(Georgia Institute of Technology, 1993-09)
Yuan, B. - S.; Book, Wayne J.; Huggins, J. D.
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 x 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 non-linear 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.
(Georgia Institute of Technology, 1989-12)
Yuan, Bau-San; Book, Wayne J.; Huggins, J. D.
A robust adaptive control is derived by signal-synthesis
methods for a light, flexible two degree-of-freedom manipulator. The
controller for each joint is decentralized, using measurements of one
joint's position as well as one link's strain. The coupling to other
dynamics is treated as a bounded uncertainty in the model. A stability
proof has been developed and is outlined. Performance of the advanced
controller is compared to a Linear Quadratic Regulator (LOR) and to an independent joint control. Both simulations and experiments are
presented. The cases of payload variations are considered at this point.