Optimal zeroing dynamics with applications to control of serial and parallel manipulators

The appearance of robot manipulators has dramatically improved the productivity in manufacturing. Serial and parallel manipulators are 2 classes of most popularly investigated manipulators, which have been playing an important role in robotic domain for a long time. Optimal control theory is a widely employed method that can achieve the objective constrained by some equations as subtasks, whereas zeroing dynamics is another powerful method to solve time-varying problems with an exponential rate of error convergence. Intuitively, the cross-fertilization of optimal control theory and zeroing dynamics may reach the capability to deal with time-varying problem in a cost-optimal manner. In this paper, we make progress along this direction by combining the optimal control theory and zeroing dynamics to propose a novel method called optimal zeroing dynamics for motion control of manipulators. The proposed method is applied to the control of serial and parallel manipulators, and the corresponding results have illustrated high accuracy and low sensitivity of the proposed optimal zeroing dynamics to disturbances.