Vibration avoidance method for flexible robotic arm manipulation

A new principle, run with flexible deformation, for avoiding vibration throughout trajectories of a flexible robot manipulator is proposed. It comprises the hysteretic and leading mechanisms to maintain a steady pace of flexible (neutral surface) evolution with rigid (joint axis) advance, with the surface staying on a single side of the axis for constant deformation. A simple proportional-derivative (PD) controller is presented to realize the mechanisms, capable of adapting deformation into an invariant set that the single-sided pace-keeping is dependable over a steady or transient period. Analytically this set is the dynamic equilibrium target, in which negativeness of the Lyapunov function's derivative is uncertain, and is proven globally uniformly asymptotically stable via a generalized Lyapunov and LaSalle's argument. Further, the desired deformation is same stable in the sense of Lyapunov theorem due to recursive slowdown by the controller. The theoretical work is validated by the numerical simulations, which shows that the desired performance is well achieved. Significant advantages such as vibration-free servo control of a flexible-axis-based trajectory are demonstrated.