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

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

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

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

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

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.

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

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

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

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)

Case Study Orthoglide robot Acceleration: 2g Workspace: Cube edge of 25 cm Isotropy properties Manufacturer’s drive gains: 2000 Payload ML = 1.983 Kg± 0.005 Kg

DHm Parameters

Identification Results Results cross-validation Identification of a new mass of 1.136 Kg With manufacturer’s gains: id. Mass = 1.09 With new gains: id. Mass = 1.14

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.