Suboptimal Trajectory Planning Algorithm for Robotic Manipulators

This paper presents a Fourier-based suboptimal control approach for the trajectory planning of robotic manipulators modelled as coupled rigid bodies. The basic idea of the method is to convert a standard optimal control problem of infinite dimensionality (in time) 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 can then be solved via a nonlinear programming numerical algorithm given a performance index which is a continuous function of time. This method can be applied to a large class of problems with different performance indices and requires no model simplification. Manipulator control problems with free final time and states and with inequality constraints can be handled effectively. The method is demonstrated in two examples of trajectory planning for a planar robotic manipulator model.