New computational framework for trajectory optimization of higher-order dynamic systems

By the use of tools from systems theory, it is now well known that classes of linear and nonlinear dynamic systems in first-order form can he alternat ively written in higher-order form, that is, as sets of higher-order differ ential equations. Input-state linearization is one of the popular tools to achieve such a transformation. For mechanical systems, the equations of mot ion naturally have a second-order form. For real-time planning and control, a higher-order form offers a number of advantages compared to the first-or der form. The question of trajectory optimization of higher-order systems w ith general nonlinear constraints is addressed. First, we develop the optim ality conditions directly using their higher-order form. These conditions a re then used to develop computational approaches. A general purpose program has been developed to benchmark computations between problems posed in alt ernate higher-order and first-order forms. The program implements both dire ct and indirect methods and uses collocation in conjunction with a nonlinea r programming solver.