T. Veeraklaew et Sk. Agrawal, New computational framework for trajectory optimization of higher-order dynamic systems, J GUID CON, 24(2), 2001, pp. 228-236
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.