The hybrid adaptive control algorithms used for flexible manipulators are presented. The advantages of the hybrid adaptive control against the pure continuous-time adaptive control or discrete-time adaptive control are also discussed. From a practical standpoint, the infrequent adjustment of the control parameters makes for more robust adaptive control while from a theoretical point of view, the algorithms are attractive since they provide a unified framework for the design of hybrid adaptive systems. The hybrid adaptive controllers also do not require the complex mathematical model of the arm dynamics or any knowledge of the arm dynamic parameters or the load parameters such as mass and stiffness. Simulation results are given to illustrate the proposed hybrid adaptive control strategies.
This paper is concerned with the dynamic modeling of two coordinating robots having flexible links. The formulation of the dynamics is conducted analytically using Hamilton's extended principle. The resultant equations consist of inertial, cariolis, centrifugal, gravitational. and exerted force terms. They are expressed by independent generalized coordinates. The complete model of two coordinating flexible robots grasping an object in terms of a coupled system of ordinary and partial differential equations is established. A finite dimensional model is also developed from this model which decouples the rigid joint motion from the flexible motion. JNTRODUCTIOYA variety of schemes for formulating the dynamic equations of two coordinating robots with rigid links grasping an object has been extensively studied by many researchers [I], (21, 13). An efficient method, however, for formulating the dynamic model of two coordinating flexible robots is not commonly known, especially for the two-link manipulator case containing both rigid and flexible links. The dynamic equatibns for flexible manipulators by means of Hamilton's principle or Lagrangian method were formulated [4], [5]. In these papers, the authors were only concerned with stand-alone manipulators having one or two flexible links.The objective of this paper is to develop a dynamic model of two coordinating robots having flexible links which would eventually be suitable for control and optimization studies. The workspace in which the two robots move is assumed to be free of any obstacles. First an approach to deriving the dynamic equations of two coordinating robots with one rigid link and one flexible link is developed using Hamilton's principle. The terms associated with the rigid and elastic links are treated separately. Then the kinematic constraints and boundary conditions for mode shapes of pinned-free beam and clamped-free beam are described. Similarly, the kinematic constraints between the two flexible robots are described, based on the assumption that the deflection is very small compared with the length of link ( 0.1 length) and that the two flexible robots do not lose grasp of the object or collide with one another. Consequantly, the dynamics of the load is obtained by applying Newton's law of motion, assuming that the load does not rotate around its center of mass. The constrained mode expansion method is finally applied to the complete dynamic model. The representation will lead to rigorous analytical investigations using infinite 8"nsional system theory. Finite dimensional models can be eas:ly obtained from the resu1t.c using modal expansion techniques or other methods that approximate partial differential equations by ordinary differential equations. A finite dimensional model is developed from this mqdel which decouples the rigid joint from the motion. So, the solutions of rigid motion and deflection motion are obtained separately. Consider the single link flexible model shown in Figure 1 and defined over one domain 0 d xi 5 li where xi is the spa...
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