Mathematical Background

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Abstract

Robot manipulators are highly nonlinear dynamic systems. When a desired task has to be accomplished, there are many issues to be solved to get the best possible performance. First of all the task has to be planned and expressed in such a way that it can be executed by the robot. Perhaps the most common practice consists in defining particular desired trajectories or references for each robot joint and then implement a control algorithm to follow these trajectories. This may well imply the computation of inverse kinematics online, but assuming that this is done, then the most relevant challenge becomes the design of a control scheme. Also the most common approach is to define an error between desired and actual trajectories, so that if it vanishes then the task is accomplished. There are many analytical tools for control design, each of them with pros and cons, e.g. passivity or Lyapunov theory. In this section, we focus on the latter and provide the reader with the most basic definitions and theorems that will be employed in the rest of the book in the solution of many different problems.

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Arteaga, M. A., Gutiérrez-Giles, A., & Pliego-Jiménez, J. (2022). Mathematical Background. In Lecture Notes in Electrical Engineering (Vol. 798, pp. 103–128). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-85980-0_4

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