Enhancing Robustness and Accuracy in Nonlinear System Identification with Applications to Industrial Robotics

Nonlinear system identification is the procedure of obtaining nonlinear models of dynamical systems, based on input-output measurements collected from them. It is an important stepping stone for high performance applications in control engineering, and various other disciplines.

Many engineering challenges can be solved by shifting from the linear to the nonlinear domain. However, the complexity of dealing with nonlinearities in system identification is typically magnitudes higher than considering only linear models, both computationally and in terms of engineering time. The choices made with respect to the experiment design, the model structure, and the formulation of the fitting criterion have a profound effect on the final accuracy of the resulting model, and the effort needed to achieve it.

In nonlinear system identification, there is a demand for methods that can retrieve accurate models in a robust way. Particularly, fitting the complex manifold of nonlinear models to the measurement data is a non-convex optimization problem, susceptible to local minima, and dependent on the initial parameters, thus, there is a need for formulations that are more robust against these issues. Furthermore, it is still challenging to create simulation models that provide accurate long-term predictions. Often model accuracy needs to be balanced with complexity so that the model is sufficient for its final application.    

The research presented in this thesis covers four main topics that contribute to solving these issues, illustrated with selected use cases in industrial robotics. First, in relation to experiment design, we present an improved excitation signal design method for minimizing the crest factor of multisine signals, for accurate identification in cases when the dynamic range in the experiment is the most scarce resource. Second, we discuss and slightly extend ReSMILE, a local method for identifying linear parameter varying (LPV) models based on B-splines. ReSMILE allows for an accuracy-complexity trade-off, demonstrated on a dataset collected from an overhead crane. Third, we compare multiple, so-called shooting methods for identifying phyisics-based nonlinear state-space models, to find out which is the most robust with respect to local minima, with thorough evaluations on models of an electromechanical positioning system and a nonlinear mass-spring-damper. Fourth, for the forward dynamics of a robot arm, we propose a combination of physics-based and black-box models that effectively uses the knowledge about the physical structure in order to achieve an accuracy that is even better than that of a black-box model alone. We verify this in a comparison of different combined model structures.  

The goals of the thesis, along with the discussion of the mentioned extensions, are to aid the user in making well-informed choices in nonlinear system identification with respect to excitation signal design, model structure selection, optimization problem formulations, and to increase industrial uptake by providing easy-to-use toolboxes for the methods investigated for grey-box and LPV identification.