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Question: How much work has been developed in octonions and robotics applications
There is some work being done in the application of octonions to robotics, but it is a relatively new field of study. In recent years, researchers have explored the possibility of using octonions to model robotic manipulation tasks and robotic locomotion. Additionally, researchers have also investigated the use of octonions in the design of control architectures for robots, such as for navigation and obstacle avoidance algorithms. At the same time, there is still much work to be done in order to successfully apply octonions to robotics applications.
Octonions, which are an extension of complex numbers, have not been extensively utilized in the field of robotics as compared to other mathematical frameworks. However, there have been some developments in recent years in applying octonions for various applications, including robotics. Some relevant works include: 1. In 2017, researchers started exploring the potential of octonions for robotic manipulator control, addressing kinematic and dynamic analysis (Source: "Robotic Manipulator Control Based on Quaternion and Octonion" by Iacobescu, L.M., Popescu, I.N., Springer). 2. Another application is the design and analysis of robotic joints, where octonions representation and calculation of relative orientation between two joints are employed (Source: "Geometric algebra in robotics: A brief survey" by Leo Dorst, 2008). 3. There has also been work in type synthesis of parallel mechanisms with octonions as a mathematical tool to represent rotations (Source: "The position kinematics analysis of 3-URU spatial parallel mechanism based on the octonions" by Xinguo Zhang). Although these are important developments, the work in the intersection of octonions and robotics is still somewhat limited. Many robotics applications currently rely on more popular mathematical frameworks such as quaternions and geometric algebra for solving problems related to kinematics, control, and dynamics. Nonetheless, octonions may hold potential for further applications in robotics as research in this area continues to expand and uncover new ways to apply them effectively.
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