Flexible-Link Manipulator Force Control

The force control problem for flexible link manipulators is addressed. The controller design is based on the inner/outer loop strategy proposed by Anderson and Spong [1]. The inner loop controller linearizes the underlying rigid arm dynamics and produces a vibration free output. The rigid arm dynamics are recovered through application of the singular perturbation method and a nonlinear feedback linearization scheme based on the inverse dynamics approach is employed. Subsequently a fast control based on the input shaping scheme is designed to stabilize the flexible dynamics subsystem. The resulting controller corresponds to a feedforward term that convolves in real-time the desired reference input with a sequence of impulses and produces a near vibration free output. The outer loop is a control law responsible for achieving other goals such as robustness, disturbance rejection, etc. The controller structure depends on the characteristics of the environment modeled as a combination of mass, damping and stiffness matrices. The outer loop additionally colors the input so that no energy is injected around the flexible modes. Additional robustness is achieved through an adaptive frequency filter which identifies the modal frequencies of the system and subsequently adjusts the nulls of the notch filter and the spacing between the impulses within the input shaping algorithm. Application of the aforementioned scheme on a one and two flexible link manipulator is presented to demonstrate its effectiveness.