Optimal parameter estimation for long-term prediction in the presence of model mismatch applied to a two-link flexible joint robot

Ryan Sangjun Lee, Purdue University

Abstract

For nonlinear multi-input multi-output (MIMO) systems such as multi-link robotic manipulators, finding a correct, physically-derived model structure is almost impossible, so that significant model mismatch is nearly inevitable. Though Lagrange equation gives us a systematic way to build a dynamic model based on the laws of physics, the accuracy of the model as a long-term predictor for multi-link robotic manipulators is often not good enough for model-dependent precision control techniques and computer simulation. Moreover, in the presence of model mismatch, the use of least-squares minimization of the one-step-ahead prediction error (residual error) to estimate unknown parameters in a given model structure often leads to model predictions that are extremely inaccurate beyond a short time interval. In this work, for better model accuracy, a MIMO nonlinear autoregressive moving average with exogenous inputs (NARMAX) model with more mathematical degrees of freedom is constructed partly based on the Lagrangian model. For more accurate parameter estimation in the presence of significant model mismatch, a method of optimal parameter estimation for accurate long-term prediction models is developed in this research. For many practical cases where a correct model and the correct number of degrees of freedom for a given model structure are unknown, we combine the use of long-term prediction error with frequency-based regularization to produce more accurate long-term prediction models for actual MIMO nonlinear systems. When the proposed Fourier-regularized optimal parameter estimation (OPE) method was used to estimate the parameters of the MIMO NARMAX model, the identified high-order model showed significantly better model accuracy compared to the Lagrangian model. Though the Fourier-regularization was very helpful to avoid overfitting and yield more accurate parameter estimation, the high-order MIMO NARMAX model was composed of many redundant regressors with a large number of parameters. To find an optimal model structure of the MIMO NARMAX model, L1 regularization method is used in this research to yield sparse model structures and overcome the ill-posedness of parameter estimation due to the redundant model structure. Though the L1 and L 2 regularization methods are useful to solve ill-posed inverse problems, the simulation results of identified models with L1 /L2 - regularized parameters showed significant model discrepancy between actual outputs and simulated outputs. Since the L1 and L2 regularization methods try to minimize both residual error and the L1/L2 norm of a parameter vector, these methods do not guarantee accurate long-term prediction models in the presence of significant model mismatch. For more accurate parameter estimation for the sparse models obtained by the L1 regularization, parameters were re-estimated by the proposed method of Fourier-regularized optimal parameter estimation using simulation error. The identified sparse models with the parameters reestimated using the OPE method showed comparable long-term prediction accuracy with a significantly fewer number of regressors compared to the high-order model.

Degree

Ph.D.

Advisors

Buzzard, Purdue University.

Subject Area

Mechanical engineering|Robotics

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