1. Total Least Square Identification of Parallel Robots
Sébastien Briot and Maxime Gautier
IRCCyN – Nantes
Nantes

2. Introduction Applications of parallel robots
Force control, haptic devices, Flight/train/driving simulators
Require a correct reconstruction of ouput efforts
Force/torque sensors can sometimes be used => costly
Off line identification of the robot dynamic parameters c
IDIM requires: actual joints position, velocity and acceleration
actual joint torques t
available data:
joint position (encoders) q, sampling + band-pass filtering 
Current motor reference vt of the current amplifier
Joint j: , = the total drive gain ,
Nj gear ratio (Nj > 50), Ktj torque constant, Gj gain of the current amplifier

3. Introduction Usual identification of gtj New method
N, Gi and Kt identified separately by heavy tests on amplifier, motor
Needs to open the drive chain
Small errors on Gi and Kt involves large errors (N>50) on the drive gain gti
New method
Global identification of dynamic parameters + the total drive gains gtj
Use the accurate mass of a payload, weighed with a balance
Coupled identification, all joints together
Experimental results: improvement of the robot parameter dynamic identification

4. Dynamic Modeling Parallel robots can be seen in dynamics as
A tree structure + platform
Loops are closed using constraints equations (Jacobian matrices)

5. Inverse Dynamic Identification Model (IDIM)
The IDIM of the tree structure can be written under the form
tidmtree is the vector of the virtual input torques, Fsttree is the jacobian matrix
qtree the vector of joint coordinates
csttree is the vector of the standard dynamic parameters
Platform reactions
x the platform position, v platform twist
cpl is the vector of the standard dynamic parameters

6. Inverse Dynamic Identification Model (IDIM)
Use of the constraint equations
Obtention of kinematic relationships
IDIM of the parallel robot
Minimal IDIM
Obtained by elimination of columns of F that are linearly related.

7. Inverse Dynamic Identification Model (IDIM)
Use of a straightforward way for the derivation of Jtree
express the kinematic relation between the platform twist v and the velocities vtk of all leg extremities Cmk,k.
express the kinematic relation between the velocities vtk of all leg extremities Cmk,k and the velocities of all joints of the tree structure
combine these two relations with
to obtain

8. Drive Gain identification
Requires the scaling using known parameters => the payload
IDIM with the payload
Fu,kL the jacobian matrices corresponding to the payload parameters
cuL is the vector of the unknown payload dynamic parameters
ckL is the vector of the unknown payload dynamic parameters
Because of perturbations
e is the vector of errors
Sampled and filtered IDIM
Y is the vector regrouping all torques samples, W is the observation matrix, r is the vector of errors

9. Drive Gain Identification
Payload identification: carrying out two trajectories
First line of W => trajectory without a payload
Second line of W => trajectory with a payload
Can be rewritten as
Can be solved using Total Least Square Techniques
Without perturbations, r = 0 and Wtot is rank deficient
In reality, not the case => find the matrix such that
This matrix minimizes the Frobenius norm

10. Total Least Square Solution
It can be proven that a solution can be obtained as
Vend is the last column of matrix V obtained via the SVD of
The robot dynamic parameters can be obtained as
In this work, ckL : payload mass ML only (very accurate value)

11. Case Study Orthoglide robot Acceleration: 2g Workspace:
Cube edge of 25 cm
Isotropy properties
Manufacturer’s drive gains: 2000
Payload
ML = Kg± Kg

12. DHm Parameters

13. Identification Results
Results cross-validation
Identification of a new mass of Kg
With manufacturer’s gains: id. Mass = 1.09
With new gains: id. Mass = 1.14

14. Conclusions New approach for drive gain identification
Global identification of all joint drive gains and robot dynamic parameters
Method is very simpler to implement than previous ones
Obtained results show the importance of the drive gains identification
Future works
Force control, use of ground efforts for identification, etc.