  This paper deals with time-optimal control of nonlinear continuous-time
systems based on direct collocation. The underlying discretization grid is
variable in time, as the time intervals are subject to optimization. This
technique differs from approaches that are usually based on a time
transformation. Hermite-Simpson collocation is selected as common
representative in the field of optimal control and trajectory optimization.
Hereby, quadratic splines approximate the system dynamics. Several splines of
different order are suitable for the control parameterization. A comparative
analysis reveals that increasing the degrees of freedom in control, e.g.
quadratic splines, is not suitable for time-optimal control problems due to
constraint violation and inherent oscillations. However, choosing constant or
linear control splines points out to be very effective. A major advantage is
that the implicit solution of the system dynamics is suited for stiff systems
and often requires smaller grid sizes in practice.
