Estimation of model parameters in a dynamic system can be significantly improved with the choice of experimental trajectory. For general nonlinear dynamic systems, finding globally “best” trajectories is typically not feasible; however, given an initial estimate of the model parameters and an initial trajectory, we present a continuous-time optimization method that produces a locally optimal trajectory for parameter estimation in the presence of measurement noise. The optimization algorithm is formulated to find system trajectories that improve a norm on the Fisher information matrix (FIM). A double-pendulum cart apparatus is used to numerically and experimentally validate this technique. In simulation, the optimized trajectory increases the minimum eigenvalue of the FIM by three orders of magnitude, compared with the initial trajectory. Experimental results show that this optimized trajectory translates to an order-of-magnitude improvement in the parameter estimate error in practice.
In this paper we adressed the problem of finding exciting trajectories for the identification of manipulator link inertia parameters. This can be formulated as a constraint nonlinear optimization problem. The new approach in the presented method is the parameterization of the trajectories with optimized B-splines. Experiments are carried out on a 7 joint Light-Weight robot with torque sensoring in each joint. Thus, unmodeled joint friction and noisy motor current measurements must not be taken into account. The estimated dynamic model is verified on a different validation trajectory. The results show a clear improvement of the estimated dynamic model compared to a CAD-valued model. This paper concerns the problem of dynamic parameter identification of robot manipulators and proposes a closed-loop identification procedure using modified Fourier series (MFS) as exciting trajectories. First, a static continuous friction model is involved to model joint friction for realizable friction compensation in controller design. Second, MFS satisfying the boundary conditions are firstly designed as periodic exciting trajectories. To minimize the sensitivity to measurement noise, the coefficients of MFS are optimized according to the condition number criterion. Moreover, to obtain accurate parameter estimates, the maximum likelihood estimation (MLE) method considering the influence of measurement noise is adopted. The proposed identification procedure has been implemented on the first three axes of the QIANJIANG-I 6-DOF robot manipulator. Experiment results verify the effectiveness of the proposed approach, and comparison between identification using MFS and that using finite Fourier series (FFS)... This paper describes a new approach to the parameterization of robot excitation trajectories for optimal robot identification. The trajectory parameterization is based on a combined Fourier series and polynomial functions. The coefficients of the Fourier series are optimized for minimal sensitivity of the identification to measurement disturbances, which is measured as the d-optimality criterion, taking into account motion constraints in joint and Cartesian space. This parameterization satisfies both the guarantees of convergence by adding terms and the matching of the boundary conditions. Application of the method for the identification of the CRS A465 industrial robot proves the validity of the proposed approach. This paper considers a recently proposed framework for experiment design in system identification for control. We study model based control design methods, such as Model Predictive Control, where the model is obtained by means of a prediction error system identification method. The degradation in control performance due to uncertainty in the model estimate is specified by an application cost function. The objective is to find a minimum variance input signal, to be used in system identification experiment, such that the control application specification is guaranteed with a given probability when using the estimated model in the control design. We provide insight in the potentials of this approach by finite impulse response model examples, for which it is possible to analytically solve the optimal input problem. The examples show how the control specifications directly affect the excitation conditions in the system identification experiment.