This paper discusses experimental robot identification based on a statistical framework. It presents a new approach toward the design of optimal robot excitation trajectories, and formulates the maximum-likelihood estimation of dynamic robot model parameters. The differences between the new design approach and the existing approaches lie in the parameterization of the excitation trajectory and in the optimization criterion. The excitation trajectory for each joint is a finite Fourier series. This approach guarantees periodic excitation which is advantageous because it allows: 1) time-domain data averaging; 2) estimation of the characteristics of the measurement noise, which is valuable in case of maximum-likelihood parameter estimation. In addition, the use of finite Fourier series allows calculation of the joint velocities and accelerations in an analytic way from the measured position response, and allows specification of the bandwidth of the excitation trajectories. The optimization criterion is the uncertainty on the estimated parameters or a lower bound for it, instead of the often used condition of the parameter estimation problem. Simulations show that this criterion yields parameter estimates with smaller uncertainty bounds than trajectories optimized according to the classical criterion. Experiments on an industrial robot show that the presented trajectory design and maximum-likelihood parameter estimation approaches complement each other to make a practicable robot identification technique which yields accurate robot models.

This paper presents a new dynamical friction model structure which allows accurate modeling both in the sliding and the presliding regimes. Transition between these two regimes is accomplished without a switching function. The model incorporates a hysteresis function with nonlocal memory and arbitrary transition curves. These last aspects prove essential for modeling presliding friction that is encountered in real physical situations. The model as a whole can also handle the Stribeck effect and stick-slip behavior as has been demonstrated by validation on a KUKA IR 361 robot. In this sense, this model can be considered as more complete in comparison with others found in the literature. The general friction model allows modeling of individual friction systems through the identification of a set of parameters that determine the complete behavior of the system. In this way, the model structure has been used to identify the friction behavior of a linear slide as well as that of the above mentioned KUKA robot. The results of the latter identification have been consequently used for feedforward friction compensation to obtain the most accurate tracking.

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This paper describes the parameterization of robot excitation trajectories for optimal robot identification based on finite Fourier series. The coefficients of the Fourier series are optimized for minimal sensitivity of the identification to measurement disturbances, which is measured as the condition number of a regression matrix, taking into account motion constraints in joint and cartesian space. This approach allows obtaining small condition numbers with few coefficients for each joint, which simplifies the optimization problem significantly. The periodicity of the resulting trajectories and the fact that one has total control over their frequency content, are additional features of the presented parameterization approach. They allow further optimization of the excitation experiments through time domain data averaging and optimal selection of the excitation bandwidth, which both help the reduction of the disturbance level on the measurements, and therefore improve the identification accuracy.

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