Unmanned system performance depends heavily on both how the system is planned to be operated and the design of the unmanned system, both of which can be heavily impacted by uncertainty. This dissertation presents methods for simultaneously optimizing both of these aspects of an unmanned system when subject to uncertainty. This simultaneous optimization under uncertainty of unmanned system design and planning is demonstrated in the context of optimizing the design and flight path of an unmanned aerial vehicle (UAV) subject to an unknown set of wind conditions. This dissertation explores optimizing the path of the UAV down to the level of determining flight trajectories accounting for the UAVs dynamics (motion planning) while simultaneously optimizing design. Uncertainty is considered from the robust (no probability distribution known) standpoint, with the capability to account for a general set of uncertain parameters that affects the UAVs performance.

New methods are investigated for solving motion planning problems for UAVs, which are applied to the problem of mitigating the risk posed by UAVs flying over inhabited areas. A new approach to solving robust optimization problems is developed, which uses a combination of random sampling and worst case analysis. The new robust optimization approach is shown to efficiently solve robust optimization problems, even when existing robust optimization methods would fail. A new approach for robust optimal motion planning that considers a “black-box” uncertainty model is developed based off the new robust optimization approach. The new robust motion planning approach is shown to perform better under uncertainty than methods which do not use a “black-box” uncertainty model. A new method is developed for solving design and path planning optimization problems for unmanned systems with discrete (graph-based) path representations, which is then extended to work on motion planning problems. This design and motion planning approach is used within the new robust optimization approach to solve a robust design and motion planning optimization problem for a UAV. Results are presented comparing these methods against a design study using a DOE, which show that the proposed methods can be less computationally expensive than existing methods for design and motion planning problems.