Exponential stability of dual flexible arms for grasping and orientation control

Abstract

The stability of two one-link flexible arms for grasping and orientation control of an object is studied. Flexible arms are modelled by Euler–Bernoulli beam model and the overall system is represented by a hybrid partial differential equation (PDE)–ordinary differential equation (ODE) model. The authors' primary concern is the stability analysis of this hybrid PDE–ODE model. In particular, they use the frequency domain method and prove the exponential stability of this system under their previously proposed boundary controller. In addition, they discuss the robustness of the closed-loop system with respect to the several disturbances including disturbances distributed over the arms and disturbances acting at boundaries. Finally, simulation results are presented to investigate the theoretical results.