Abstract:
The problem addressed in this research is the in-flight generation of trajectories for
autonomous unmanned aircraft, which requires a method of generating pseudo-optimal
trajectories in near-real-time, on-board the aircraft, and without external intervention.
The focus of this research is the enhancement of a particular inverse dynamics direct
method that is a candidate solution to the problem. This research introduces the
following contributions to the method.
A quaternion-based inverse dynamics model is introduced that represents all
orientations without singularities, permits smooth interpolation of orientations, and
generates more accurate controls than the previous Euler-angle model.
Algorithmic modifications are introduced that: overcome singularities arising from
parameterization and discretization; combine analytic and finite difference expressions
to improve the accuracy of controls and constraints; remove roll ill-conditioning when
the normal load factor is near zero, and extend the method to handle negative-g
orientations. It is also shown in this research that quadratic interpolation improves the
accuracy and speed of constraint evaluation.
The method is known to lead to a multimodal constrained nonlinear optimization
problem. The performance of the method with four nonlinear programming algorithms
was investigated: a differential evolution algorithm was found to be capable of over
99% successful convergence, to generate solutions with better optimality than the quasi-
Newton and derivative-free algorithms against which it was tested, but to be up to an
order of magnitude slower than those algorithms. The effects of the degree and form of
polynomial airspeed parameterization on optimization performance were investigated,
and results were obtained that quantify the achievable optimality as a function of the
parameterization degree.
Overall, it was found that the method is a potentially viable method of on-board near-
real-time trajectory generation for unmanned aircraft but for this potential to be realized
in practice further improvements in computational speed are desirable. Candidate
optimization strategies are identified for future research.
