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The work presented in this paper is a ground-breaking initiative to design a translational optimal controller named HEX2OQTAL. The controller is capable of producing high precision translational tracking using a linearized model of a trajectory error based on a quaternion attitude representation. This control contribution is general in the sense that it is agnostic of the underlying vehicle; the results are presented for an unmanned aerial vehicle (UAV) experimentally, a spacecraft scenario in simulation, and a precision planetary landing scenario. The paper presents a full derivation from base principles, a proof of stability, and real-time repeatable experimental UAV results (25 tests per controller per scenario). These results show that the developed controller presented here is far more precise than the most common industry standard controllers, such as PID and classical LQR. The obtained results show the potential of this controller not only as an accurate and adaptable controller, but also in high precision trajectory tracking control. [ABSTRACT FROM PUBLISHER]