Pierre Olivier Vandanjon

A New Closed-Loop Output Error Method for Parameter Identification of Robot Dynamics

Offline robot dynamic identification methods are mostly based on the use of the inverse dynamic model, which is linear with respect to the dynamic parameters. This model is sampled while the robot is tracking reference trajectories that excite the system dynamics. This allows using linear least-squares techniques to estimate the parameters. The efficiency of this method has been proved through the experimental identification of many prototypes and industrial robots. However, this method requires the joint force/torque and position measurements and the estimate of the joint velocity and acceleration, through the bandpass filtering of the joint position at high sampling rates. The proposed new method called DIDIM requires only the joint force/torque measurement, which avoids the calculation of the velocity and acceleration by bandpass filtering of the measured position. It is a closed-loop output error method where the usual joint position output is replaced by the joint force/torque. It is based on a closed-loop simulation of the robot using the direct dynamic model, the same structure of the control law, and the same reference trajectory for both the actual and the simulated robot. The optimal parameters minimize the 2-norm of the error between the actual force/torque and the simulated force/torque. This is a nonlinear least-squares problem which is dramatically simplified using the inverse dynamic model to obtain an analytical expression of the simulated force/torque, linear in the parameters. A validation experiment on a two degree-of-freedom direct drive rigid robot shows that the new method is efficient.

A Generic Instrumental Variable Approach for Industrial Robot Identification

This paper deals with the important topic of industrial robot identification. The usual identification method is based on the inverse dynamic identification model and the least squares technique. This method has been successfully applied on several industrial robots. Good results can be obtained, provided a well tuned derivative band-pass filtering of joint positions is used to calculate the joint velocities and accelerations. However, one cannot be sure whether or not the band-pass filtering is well tuned. An alternative is the instrumental variable (IV) method, which is robust to data filtering and is statistically optimal. In this paper, a generic IV approach suitable for robot identification is proposed. The instrument set is the inverse dynamic model built from simulated data calculated from simulation of the direct dynamic model. The simulation is based on previous estimates and assumes the same reference trajectories and the same control structure for both actual and simulated robots. Finally, gains of the simulated controller are updated according to IV estimates to obtain a valid instrument set at each step of the algorithm. The proposed approach validates the inverse and direct dynamic models simultaneously, is not sensitive to initial conditions, and converges rapidly. Experimental results obtained on a six-degrees-of-freedom industrial robot show the effectiveness of this approach: 60 dynamic parameters are identified in three iterations.

Joint stiffness identification from only motor force/torque data

This paper deals with joint stiffness identification with only actual motor force/torque data instead of motor and load positions. The parameters are estimated by using the DIDIM method which needs only input data. This method was previously validated on a 6 DOF rigid robot and is now extended to flexible systems. The criterion to be minimized is the quadratic error between the measured actual motor force/torque and the simulated one. The optimal parameters are calculated with the Nelder - Mead simplex algorithm. An experimental setup exhibits the experimental identification results and shows the effectiveness of our approach.

Experimental joint stiffness identification depending on measurements availability

This paper addresses the important topic of joint flexibility identification. Three dynamic models depending on measurements availability are compared. The parameters are estimated by using the ordinary least squares of an over linear system obtained from the sampling of the dynamic model along a closed loop tracking trajectory. An experimental setup exhibits the experimental identification results.

Application of viability theory for road vehicle active safety during cornering manoeuvres

Viability theory proposes geometric metaphors in addition to classical ordinary differential equation analysis. In this paper, advantages of applying viability theory to road safety domain are presented. The exact issue is to determine if, from an initial state of a vehicle/road/driver system, a soft controls strategy is compatible with a safe driving sequence. The case of a car negotiating a curve is considered. The application of the viability theory to this issue offers the advantage to avoid classical full computing of the system. Instead of that, it consists on verifying that the states and the controls belong to a subset called the viability kernel. The construction and the use of the viability kernel for a vehicle system dynamic is proposed by using support vector machines algorithm. Then, the applicability of this theory is demonstrated through experimental tests. This innovative application of the viability theory to vehicle dynamics with road safety concerns could benefit to robust embedded warning systems.

Comparison Between the CLOE Method and the DIDIM Method for Robots Identification

This brief deals with the identification of industrial robots. The usual identification method is based on the use of the inverse dynamic identification model and the least-squares technique. Another approach is the direct and inverse dynamic identification models (DIDIM) method, which is a closed-loop output error (CLOE) method minimizing the quadratic error between the actual and simulated joint torques. In this brief, the DIDIM method is compared with the usual CLOE method, which minimizes the quadratic error between the actual and simulated joint positions. The comparison is carried out on six degrees of freedom industrial robot. The experimental results show that the DIDIM method needs three iterations to identify 60 parameters while the usual CLOE method needs 20 iterations.

A Durbin-Wu-Hausman test for industrial robots identification

This paper deals with the topic of industrial robots identification. The usual identification method is based on the use of the inverse dynamic model (IDM) and least squares (LS) technique. Good results can be obtained provided that a well-tuned bandpass filtering is used. However, we are always in doubt if regressors are exogenous i.e. statistically uncorrelated with error terms. Surprisingly, in papers dealing with identification of real-world systems, exogeneity assumption is never verified whereas it is a fundamental condition to obtain unbiased estimates. In Econometrics, the Durbin-Wu-Hausman test (DWH-test) is a theoretical method for investigating whether regressors are exogenous or not. The DWH-test makes of the Two Stage Lesat Squares estimator (2SLS) and an augmented LS regression. However, this test cannot be used as is for robots identification: instruments set is supposed to be valid and restrictive statistical assumptions are made while they are quite implausible in practice. In this paper, we aim at bridging the gap between Econometrics and Control engineering practices by introducing a revisited version relevant for robots identification. An experimental validation performed on a 2 degrees of freedom (DOF) robot shows the effectiveness and the usefulness of this revisited DWH-test.

Using robust regressions and residual analysis to verify the reliability of LS estimation: Application in robotics

Usually, the identification of the dynamic parameters of robot makes use of the inverse dynamic model which is linear with respect to the parameters. This model is sampled while the robot is tracking exciting trajectories. This allows using linear least squares (LS) techniques to estimate the parameters. The efficiency of this method has been proved through experimental identifications of a lot of prototypes and industrial robots. However, it is known that LS estimators are sensitive to outliers and leverage points. Thus, it may be helpful to verify their reliability. This is possible by using robust regressions and residual analysis. Then, we compare the results with those obtained with classical LS regression. This paper deals with this issue and introduces the experimental identification and residual analysis of an one degree of freedom (DOF) haptic interface using the Hubers estimator. To verify the pertinence of our analyses, this comparison is also performed on a medical interface consisting of a complex mechanical structure.