Computationally efficient 3D orientation (3DO) tracking using gyroscope angular velocity measurements enables a short execution time and low energy consumption for the computing device. These are essential requirements in today's wearable device environments, which are characterized by limited resources and demands for high energy autonomy. We show that the computational efficiency of 3DO tracking is significantly improved by correctly interpreting each triplet of gyroscope measurements as simultaneous (using the rotation vector called the Simultaneous Orthogonal Rotation Angle, or SORA) rather than as sequential (using Euler angles) rotation. For an example rotation of 90°, depending on the change in the rotation axis, using Euler angles requires 35 to 78 times more measurement steps for comparable levels of accuracy, implying a higher sampling frequency and computational complexity. In general, the higher the demanded 3DO accuracy, the higher the computational advantage of using the SORA. Furthermore, we demonstrate that 12 to 14 times faster execution is achieved by adapting the SORA-based 3DO tracking to the architecture of the executing low-power ARM Cortex® M0+ microcontroller using only integer arithmetic, lookup tables, and the small-angle approximation. Finally, we show that the computational efficiency is further improved by choosing the appropriate 3DO computational method. Using rotation matrices is 1.85 times faster than using rotation quaternions when 3DO calculations are performed for each measurement step. On the other hand, using rotation quaternions is 1.75 times faster when only the final 3DO result of several consecutive rotations is needed. We conclude that by adopting the presented practices, the clock frequency of a processor computing the 3DO can be significantly reduced. This substantially prolongs the energy autonomy of the device and enhances its usability in day-to-day measurement scenarios.
Keywords: 3D gyroscope; 3D orientation; SORA; angular velocity; computational efficiency; motion tracking.