Forward and Inverse Problems Relating to an Assistive Robotic Manipulator in an Uncertain Environment

Researchers have investigated the dynamics of oscillation of a single-link assistive manipulator and carried out vibration analysis of the same due to its great application in real life. Thus, studying the dynamics of flexible assistive robots and developing the model is indeed an interesting research topic. It is possible that the exact solution to the equations associated with such a single-link manipulator does not always exist. We used a numerical method, viz., Galerkin’s method to solve the governing differential equations of the problem, and the corresponding frequency of oscillation was calculated. This is known as the forward problem. On the other hand, the inverse problem is to compute values of the unknowns when the frequency is known by experiment, but the values of the remaining parameters are not known. With this backdrop, the purpose of this chapter is to investigate forward and inverse problems related to single-link robotic manipulators using Euler’s beam theory to define the system dynamics. Firstly, the frequencies of the first four modes of vibration have been calculated. Furthermore, the frequency is assumed to be known (experimental outcome), and the inverse case is studied using Young’s modulus and density of the material of manufacturing of the manipulator as unknown parameters. Besides, the system of single-link manipulators has been studied in uncertain environments using fuzzy theory for forward and inverse problems.