Exponential stability of dual flexible arms for grasping and orientation control

Abstract

This paper studies the stability of two one-link flexible arms for grasping and orientation control of an object. Flexible arms are modeled by Euler-Bernoulli beam model, and the overall system is represented by a hybrid PDE-ODE model. Our primary concern is the stability analysis of this hybrid PDE-ODE model. In particular, we use the frequency domain method and prove the exponential stability of this system under our previously proposed boundary controller. In addition, we 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.

Boundary control for PDE flexible manipulators: Accommodation to both actuator faults and sensor faults

“…However, the ODE model could lead to spillover problem because it only considers finite modes. To get accurate dynamic model of the flexible manipulators, partial differential equation (PDE) dynamic model should be used for flexible mechanical systems [18][19][20][21][22][23].…”