This paper proposes and compares the state estimation scheme and performance of the Extended Kalman Filter and the Unscented Kalman Filter. A highly nonlinear flexible manipulator is targeted by the study to evaluate the effectiveness and robustness of the proposed filters facing an online accurate estimation problem. An Euler-Bernoulli cantilever beam models the manipulator, and the elastic movement is approximated using the assumed modes method. The Hamilton’s principle yields the system nonlinear equations. This article compares, via the included numerical simulation results, the efficiency of the state estimate reflected by the estimation error and the time required by the filters to converge.
The input–output control strategy needs all of the states feedback. However, in flexible link robot manipulators, measuring the time rate of elastic degrees of freedom is practically impossible. In this paper, a new nonlinear high gain observer has been developed to estimate the elastic degrees of freedom and their time derivatives. The control strategy is based on an output redefinition approach which stabilizes the zero dynamics of the manipulator. Finally, the results are presented by implementing the proposed observer and controller on a single link flexible manipulator. Numerical simulations will support the validity of our research results.
We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero.