Linearization of the dynamics of a robot manipulator using the dual number algebra and its applications to manipulator control.

摘要

As an effective way of circumventing the difficulties of control of a robot manipulator due to its highly nonlinear and strongly coupled dynamics, a new method of linearization of the manipulator dynamics is presented. As a basis of the work, the (first- and nth-order) dual number algebra is presented and implemented on the computer.; The first-order dual number algebra is used in formulating the kinematic and dynamic equations of a robot manipulator and presenting two new methods for the inverse kinematic solutions. The resulting new dynamic equations are very concise, and their structure provides significant insight into the methods used for linearization. Based on these dynamic formulations, a new linearization method of the manipulator dynamics is presented in two forms: the recursive and nonrecursive formulations.; The nth-order dual number algebra provides a very simple way to evaluate the higher-order partial derivatives of dynamic equations. As an example application, this algebra is used to compute the second-order partial derivatives of the manipulator dynamic equations.; The linearized dynamic models are applied to two optimal control problems of a robot manipulator to demonstrate their utility in handling control problems: the trajectory optimization and the trajectory tracking control.; The measurement of the required computational time for linearization shows that the method using the dual number algebra significantly reduces the computation time over conventional methods, and a further reduction can be achieved by using the recursive formulation rather than the nonrecursive formulation. The trajectory optimization using the first-order gradient method is found to be quite satisfactory for a PUMA-560 manipulator. The simulation of the trajectory tracking control is also satisfactorily performed with the actual numerical values of a PUMA-560 manipulator.; The dual number algebra provides a very convenient tool for kinematics and dynamics analysis of nonlinear systems such as robot manipulators. The linearization based on the dual number formulations of the manipulator dynamics is very concise and computationally efficient. This linearization not only makes it much easier to handle various kinds of control problems, but also has great potential in implementing many existing control methods for robot manipulators. The convenient computation of second- and higher-order partial derivatives enhances our ability to implement more sophisticated schemes for manipulator control.