
Patrik Axelsson, Rickard Karlsson, and Mikael Norrlöf
Tool Position Estimation of a Flexible Industrial Robot using Recursive Bayesian Methods
AUTOMATIC CONTROLREGLERTEKNIK
LINKÖPINGS UNIVERSITET
Problem Formulation 3(12)
Controller Robot
Observer
Xref u
d
X
qm
Want to control the TCP. Can only measure the motor angles qm.
Feedback of qm does not work sufficiently due to flexible joints.
If the TCP can be measured it is natural to feedback it.
What can we do instead of measuring the TCP?
Patrik Axelsson, Rickard Karlsson, and Mikael Norrlöf
Tool Position Estimation of a Flexible Industrial Robot using Recursive Bayesian Methods
AUTOMATIC CONTROLREGLERTEKNIK
LINKÖPINGS UNIVERSITET
Problem Formulation 3(12)
Controller Robot
Observer
Xref u
d
X
qm
Want to control the TCP. Can only measure the motor angles qm.
Feedback of qm does not work sufficiently due to flexible joints.
If the TCP can be measured it is natural to feedback it.
What can we do instead of measuring the TCP?
Patrik Axelsson, Rickard Karlsson, and Mikael Norrlöf
Tool Position Estimation of a Flexible Industrial Robot using Recursive Bayesian Methods
AUTOMATIC CONTROLREGLERTEKNIK
LINKÖPINGS UNIVERSITET
Problem Formulation 4(12)
Controller Robot
Observer
Xref u
d
X
qm
Let the acceleration of the tool be a measurement.
Use an observer to estimate the TCP.
How can we estimate the TCP?
Patrik Axelsson, Rickard Karlsson, and Mikael Norrlöf
Tool Position Estimation of a Flexible Industrial Robot using Recursive Bayesian Methods
AUTOMATIC CONTROLREGLERTEKNIK
LINKÖPINGS UNIVERSITET
Problem Formulation 4(12)
Controller Robot
Observer
Xref u
d
X
qmX
Let the acceleration of the tool be a measurement.
Use an observer to estimate the TCP.
How can we estimate the TCP?
Patrik Axelsson, Rickard Karlsson, and Mikael Norrlöf
Tool Position Estimation of a Flexible Industrial Robot using Recursive Bayesian Methods
AUTOMATIC CONTROLREGLERTEKNIK
LINKÖPINGS UNIVERSITET
Problem Formulation 4(12)
Controller Robot
Observer
Xref u
d
X
qmX
X
Let the acceleration of the tool be a measurement.
Use an observer to estimate the TCP.
How can we estimate the TCP?
Patrik Axelsson, Rickard Karlsson, and Mikael Norrlöf
Tool Position Estimation of a Flexible Industrial Robot using Recursive Bayesian Methods
AUTOMATIC CONTROLREGLERTEKNIK
LINKÖPINGS UNIVERSITET
Problem Formulation 4(12)
Controller Robot
Observer
Xref u
d
X
qmX
X
Let the acceleration of the tool be a measurement.
Use an observer to estimate the TCP.
How can we estimate the TCP?
Patrik Axelsson, Rickard Karlsson, and Mikael Norrlöf
Tool Position Estimation of a Flexible Industrial Robot using Recursive Bayesian Methods
AUTOMATIC CONTROLREGLERTEKNIK
LINKÖPINGS UNIVERSITET
Bayesian State-space Estimation 5(12)
Model:
xt+1 = f (xt, ut, wt),
yt = h(xt) + et.
Bayesian inference:
p(xt+1|Yt) =∫
Rnp(xt+1|xt)p(xt|Yt)dxt,
p(xt|Yt) =p(yt|xt)p(xt|Yt−1)
p(yt|Yt−1).
The Kalman filter is the optimal choice for linear models.Approximative filters have to be used for nonlinear models.
In this work
• Extended Kalman filter (EKF)– Approximate the system with a linearisation of the nonlinear
equations.– Assume additive Gaussian noise.
• Particle filter (PF)– Approximate the posterior distribution with a large number of
particles.– The optimal proposal distribution approximated using an EKF.
Patrik Axelsson, Rickard Karlsson, and Mikael Norrlöf
Tool Position Estimation of a Flexible Industrial Robot using Recursive Bayesian Methods
AUTOMATIC CONTROLREGLERTEKNIK
LINKÖPINGS UNIVERSITET
Bayesian State-space Estimation 5(12)
Model:
xt+1 = f (xt, ut, wt),
yt = h(xt) + et.
Bayesian inference:
p(xt+1|Yt) =∫
Rnp(xt+1|xt)p(xt|Yt)dxt,
p(xt|Yt) =p(yt|xt)p(xt|Yt−1)
p(yt|Yt−1).
The Kalman filter is the optimal choice for linear models.Approximative filters have to be used for nonlinear models.In this work• Extended Kalman filter (EKF)
– Approximate the system with a linearisation of the nonlinearequations.
– Assume additive Gaussian noise.
• Particle filter (PF)– Approximate the posterior distribution with a large number of
particles.– The optimal proposal distribution approximated using an EKF.
Patrik Axelsson, Rickard Karlsson, and Mikael Norrlöf
Tool Position Estimation of a Flexible Industrial Robot using Recursive Bayesian Methods
AUTOMATIC CONTROLREGLERTEKNIK
LINKÖPINGS UNIVERSITET
Bayesian State-space Estimation 5(12)
Model:
xt+1 = f (xt, ut, wt),
yt = h(xt) + et.
Bayesian inference:
p(xt+1|Yt) =∫
Rnp(xt+1|xt)p(xt|Yt)dxt,
p(xt|Yt) =p(yt|xt)p(xt|Yt−1)
p(yt|Yt−1).
The Kalman filter is the optimal choice for linear models.Approximative filters have to be used for nonlinear models.In this work• Extended Kalman filter (EKF)
– Approximate the system with a linearisation of the nonlinearequations.