Optimal trajectory planning of robotic manipulators via quasi-linearization and state parameterization

A numerical algorithm has been developed to solve the problem of optimal control of robotic manipulators. A quasi-linearization method is used to convert a nonlinear optimal control problem into a sequence of LQ (linear quadratic) problems, which are solved by an efficient Fourier-based state parameterization approach. The update laws for the nominal trajectory ensure satisfaction of the terminal conditions. In contrast to dynamic-programming-based methods, the proposed approach does not demand extensive computer storage requirements and thus is capable of achieving optimality without limiting the degrees of freedom of the trajectory. Compared to nonlinear-programming-based methods, the approach offers significant advantages in computational efficiency. Compared to calculus-of-variations-based methods, the approach eliminates the requirement of solving a two-point boundary-value problem and therefore is more robust and efficient.