DESIGNING MANIPULATOR TRAJECTORIES BY NONLINEAR PROGRAMMING.

A nonlinear programming approach for the optimal motion planning of robotic manipulators is presented. In this approach a standard optimal control problem of infinite dimensionality (in time) is converted into an optimization problem of finite dimensionality by approximating the manipulator trajectories by the sum of a polynomial and a set of appropriate eigenfunctions. The optimal control problem is then solved via a nonlinear programming numerical algorithm given a performance index which is a continuous function of time. This method can be used for trajectory planning of high degree-of-freedom manipulators once motion specifications and constraints have been identified. Examples of trajectory planning of a planar robotic manipulator with free and constrained final time and states are presented.