| Modern automated machines have complex dynamics. Planned trajectories that do not comply with such dynamics have a small likelihood of successful implementation. Moreover, goals and environment may not be fully known in advance. All of this makes the capability of on-line planning an essential feature.; Dynamic optimization theory provides a framework for such problems. An attempt to make it viable for on-line applications has been pursued based on advances in the theory of differentially flat systems. These systems have an algebraic representation of the states and inputs in terms of a vector-function of the states, the flat output, and some of its higher-order time derivatives. This dissertation takes place in this context, and new results are given that apply to partially linearizable systems, discrete-time systems, and groups of flat systems.; Partially linearizable systems have a residual dynamics that does not have an algebraic structure, but we show that it is still possible to have efficient planning schemes.; The study of discrete time formulations shows that an equivalent to the higher-order in derivatives of the continuous case is identified as being a set of future discrete values of the flat output, and trajectory generation methods are build upon such structures.; For groups of systems, formation laws allow for a parameterization of the members' trajectories by the leader's flat output. Maneuvers within the formation are locally planned with simplifying assumptions, while the global motion of the group is planned according to the full problem. |
