TY - JOUR
T1 - Orientation Modeling Using Quaternions and Rational Trigonometry
AU - Martínez, Rogelio
AU - Zamora, Erik
AU - Sossa, Humberto
AU - Arce, Fernando
AU - Soriano, Luis Arturo
N1 - Publisher Copyright:
© 2022 by the authors.
PY - 2022/9
Y1 - 2022/9
N2 - In recent years, the recreational and commercial use of flight and driving simulators has become more popular. All these applications require the calculation of orientation in either two or three dimensions. Besides the Euler angles notation, other alternatives to represent rigid body rotations include axis-angle notation, homogeneous transformation matrices, and quaternions. All these methods involve transcendental functions in their calculations, which represents a disadvantage when these algorithms are implemented in hardware. The use of transcendental functions in software-based algorithms may not represent a significant disadvantage, but in hardware-based algorithms, the potential of rational models stands out. Generally, to calculate transcendental functions in hardware, it is necessary to utilize algorithms based on the CORDIC algorithm, which requires a significant amount of hardware resources (parallel) or the design of a more complex control unit (pipelined). This research presents a new procedure for model orientation using rational trigonometry and quaternion notation, avoiding trigonometric functions for calculations. We describe the orientation of a gimbal mechanism presented in many applications, from autonomous vehicles such as cars or drones to industrial manipulators. This research aims to compare the efficiency of a rational implementation to classical modeling using the techniques mentioned above. Furthermore, we simulate the models with software tools and propose a hardware architecture to implement our algorithms.
AB - In recent years, the recreational and commercial use of flight and driving simulators has become more popular. All these applications require the calculation of orientation in either two or three dimensions. Besides the Euler angles notation, other alternatives to represent rigid body rotations include axis-angle notation, homogeneous transformation matrices, and quaternions. All these methods involve transcendental functions in their calculations, which represents a disadvantage when these algorithms are implemented in hardware. The use of transcendental functions in software-based algorithms may not represent a significant disadvantage, but in hardware-based algorithms, the potential of rational models stands out. Generally, to calculate transcendental functions in hardware, it is necessary to utilize algorithms based on the CORDIC algorithm, which requires a significant amount of hardware resources (parallel) or the design of a more complex control unit (pipelined). This research presents a new procedure for model orientation using rational trigonometry and quaternion notation, avoiding trigonometric functions for calculations. We describe the orientation of a gimbal mechanism presented in many applications, from autonomous vehicles such as cars or drones to industrial manipulators. This research aims to compare the efficiency of a rational implementation to classical modeling using the techniques mentioned above. Furthermore, we simulate the models with software tools and propose a hardware architecture to implement our algorithms.
KW - gimbal mechanism
KW - orientation
KW - quaternions
KW - rational trigonometry
KW - spherical wrist
UR - http://www.scopus.com/inward/record.url?scp=85138599019&partnerID=8YFLogxK
U2 - 10.3390/machines10090749
DO - 10.3390/machines10090749
M3 - Artículo
AN - SCOPUS:85138599019
SN - 2075-1702
VL - 10
JO - Machines
JF - Machines
IS - 9
M1 - 749
ER -