Dynamic Analysis And Programming Of Cooperation Of Flexible Manipulators

The cooperation of flexible manipulators is one of the advanced topics in the robotics research. A literature search reveals little results on the cooperation of flexible manipulators. The dynamic models of flexible-link manipulators, manipulators with joint and link flexibility and the cooperation of flexible manipulators are developed. The forward dynamics, inverse dynamics and trajectory tracking of the flexible robot arms and further the forward dynamics, inverse dynamics, trajectory tracking redundant actuation, internal forces and dynamic load-carrying capacity of cooperating manipulators have been systematically studied. The methods have been developed further and used for the constrained flexible manipulators and flexible manipulators cooperating constrained objects.First of all, using the Timoshenko beam theory and the Finite Element Method, according to Lagrange equation, the dynamic models of flexible-link manipulators and those with joint and link flexibility are proposed base on actual displacement. The dynamic equations are derived, which can be used to obtain the trajectory of the end-effector for given input joint angles or input joint torques. With boundary conditions different from the conventional method, the dynamic equation is developed, which can be used to find input joint angles or input joint torques for the specified trajectory of the end-effector.Then, according to the kinematic and dynamic constrains of the cooperation, the dynamic models of multiple flexible robot arms cooperating a rigid body are developed by the proposed dynamic models of flexible manipulators. The dynamic models of the cooperation of the flexible robot arms have been derived, which can be used to obtain the trajectory of the mass center of the cooperated object for given joint input. Assuming the actual mass center of the cooperated object, instead of the nominal rigid position determined by the kinematics of the rigid link counterpart, to be the boundary constraint and to satisfy the anticipated trajectory, the dynamic model is developed with the proposed load distribution method. The model can be used to find perfect input joint angles or input joint torques for specified trajectory of the mass center of the cooperated object. The inverse dynamics, forward dynamics, load distribution, trajectory tracking internal forces and allowable dynamicload-carrying capacity of the cooperation of the flexible manipulators have been discussed through analyses and numerical simulations.After that, the dynamic programming of cooperating flexible manipulators has been studied and a new measure, namely, the input power measure, has been proposed for the first time. Compared with the results of the other objective functions such as minimum input joint torques and minimum input joint angular velocity, the power consumption can be decreased and the kinematical and dynamical performances will be better by dynamic programming when taking the minimum joint input power as the objective function.Finally, using the Finite Element Method, according to the kinematic and dynamic constrains between the operated object and the environment, the dynamic models have been developed for constrained flexible manipulators and flexible robot arms cooperating constrained objects by the proposed dynamic models of flexible manipulators for the first time. Because the actual position has been assumed to be the boundary constraint, the proposed dynamic models have overcome the weakness that the conventional method is not convenient for the dynamic analysis of the kind of constrained flexible systems. The issues, inverse dynamics, trajectory tracking, load distribution and maximum dynamic contact force exerted on the environment, have been discussed through numerical simulations.