Inverse Problems in Mechatronics: From Calibration and Measurement to Control and Design
Institute for Automation, University of Leoben, Leoben, Austria
December 20, 2016 at 2:00 PM
In this seminar, we present the concept of an inverse problem, giving several examples of such problems which arise in mechatronics, and some approaches to their solution. Fundamentally, measurement itself is an inverse problem: From the effects, determine the cause. In vision assisted robotics, the problems of calibration and measurement (e.g., of 3D position) implicitly comprise two challenging inverse problems to solve; the inversion of a many-to-one projective transformation, and the modelling of geometric errors from statistics. Correspondingly, the solution of an inverse problem requires regressive reasoning or synthesis, and hence such problems can often have either no solution, or an infinite family of solutions. For example, the problem of optimal control is to select a particular path from an infinite set of paths with identical boundary conditions. One of the more fundamental inverse problems in mechanical engineering is the design of a mechanism to perform a desired task; the solution is inevitably non-unique.
In mechatronics, to deal with digital signals, discrete methods are required to solve both direct and inverse problems. In general, we may discretize a linear integro-differential operator as a matrix, while simultaneously incorporating some form of regularization (e.g., data smoothing). This yields a highly intuitive method for solving ODE and PDE as well as corresponding inverse problems. With this new approach, we give practical examples of the inverse problems of optimal control, the parameter identification problem for systems, as well as the design of distributed parameter systems for a desired response. Applications of the methods presented include the design of a beam with desired mode shapes, or a robotic manipulator with muscle-like dynamics.
Matthew Harker was born in Toronto, Canada. He obtained the B.Eng. degree in mechanical engineering with a specialization in mechatronics from McGill University, Montreal, QC, Canada, in 2003, and the Dr.mont. (Ph.D.) degree in mechanical engineering from the Mining University of Leoben, Leoben, Austria, in 2008. His doctoral thesis was on the topic of algebraic and geometric techniques for optimization in digital image-based precision measurement systems (metric vision). In 2016 he obtained his habilitation (docent) in Automation Engineering, with the Habilitationsschrift “Differential Equations, Inverse Problems, and Fractional Calculus in Mechatronics.” He is currently a Privat-Dozent with the Chair for Automation, University of Leoben, Leoben, Austria. His area of research is geometric, probabilistic, and discrete integro-differential methods for the regularized solution of inverse problems that arise in the field of mechatronics and cyber-physical systems.