Optimal design of robotic manipulator trajectories : a nonlinear programming approach

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 (explicit or implicit) junction 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..