Bau-San Yuan

Direct Adaptive Control of a One-Link Flexible Arm with Tracking

A robust tracking controller for a one-link flexible arm based on a model reference adaptive control approach is proposed. In order to satisfy the model matching conditions, the reference model is chosen to be the optimally controlled linearized model of the system. The resulting controller overcomes the fundamental limitation in previously published research on direct adaptive control of flexible robots that required additional actuators solely to control the flexible degrees of freedom. The nominal trajectory is commanded by means of a tracking control. Simulation results for the prototype in the laboratory show improvements obtained with the outer adaptive feedback loop compared to a pure optimal regulator control. Robustness is tested by varying the payload mass.

Dynamics of Flexible Manipulator Arms: Alternative Derivation, Verification, and Characteristics for Control

This work seeks to provide an effective way for developing the dynamics of a multi-link flexible manipulator consisting of rotary joints connecting two links. Kinematics of both the rotary joint motion and the link deformation are described by 4×4 transformation matrices as proposed in previous works (Book, 1984). The link deflection is assumed small so that the link transformation can be composed of summations of assumed link shapes. To determine the appropriate choice of component mode shapes, two essential techniques employed here are experimental and finite element methods. The resulting equations of motion allow the complete nonlinear model to be recursively derived from the Jacobian matrix and the mass properties via symbolic manipulation. Two prototype models of flexible manipulators are used to verify the dynamics with frequency and time responses. This paper contributes several new results: (1) the velocity terms (Coriolis and centrifugal forces) are related to variations in the mass matrix, (2) the skew symmetry of certain useful terms are shown, (3) the system is theoretically demonstrated to be stable with joint P.D. controllers in addition to an experimental approach, (4) practical and effective incorporation of actuator dynamics (hydraulic cylinder) and structural complexity (non-uniform cross section) is achieved through selection of mode shapes, (5) geometric constraints are incorporated through simplified coordinate transformations and (6) the results are verified on two physical cases.

Model reference adaptive control of a link flexible arm

Based on a model reference adaptive control approach, a robust controller for a one link flexible arm moving along a pre-defined trajectory is proposed. In order to satisfy the perfect model following conditions, the model is chosen from the linearized model of the system as optimally controlled. The nominal trajectory is commanded to the system by means of a dynamic filter. Simulation results for the prototype in the laboratory show the improvements obtained with the outer adaptive feed-back loop with respect to a pure optimal control regulator. Robustness is finally tested by varying the nominal payload mass.

Control of a Multi-Link Flexible Manipulator with a Decentralized Approach

Abstract This work seeks to provide an effective way for the development of the dynamics of a multi-link flexible manipulator. Due to the presence of nonlinearities, uncertainty, and link flexibility, a decentralized control is implemented here to provide robust stability without increasing the burden of on-line computation. Simulations and experiments show agreement with the analytic work.

Small Motion Experiments on a Large Flexible Arm with Strain Feedback

Initial experiments on state space feedback control of a large flexible manipulator with a parallel linkage drive are described. A linear controller using joint angle and strain measurements was designed to minimize a quadratic performance index with a prescribed stability margin. It is based on a simplified model that accounts for the constraints of the parallel linkage kinematically rather than through constraint forces. The results show substantial improvement over a simple P.D.joint control.