Attainable Moment Set Optimization to Support Configuration Design: A Required Moment Set Based Approach

In this paper, we discuss an attainable moment set (AMS) optimization methodology considering a system’s required moment set (RMS). The AMS describes the achievable moments from a system, given its input limits. An RMS, like an AMS, is a convex set in the moment space, describing the required moments for a system to meet the designed mission profile and disturbance rejection requirements. Given the configuration of a system, its mission requirements, and the derived RMS, the proposed optimization maximizes coverage of the AMS onto the RMS, thus ensuring the system possesses the guaranteed controllability to fulfill its required missions from a design level. To achieve this goal, the variables to optimize are chosen as effector settings, such as the installation position and angle of propellers and control surfaces, which effectively change the AMS without a vast impact on major design parameters, such as mass and moment of inertia. Since the optimization includes massive geometry operations of rays intersecting polyhedron, an efficient intersection solver is proposed to speed up the optimization process. The described method is applied to an electric-vertical-take-of-landing vehicle (eVTOL) with eight hover propellers, which delivers a highly improved coverage of the RMS compared to its initial design.